add decodable & ctc_beam_search_deocder

speechx/speechx/decoder/common.h

+#include "base/basic_types.h"
+
+struct DecoderResult {
+  BaseFloat acoustic_score; 
+  std::vector<int32> words_idx;
+  std::vector<pair<int32, int32>> time_stamp;
+};

speechx/speechx/decoder/ctc_beam_search_decoder.cc

+#include "decoder/ctc_beam_search_decoder.h"
+
+#include "base/basic_types.h"
+#include "decoder/ctc_decoders/decoder_utils.h"
+
+namespace ppspeech {
+
+using std::vector;
+using FSTMATCH = fst::SortedMatcher<fst::StdVectorFst>;
+
+CTCBeamSearch::CTCBeamSearch(std::shared_ptr<CTCBeamSearchOptions> opts) :
+    opts_(opts),
+    vocabulary_(nullptr),
+    init_ext_scorer_(nullptr), 
+    blank_id(-1),
+    space_id(-1),
+    root(nullptr) {
+
+    LOG(INFO) << "dict path: " << _opts.dict_file;
+    vocabulary_ = std::make_shared<vector<string>>();
+    if (!basr::ReadDictToVector(_opts.dict_file, *vocabulary_)) {
+        LOG(INFO) << "load the dict failed";
+    }
+    LOG(INFO) << "read the vocabulary success, dict size: " << vocabulary_->size();
+
+    LOG(INFO) << "language model path: " << _opts.lm_path;
+    init_ext_scorer_ = std::make_shared<Scorer>(_opts.alpha, 
+                                                _opts.beta, 
+                                                _opts.lm_path, 
+                                                *vocabulary_);
+}
+
+void CTCBeamSearch::InitDecoder() {
+    
+    blank_id = 0;
+    auto it = std::find(vocabulary_->begin(), vocabulary_->end(), " ");
+    
+    space_id = it - vocabulary_->begin();
+    // if no space in vocabulary
+    if ((size_t)space_id >= vocabulary_->size()) {
+        space_id = -2;
+    }  
+
+    clear_prefixes();
+    
+    root = std::make_shared<PathTrie>();
+    root->score = root->log_prob_b_prev = 0.0;
+    prefixes.push_back(root.get());
+    if (init_ext_scorer_ != nullptr && !init_ext_scorer_->is_character_based()) {
+        auto fst_dict =
+            static_cast<fst::StdVectorFst *>(init_ext_scorer_->dictionary);
+        fst::StdVectorFst *dict_ptr = fst_dict->Copy(true);
+        root->set_dictionary(dict_ptr);
+        
+        auto matcher = std::make_shared<FSTMATCH>(*dict_ptr, fst::MATCH_INPUT);
+        root->set_matcher(matcher);
+    }
+}
+
+void CTCBeamSearch::ResetPrefixes() {
+  for (size_t i = 0; i < prefixes.size(); i++) {
+    if (prefixes[i] != nullptr) {
+      delete prefixes[i];
+      prefixes[i] = nullptr;
+    }
+  }
+}
+
+int CTCBeamSearch::DecodeLikelihoods(const vector<vector<float>>&probs, 
+                                      vector<string>& nbest_words) {
+  std::thread::id this_id = std::this_thread::get_id();
+  Timer timer;
+  vector<vector<double>> double_probs(probs.size(), vector<double>(probs[0].size(), 0));
+
+  int row = probs.size();
+  int col = probs[0].size();
+  for(int i = 0; i < row; i++) {
+    for (int j = 0; j < col; j++){
+      double_probs[i][j] = static_cast<double>(probs[i][j]);
+    }
+  }
+
+  timer.Reset();
+  vector<std::pair<double, string>> results = AdvanceDecoding(double_probs);
+  LOG(INFO) <<"ctc decoding elapsed time(s) " << static_cast<float>(timer.Elapsed()) / 1000.0f;
+  for (const auto& item : results) {
+    nbest_words.push_back(item.second);
+  }
+  return 0;
+} 
+
+vector<std::pair<double, string>> CTCBeamSearch::AdvanceDecoding(const vector<vector<double>>& probs_seq) {
+  size_t num_time_steps = probs_seq.size();
+  size_t beam_size = _opts.beam_size;
+  double cutoff_prob = _opts.cutoff_prob;
+  size_t cutoff_top_n = _opts.cutoff_top_n;
+    
+  for (size_t time_step = 0; time_step < num_time_steps; time_step++) {
+    const auto& prob = probs_seq[time_step];
+
+    float min_cutoff = -NUM_FLT_INF;
+    bool full_beam = false;
+    if (init_ext_scorer_ != nullptr) {
+      size_t num_prefixes = std::min(prefixes.size(), beam_size);
+      std::sort(prefixes.begin(), prefixes.begin() + num_prefixes,
+                prefix_compare);
+            
+      if (num_prefixes == 0) {
+        continue;
+      }
+      min_cutoff = prefixes[num_prefixes - 1]->score +
+                      std::log(prob[blank_id]) -
+                      std::max(0.0, init_ext_scorer_->beta);
+
+      full_beam = (num_prefixes == beam_size);
+    }
+        
+    vector<std::pair<size_t, float>> log_prob_idx =
+                get_pruned_log_probs(prob, cutoff_prob, cutoff_top_n);
+
+    // loop over chars
+    size_t log_prob_idx_len = log_prob_idx.size();
+    for (size_t index = 0; index < log_prob_idx_len; index++) {            
+      SearchOneChar(full_beam, log_prob_idx[index], min_cutoff);
+        
+    prefixes.clear();
+        
+    // update log probs
+    root->iterate_to_vec(prefixes);
+    // only preserve top beam_size prefixes
+    if (prefixes.size() >= beam_size) {
+      std::nth_element(prefixes.begin(),
+                       prefixes.begin() + beam_size,
+                       prefixes.end(),
+                       prefix_compare);
+      for (size_t i = beam_size; i < prefixes.size(); ++i) {
+        prefixes[i]->remove();
+      }
+    } // if 
+  } // for probs_seq
+
+  // score the last word of each prefix that doesn't end with space
+  LMRescore();
+  CalculateApproxScore();
+  return get_beam_search_result(prefixes, *vocabulary_, beam_size);
+}
+
+int CTCBeamSearch::SearchOneChar(const bool& full_beam,
+                                 const std::pair<size_t, float>& log_prob_idx,
+                                 const float& min_cutoff) {
+  size_t beam_size = _opts.beam_size;
+  const auto& c = log_prob_idx.first;
+  const auto& log_prob_c = log_prob_idx.second;
+  size_t prefixes_len = std::min(prefixes.size(), beam_size);
+    
+  for (size_t i = 0; i < prefixes_len; ++i) {
+    auto prefix = prefixes[i];
+    if (full_beam && log_prob_c + prefix->score < min_cutoff) {
+      break;
+    }
+
+    if (c == blank_id) {
+      prefix->log_prob_b_cur = log_sum_exp(
+                              prefix->log_prob_b_cur, 
+                              log_prob_c +
+                              prefix->score);
+      continue;
+    }
+
+    // repeated character
+    if (c == prefix->character) {
+      // p_{nb}(l;x_{1:t}) = p(c;x_{t})p(l;x_{1:t-1})
+      prefix->log_prob_nb_cur = log_sum_exp(
+                                  prefix->log_prob_nb_cur,
+                                  log_prob_c + 
+                                  prefix->log_prob_nb_prev);
+    }
+
+    // get new prefix
+    auto prefix_new = prefix->get_path_trie(c);
+    if (prefix_new != nullptr) {
+      float log_p = -NUM_FLT_INF;
+      if (c == prefix->character &&
+        prefix->log_prob_b_prev > -NUM_FLT_INF) { 
+         // p_{nb}(l^{+};x_{1:t}) = p(c;x_{t})p_{b}(l;x_{1:t-1})
+        log_p = log_prob_c + prefix->log_prob_b_prev;
+      } else if (c != prefix->character) {
+        // p_{nb}(l^{+};x_{1:t}) = p(c;x_{t}) p(l;x_{1:t-1})
+        log_p = log_prob_c + prefix->score;
+      }
+
+      // language model scoring
+      if (init_ext_scorer_ != nullptr &&
+          (c == space_id || init_ext_scorer_->is_character_based())) {
+        PathTrie *prefix_to_score = nullptr;
+        // skip scoring the space
+        if (init_ext_scorer_->is_character_based()) {
+            prefix_to_score = prefix_new;
+        } else {
+            prefix_to_score = prefix;
+        }
+
+        float score = 0.0;
+        vector<string> ngram;
+        ngram = init_ext_scorer_->make_ngram(prefix_to_score);
+        // lm score: p_{lm}(W)^{\alpha} + \beta
+        score = init_ext_scorer_->get_log_cond_prob(ngram) *
+                                init_ext_scorer_->alpha;
+        log_p += score;
+        log_p += init_ext_scorer_->beta;
+      }
+      // p_{nb}(l;x_{1:t})
+      prefix_new->log_prob_nb_cur =
+                      log_sum_exp(prefix_new->log_prob_nb_cur, 
+                                  log_p);
+    }
+  } // end of loop over prefix
+  return 0;
+}
+
+void CTCBeamSearch::CalculateApproxScore() {
+  size_t beam_size = _opts.beam_size;
+  size_t num_prefixes = std::min(prefixes.size(), beam_size);
+  std::sort(
+      prefixes.begin(), 
+      prefixes.begin() + num_prefixes, 
+      prefix_compare);
+
+  // compute aproximate ctc score as the return score, without affecting the
+  // return order of decoding result. To delete when decoder gets stable.
+  for (size_t i = 0; i < beam_size && i < prefixes.size(); ++i) {
+    double approx_ctc = prefixes[i]->score;
+    if (init_ext_scorer_ != nullptr) {
+      vector<int> output;
+      prefixes[i]->get_path_vec(output);
+      auto prefix_length = output.size();
+      auto words = init_ext_scorer_->split_labels(output);
+      // remove word insert
+      approx_ctc = approx_ctc - prefix_length * init_ext_scorer_->beta;
+      // remove language model weight:
+      approx_ctc -=
+          (init_ext_scorer_->get_sent_log_prob(words)) * init_ext_scorer_->alpha;
+    }
+    prefixes[i]->approx_ctc = approx_ctc;
+  }
+}
+
+void CTCBeamSearch::LMRescore() {
+  size_t beam_size = _opts.beam_size;
+  if (init_ext_scorer_ != nullptr && !init_ext_scorer_->is_character_based()) {
+    for (size_t i = 0; i < beam_size && i < prefixes.size(); ++i) {
+      auto prefix = prefixes[i];
+      if (!prefix->is_empty() && prefix->character != space_id) {
+        float score = 0.0;
+        vector<string> ngram = init_ext_scorer_->make_ngram(prefix);
+        score = init_ext_scorer_->get_log_cond_prob(ngram) * init_ext_scorer_->alpha;
+        score += init_ext_scorer_->beta;
+        prefix->score += score;
+      }
+    }
+  }
+}
+
+} // namespace ppspeech
\ No newline at end of file

speechx/speechx/decoder/ctc_beam_search_decoder.h

+#include "base/basic_types.h"
+
+#pragma once
+
+namespace ppspeech {
+
+struct CTCBeamSearchOptions {
+    std::string dict_file;
+    std::string lm_path;
+    BaseFloat alpha;
+    BaseFloat beta;
+    BaseFloat cutoff_prob;
+    int beam_size;
+    int cutoff_top_n;
+    int num_proc_bsearch;
+    CTCBeamSearchOptions() :
+        dict_file("./model/words.txt"),
+        lm_path("./model/lm.arpa"),
+        alpha(1.9f),
+        beta(5.0),
+        beam_size(300),
+        cutoff_prob(0.99f),
+        cutoff_top_n(40),
+        num_proc_bsearch(0) {
+    }
+
+    void Register(kaldi::OptionsItf* opts) {
+        opts->Register("dict", &dict_file, "dict file ");
+        opts->Register("lm-path", &lm_path, "language model file");
+        opts->Register("alpha", &alpha, "alpha");
+        opts->Register("beta", &beta, "beta");
+        opts->Register("beam-size", &beam_size, "beam size for beam search method");
+        opts->Register("cutoff-prob", &cutoff_prob, "cutoff probs");
+        opts->Register("cutoff-top-n", &cutoff_top_n, "cutoff top n");
+        opts->Register("num-proc-bsearch", &num_proc_bsearch, "num proc bsearch");
+    }
+};
+
+class CTCBeamSearch {
+public: 
+
+    CTCBeamSearch(std::shared_ptr<CTCBeamSearchOptions> opts);
+
+    ~CTCBeamSearch() {
+    }
+    bool InitDecoder();
+    int DecodeLikelihoods(const std::vector<std::vector<BaseFloat>>&probs, 
+                          std::vector<std::string>& nbest_words);
+
+    std::vector<DecodeResult>& GetDecodeResult() {
+        return decoder_results_;
+    }
+
+private:
+  void ResetPrefixes();
+  int32 SearchOneChar(const bool& full_beam,
+                      const std::pair<size_t, BaseFloat>& log_prob_idx,
+                      const BaseFloat& min_cutoff);
+  void CalculateApproxScore();
+  void LMRescore();
+  std::vector<std::pair<double, std::string>> 
+    AdvanceDecoding(const std::vector<std::vector<double>>& probs_seq);
+  CTCBeamSearchOptions opts_;
+  std::shared_ptr<Scorer> init_ext_scorer_; // todo separate later
+  std::vector<DecodeResult> decoder_results_;
+  std::vector<std::vector<std::string>> vocabulary_; // todo remove later
+
+  size_t blank_id;        
+  int space_id;
+  std::shared_ptr<PathTrie> root;
+  std::vector<PathTrie*> prefixes;
+};
+
+} // namespace basr
\ No newline at end of file

speechx/speechx/decoder/ctc_decoders

+../../../third_party/ctc_decoders
\ No newline at end of file

speechx/speechx/kaldi/decoder/lattice-faster-decoder.cc

+// decoder/lattice-faster-decoder.cc
+
+// Copyright 2009-2012  Microsoft Corporation  Mirko Hannemann
+//           2013-2018  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+//                2018  Zhehuai Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#include "decoder/lattice-faster-decoder.h"
+#include "lat/lattice-functions.h"
+
+namespace kaldi {
+
+// instantiate this class once for each thing you have to decode.
+template <typename FST, typename Token>
+LatticeFasterDecoderTpl<FST, Token>::LatticeFasterDecoderTpl(
+    const FST &fst, const LatticeFasterDecoderConfig &config)
+    : fst_(&fst),
+      delete_fst_(false),
+      config_(config),
+      num_toks_(0),
+      token_pool_(config.memory_pool_tokens_block_size),
+      forward_link_pool_(config.memory_pool_links_block_size) {
+  config.Check();
+  toks_.SetSize(1000);  // just so on the first frame we do something reasonable.
+}
+
+template <typename FST, typename Token>
+LatticeFasterDecoderTpl<FST, Token>::LatticeFasterDecoderTpl(
+    const LatticeFasterDecoderConfig &config, FST *fst)
+    : fst_(fst),
+      delete_fst_(true),
+      config_(config),
+      num_toks_(0),
+      token_pool_(config.memory_pool_tokens_block_size),
+      forward_link_pool_(config.memory_pool_links_block_size) {
+  config.Check();
+  toks_.SetSize(1000);  // just so on the first frame we do something reasonable.
+}
+
+template <typename FST, typename Token>
+LatticeFasterDecoderTpl<FST, Token>::~LatticeFasterDecoderTpl() {
+  DeleteElems(toks_.Clear());
+  ClearActiveTokens();
+  if (delete_fst_) delete fst_;
+}
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::InitDecoding() {
+  // clean up from last time:
+  DeleteElems(toks_.Clear());
+  cost_offsets_.clear();
+  ClearActiveTokens();
+  warned_ = false;
+  num_toks_ = 0;
+  decoding_finalized_ = false;
+  final_costs_.clear();
+  StateId start_state = fst_->Start();
+  KALDI_ASSERT(start_state != fst::kNoStateId);
+  active_toks_.resize(1);
+  Token *start_tok =
+      new (token_pool_.Allocate()) Token(0.0, 0.0, NULL, NULL, NULL);
+  active_toks_[0].toks = start_tok;
+  toks_.Insert(start_state, start_tok);
+  num_toks_++;
+  ProcessNonemitting(config_.beam);
+}
+
+// Returns true if any kind of traceback is available (not necessarily from
+// a final state).  It should only very rarely return false; this indicates
+// an unusual search error.
+template <typename FST, typename Token>
+bool LatticeFasterDecoderTpl<FST, Token>::Decode(DecodableInterface *decodable) {
+  InitDecoding();
+  // We use 1-based indexing for frames in this decoder (if you view it in
+  // terms of features), but note that the decodable object uses zero-based
+  // numbering, which we have to correct for when we call it.
+  AdvanceDecoding(decodable);
+  FinalizeDecoding();
+
+  // Returns true if we have any kind of traceback available (not necessarily
+  // to the end state; query ReachedFinal() for that).
+  return !active_toks_.empty() && active_toks_.back().toks != NULL;
+}
+
+
+// Outputs an FST corresponding to the single best path through the lattice.
+template <typename FST, typename Token>
+bool LatticeFasterDecoderTpl<FST, Token>::GetBestPath(Lattice *olat,
+                                       bool use_final_probs) const {
+  Lattice raw_lat;
+  GetRawLattice(&raw_lat, use_final_probs);
+  ShortestPath(raw_lat, olat);
+  return (olat->NumStates() != 0);
+}
+
+
+// Outputs an FST corresponding to the raw, state-level lattice
+template <typename FST, typename Token>
+bool LatticeFasterDecoderTpl<FST, Token>::GetRawLattice(
+    Lattice *ofst,
+    bool use_final_probs) const {
+  typedef LatticeArc Arc;
+  typedef Arc::StateId StateId;
+  typedef Arc::Weight Weight;
+  typedef Arc::Label Label;
+
+  // Note: you can't use the old interface (Decode()) if you want to
+  // get the lattice with use_final_probs = false.  You'd have to do
+  // InitDecoding() and then AdvanceDecoding().
+  if (decoding_finalized_ && !use_final_probs)
+    KALDI_ERR << "You cannot call FinalizeDecoding() and then call "
+              << "GetRawLattice() with use_final_probs == false";
+
+  unordered_map<Token*, BaseFloat> final_costs_local;
+
+  const unordered_map<Token*, BaseFloat> &final_costs =
+      (decoding_finalized_ ? final_costs_ : final_costs_local);
+  if (!decoding_finalized_ && use_final_probs)
+    ComputeFinalCosts(&final_costs_local, NULL, NULL);
+
+  ofst->DeleteStates();
+  // num-frames plus one (since frames are one-based, and we have
+  // an extra frame for the start-state).
+  int32 num_frames = active_toks_.size() - 1;
+  KALDI_ASSERT(num_frames > 0);
+  const int32 bucket_count = num_toks_/2 + 3;
+  unordered_map<Token*, StateId> tok_map(bucket_count);
+  // First create all states.
+  std::vector<Token*> token_list;
+  for (int32 f = 0; f <= num_frames; f++) {
+    if (active_toks_[f].toks == NULL) {
+      KALDI_WARN << "GetRawLattice: no tokens active on frame " << f
+                 << ": not producing lattice.\n";
+      return false;
+    }
+    TopSortTokens(active_toks_[f].toks, &token_list);
+    for (size_t i = 0; i < token_list.size(); i++)
+      if (token_list[i] != NULL)
+        tok_map[token_list[i]] = ofst->AddState();
+  }
+  // The next statement sets the start state of the output FST.  Because we
+  // topologically sorted the tokens, state zero must be the start-state.
+  ofst->SetStart(0);
+
+  KALDI_VLOG(4) << "init:" << num_toks_/2 + 3 << " buckets:"
+                << tok_map.bucket_count() << " load:" << tok_map.load_factor()
+                << " max:" << tok_map.max_load_factor();
+  // Now create all arcs.
+  for (int32 f = 0; f <= num_frames; f++) {
+    for (Token *tok = active_toks_[f].toks; tok != NULL; tok = tok->next) {
+      StateId cur_state = tok_map[tok];
+      for (ForwardLinkT *l = tok->links;
+           l != NULL;
+           l = l->next) {
+        typename unordered_map<Token*, StateId>::const_iterator
+            iter = tok_map.find(l->next_tok);
+        StateId nextstate = iter->second;
+        KALDI_ASSERT(iter != tok_map.end());
+        BaseFloat cost_offset = 0.0;
+        if (l->ilabel != 0) {  // emitting..
+          KALDI_ASSERT(f >= 0 && f < cost_offsets_.size());
+          cost_offset = cost_offsets_[f];
+        }
+        Arc arc(l->ilabel, l->olabel,
+                Weight(l->graph_cost, l->acoustic_cost - cost_offset),
+                nextstate);
+        ofst->AddArc(cur_state, arc);
+      }
+      if (f == num_frames) {
+        if (use_final_probs && !final_costs.empty()) {
+          typename unordered_map<Token*, BaseFloat>::const_iterator
+              iter = final_costs.find(tok);
+          if (iter != final_costs.end())
+            ofst->SetFinal(cur_state, LatticeWeight(iter->second, 0));
+        } else {
+          ofst->SetFinal(cur_state, LatticeWeight::One());
+        }
+      }
+    }
+  }
+  return (ofst->NumStates() > 0);
+}
+
+
+// This function is now deprecated, since now we do determinization from outside
+// the LatticeFasterDecoder class.  Outputs an FST corresponding to the
+// lattice-determinized lattice (one path per word sequence).
+template <typename FST, typename Token>
+bool LatticeFasterDecoderTpl<FST, Token>::GetLattice(CompactLattice *ofst,
+                                           bool use_final_probs) const {
+  Lattice raw_fst;
+  GetRawLattice(&raw_fst, use_final_probs);
+  Invert(&raw_fst);  // make it so word labels are on the input.
+  // (in phase where we get backward-costs).
+  fst::ILabelCompare<LatticeArc> ilabel_comp;
+  ArcSort(&raw_fst, ilabel_comp);  // sort on ilabel; makes
+  // lattice-determinization more efficient.
+
+  fst::DeterminizeLatticePrunedOptions lat_opts;
+  lat_opts.max_mem = config_.det_opts.max_mem;
+
+  DeterminizeLatticePruned(raw_fst, config_.lattice_beam, ofst, lat_opts);
+  raw_fst.DeleteStates();  // Free memory-- raw_fst no longer needed.
+  Connect(ofst);  // Remove unreachable states... there might be
+  // a small number of these, in some cases.
+  // Note: if something went wrong and the raw lattice was empty,
+  // we should still get to this point in the code without warnings or failures.
+  return (ofst->NumStates() != 0);
+}
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::PossiblyResizeHash(size_t num_toks) {
+  size_t new_sz = static_cast<size_t>(static_cast<BaseFloat>(num_toks)
+                                      * config_.hash_ratio);
+  if (new_sz > toks_.Size()) {
+    toks_.SetSize(new_sz);
+  }
+}
+
+/*
+  A note on the definition of extra_cost.
+
+  extra_cost is used in pruning tokens, to save memory.
+
+  extra_cost can be thought of as a beta (backward) cost assuming
+  we had set the betas on currently-active tokens to all be the negative
+  of the alphas for those tokens.  (So all currently active tokens would
+  be on (tied) best paths).
+
+  We can use the extra_cost to accurately prune away tokens that we know will
+  never appear in the lattice.  If the extra_cost is greater than the desired
+  lattice beam, the token would provably never appear in the lattice, so we can
+  prune away the token.
+
+  (Note: we don't update all the extra_costs every time we update a frame; we
+  only do it every 'config_.prune_interval' frames).
+ */
+
+// FindOrAddToken either locates a token in hash of toks_,
+// or if necessary inserts a new, empty token (i.e. with no forward links)
+// for the current frame.  [note: it's inserted if necessary into hash toks_
+// and also into the singly linked list of tokens active on this frame
+// (whose head is at active_toks_[frame]).
+template <typename FST, typename Token>
+inline typename LatticeFasterDecoderTpl<FST, Token>::Elem*
+LatticeFasterDecoderTpl<FST, Token>::FindOrAddToken(
+      StateId state, int32 frame_plus_one, BaseFloat tot_cost,
+      Token *backpointer, bool *changed) {
+  // Returns the Token pointer.  Sets "changed" (if non-NULL) to true
+  // if the token was newly created or the cost changed.
+  KALDI_ASSERT(frame_plus_one < active_toks_.size());
+  Token *&toks = active_toks_[frame_plus_one].toks;
+  Elem *e_found = toks_.Insert(state, NULL);
+  if (e_found->val == NULL) {  // no such token presently.
+    const BaseFloat extra_cost = 0.0;
+    // tokens on the currently final frame have zero extra_cost
+    // as any of them could end up
+    // on the winning path.
+    Token *new_tok = new (token_pool_.Allocate())
+        Token(tot_cost, extra_cost, NULL, toks, backpointer);
+    // NULL: no forward links yet
+    toks = new_tok;
+    num_toks_++;
+    e_found->val = new_tok;
+    if (changed) *changed = true;
+    return e_found;
+  } else {
+    Token *tok = e_found->val;  // There is an existing Token for this state.
+    if (tok->tot_cost > tot_cost) {  // replace old token
+      tok->tot_cost = tot_cost;
+      // SetBackpointer() just does tok->backpointer = backpointer in
+      // the case where Token == BackpointerToken, else nothing.
+      tok->SetBackpointer(backpointer);
+      // we don't allocate a new token, the old stays linked in active_toks_
+      // we only replace the tot_cost
+      // in the current frame, there are no forward links (and no extra_cost)
+      // only in ProcessNonemitting we have to delete forward links
+      // in case we visit a state for the second time
+      // those forward links, that lead to this replaced token before:
+      // they remain and will hopefully be pruned later (PruneForwardLinks...)
+      if (changed) *changed = true;
+    } else {
+      if (changed) *changed = false;
+    }
+    return e_found;
+  }
+}
+
+// prunes outgoing links for all tokens in active_toks_[frame]
+// it's called by PruneActiveTokens
+// all links, that have link_extra_cost > lattice_beam are pruned
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::PruneForwardLinks(
+    int32 frame_plus_one, bool *extra_costs_changed,
+    bool *links_pruned, BaseFloat delta) {
+  // delta is the amount by which the extra_costs must change
+  // If delta is larger,  we'll tend to go back less far
+  //    toward the beginning of the file.
+  // extra_costs_changed is set to true if extra_cost was changed for any token
+  // links_pruned is set to true if any link in any token was pruned
+
+  *extra_costs_changed = false;
+  *links_pruned = false;
+  KALDI_ASSERT(frame_plus_one >= 0 && frame_plus_one < active_toks_.size());
+  if (active_toks_[frame_plus_one].toks == NULL) {  // empty list; should not happen.
+    if (!warned_) {
+      KALDI_WARN << "No tokens alive [doing pruning].. warning first "
+          "time only for each utterance\n";
+      warned_ = true;
+    }
+  }
+
+  // We have to iterate until there is no more change, because the links
+  // are not guaranteed to be in topological order.
+  bool changed = true;  // difference new minus old extra cost >= delta ?
+  while (changed) {
+    changed = false;
+    for (Token *tok = active_toks_[frame_plus_one].toks;
+         tok != NULL; tok = tok->next) {
+      ForwardLinkT *link, *prev_link = NULL;
+      // will recompute tok_extra_cost for tok.
+      BaseFloat tok_extra_cost = std::numeric_limits<BaseFloat>::infinity();
+      // tok_extra_cost is the best (min) of link_extra_cost of outgoing links
+      for (link = tok->links; link != NULL; ) {
+        // See if we need to excise this link...
+        Token *next_tok = link->next_tok;
+        BaseFloat link_extra_cost = next_tok->extra_cost +
+            ((tok->tot_cost + link->acoustic_cost + link->graph_cost)
+             - next_tok->tot_cost);  // difference in brackets is >= 0
+        // link_exta_cost is the difference in score between the best paths
+        // through link source state and through link destination state
+        KALDI_ASSERT(link_extra_cost == link_extra_cost);  // check for NaN
+        if (link_extra_cost > config_.lattice_beam) {  // excise link
+          ForwardLinkT *next_link = link->next;
+          if (prev_link != NULL) prev_link->next = next_link;
+          else tok->links = next_link;
+          forward_link_pool_.Free(link);
+          link = next_link;  // advance link but leave prev_link the same.
+          *links_pruned = true;
+        } else {   // keep the link and update the tok_extra_cost if needed.
+          if (link_extra_cost < 0.0) {  // this is just a precaution.
+            if (link_extra_cost < -0.01)
+              KALDI_WARN << "Negative extra_cost: " << link_extra_cost;
+            link_extra_cost = 0.0;
+          }
+          if (link_extra_cost < tok_extra_cost)
+            tok_extra_cost = link_extra_cost;
+          prev_link = link;  // move to next link
+          link = link->next;
+        }
+      }  // for all outgoing links
+      if (fabs(tok_extra_cost - tok->extra_cost) > delta)
+        changed = true;   // difference new minus old is bigger than delta
+      tok->extra_cost = tok_extra_cost;
+      // will be +infinity or <= lattice_beam_.
+      // infinity indicates, that no forward link survived pruning
+    }  // for all Token on active_toks_[frame]
+    if (changed) *extra_costs_changed = true;
+
+    // Note: it's theoretically possible that aggressive compiler
+    // optimizations could cause an infinite loop here for small delta and
+    // high-dynamic-range scores.
+  } // while changed
+}
+
+// PruneForwardLinksFinal is a version of PruneForwardLinks that we call
+// on the final frame.  If there are final tokens active, it uses
+// the final-probs for pruning, otherwise it treats all tokens as final.
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::PruneForwardLinksFinal() {
+  KALDI_ASSERT(!active_toks_.empty());
+  int32 frame_plus_one = active_toks_.size() - 1;
+
+  if (active_toks_[frame_plus_one].toks == NULL)  // empty list; should not happen.
+    KALDI_WARN << "No tokens alive at end of file";
+
+  typedef typename unordered_map<Token*, BaseFloat>::const_iterator IterType;
+  ComputeFinalCosts(&final_costs_, &final_relative_cost_, &final_best_cost_);
+  decoding_finalized_ = true;
+  // We call DeleteElems() as a nicety, not because it's really necessary;
+  // otherwise there would be a time, after calling PruneTokensForFrame() on the
+  // final frame, when toks_.GetList() or toks_.Clear() would contain pointers
+  // to nonexistent tokens.
+  DeleteElems(toks_.Clear());
+
+  // Now go through tokens on this frame, pruning forward links...  may have to
+  // iterate a few times until there is no more change, because the list is not
+  // in topological order.  This is a modified version of the code in
+  // PruneForwardLinks, but here we also take account of the final-probs.
+  bool changed = true;
+  BaseFloat delta = 1.0e-05;
+  while (changed) {
+    changed = false;
+    for (Token *tok = active_toks_[frame_plus_one].toks;
+         tok != NULL; tok = tok->next) {
+      ForwardLinkT *link, *prev_link = NULL;
+      // will recompute tok_extra_cost.  It has a term in it that corresponds
+      // to the "final-prob", so instead of initializing tok_extra_cost to infinity
+      // below we set it to the difference between the (score+final_prob) of this token,
+      // and the best such (score+final_prob).
+      BaseFloat final_cost;
+      if (final_costs_.empty()) {
+        final_cost = 0.0;
+      } else {
+        IterType iter = final_costs_.find(tok);
+        if (iter != final_costs_.end())
+          final_cost = iter->second;
+        else
+          final_cost = std::numeric_limits<BaseFloat>::infinity();
+      }
+      BaseFloat tok_extra_cost = tok->tot_cost + final_cost - final_best_cost_;
+      // tok_extra_cost will be a "min" over either directly being final, or
+      // being indirectly final through other links, and the loop below may
+      // decrease its value:
+      for (link = tok->links; link != NULL; ) {
+        // See if we need to excise this link...
+        Token *next_tok = link->next_tok;
+        BaseFloat link_extra_cost = next_tok->extra_cost +
+            ((tok->tot_cost + link->acoustic_cost + link->graph_cost)
+             - next_tok->tot_cost);
+        if (link_extra_cost > config_.lattice_beam) {  // excise link
+          ForwardLinkT *next_link = link->next;
+          if (prev_link != NULL) prev_link->next = next_link;
+          else tok->links = next_link;
+          forward_link_pool_.Free(link);
+          link = next_link; // advance link but leave prev_link the same.
+        } else { // keep the link and update the tok_extra_cost if needed.
+          if (link_extra_cost < 0.0) { // this is just a precaution.
+            if (link_extra_cost < -0.01)
+              KALDI_WARN << "Negative extra_cost: " << link_extra_cost;
+            link_extra_cost = 0.0;
+          }
+          if (link_extra_cost < tok_extra_cost)
+            tok_extra_cost = link_extra_cost;
+          prev_link = link;
+          link = link->next;
+        }
+      }
+      // prune away tokens worse than lattice_beam above best path.  This step
+      // was not necessary in the non-final case because then, this case
+      // showed up as having no forward links.  Here, the tok_extra_cost has
+      // an extra component relating to the final-prob.
+      if (tok_extra_cost > config_.lattice_beam)
+        tok_extra_cost = std::numeric_limits<BaseFloat>::infinity();
+      // to be pruned in PruneTokensForFrame
+
+      if (!ApproxEqual(tok->extra_cost, tok_extra_cost, delta))
+        changed = true;
+      tok->extra_cost = tok_extra_cost; // will be +infinity or <= lattice_beam_.
+    }
+  } // while changed
+}
+
+template <typename FST, typename Token>
+BaseFloat LatticeFasterDecoderTpl<FST, Token>::FinalRelativeCost() const {
+  if (!decoding_finalized_) {
+    BaseFloat relative_cost;
+    ComputeFinalCosts(NULL, &relative_cost, NULL);
+    return relative_cost;
+  } else {
+    // we're not allowed to call that function if FinalizeDecoding() has
+    // been called; return a cached value.
+    return final_relative_cost_;
+  }
+}
+
+
+// Prune away any tokens on this frame that have no forward links.
+// [we don't do this in PruneForwardLinks because it would give us
+// a problem with dangling pointers].
+// It's called by PruneActiveTokens if any forward links have been pruned
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::PruneTokensForFrame(int32 frame_plus_one) {
+  KALDI_ASSERT(frame_plus_one >= 0 && frame_plus_one < active_toks_.size());
+  Token *&toks = active_toks_[frame_plus_one].toks;
+  if (toks == NULL)
+    KALDI_WARN << "No tokens alive [doing pruning]";
+  Token *tok, *next_tok, *prev_tok = NULL;
+  for (tok = toks; tok != NULL; tok = next_tok) {
+    next_tok = tok->next;
+    if (tok->extra_cost == std::numeric_limits<BaseFloat>::infinity()) {
+      // token is unreachable from end of graph; (no forward links survived)
+      // excise tok from list and delete tok.
+      if (prev_tok != NULL) prev_tok->next = tok->next;
+      else toks = tok->next;
+      token_pool_.Free(tok);
+      num_toks_--;
+    } else {  // fetch next Token
+      prev_tok = tok;
+    }
+  }
+}
+
+// Go backwards through still-alive tokens, pruning them, starting not from
+// the current frame (where we want to keep all tokens) but from the frame before
+// that.  We go backwards through the frames and stop when we reach a point
+// where the delta-costs are not changing (and the delta controls when we consider
+// a cost to have "not changed").
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::PruneActiveTokens(BaseFloat delta) {
+  int32 cur_frame_plus_one = NumFramesDecoded();
+  int32 num_toks_begin = num_toks_;
+  // The index "f" below represents a "frame plus one", i.e. you'd have to subtract
+  // one to get the corresponding index for the decodable object.
+  for (int32 f = cur_frame_plus_one - 1; f >= 0; f--) {
+    // Reason why we need to prune forward links in this situation:
+    // (1) we have never pruned them (new TokenList)
+    // (2) we have not yet pruned the forward links to the next f,
+    // after any of those tokens have changed their extra_cost.
+    if (active_toks_[f].must_prune_forward_links) {
+      bool extra_costs_changed = false, links_pruned = false;
+      PruneForwardLinks(f, &extra_costs_changed, &links_pruned, delta);
+      if (extra_costs_changed && f > 0) // any token has changed extra_cost
+        active_toks_[f-1].must_prune_forward_links = true;
+      if (links_pruned) // any link was pruned
+        active_toks_[f].must_prune_tokens = true;
+      active_toks_[f].must_prune_forward_links = false; // job done
+    }
+    if (f+1 < cur_frame_plus_one &&      // except for last f (no forward links)
+        active_toks_[f+1].must_prune_tokens) {
+      PruneTokensForFrame(f+1);
+      active_toks_[f+1].must_prune_tokens = false;
+    }
+  }
+  KALDI_VLOG(4) << "PruneActiveTokens: pruned tokens from " << num_toks_begin
+                << " to " << num_toks_;
+}
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::ComputeFinalCosts(
+    unordered_map<Token*, BaseFloat> *final_costs,
+    BaseFloat *final_relative_cost,
+    BaseFloat *final_best_cost) const {
+  KALDI_ASSERT(!decoding_finalized_);
+  if (final_costs != NULL)
+    final_costs->clear();
+  const Elem *final_toks = toks_.GetList();
+  BaseFloat infinity = std::numeric_limits<BaseFloat>::infinity();
+  BaseFloat best_cost = infinity,
+      best_cost_with_final = infinity;
+
+  while (final_toks != NULL) {
+    StateId state = final_toks->key;
+    Token *tok = final_toks->val;
+    const Elem *next = final_toks->tail;
+    BaseFloat final_cost = fst_->Final(state).Value();
+    BaseFloat cost = tok->tot_cost,
+        cost_with_final = cost + final_cost;
+    best_cost = std::min(cost, best_cost);
+    best_cost_with_final = std::min(cost_with_final, best_cost_with_final);
+    if (final_costs != NULL && final_cost != infinity)
+      (*final_costs)[tok] = final_cost;
+    final_toks = next;
+  }
+  if (final_relative_cost != NULL) {
+    if (best_cost == infinity && best_cost_with_final == infinity) {
+      // Likely this will only happen if there are no tokens surviving.
+      // This seems the least bad way to handle it.
+      *final_relative_cost = infinity;
+    } else {
+      *final_relative_cost = best_cost_with_final - best_cost;
+    }
+  }
+  if (final_best_cost != NULL) {
+    if (best_cost_with_final != infinity) { // final-state exists.
+      *final_best_cost = best_cost_with_final;
+    } else { // no final-state exists.
+      *final_best_cost = best_cost;
+    }
+  }
+}
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::AdvanceDecoding(DecodableInterface *decodable,
+                                                int32 max_num_frames) {
+  if (std::is_same<FST, fst::Fst<fst::StdArc> >::value) {
+    // if the type 'FST' is the FST base-class, then see if the FST type of fst_
+    // is actually VectorFst or ConstFst.  If so, call the AdvanceDecoding()
+    // function after casting *this to the more specific type.
+    if (fst_->Type() == "const") {
+      LatticeFasterDecoderTpl<fst::ConstFst<fst::StdArc>, Token> *this_cast =
+          reinterpret_cast<LatticeFasterDecoderTpl<fst::ConstFst<fst::StdArc>, Token>* >(this);
+      this_cast->AdvanceDecoding(decodable, max_num_frames);
+      return;
+    } else if (fst_->Type() == "vector") {
+      LatticeFasterDecoderTpl<fst::VectorFst<fst::StdArc>, Token> *this_cast =
+          reinterpret_cast<LatticeFasterDecoderTpl<fst::VectorFst<fst::StdArc>, Token>* >(this);
+      this_cast->AdvanceDecoding(decodable, max_num_frames);
+      return;
+    }
+  }
+
+
+  KALDI_ASSERT(!active_toks_.empty() && !decoding_finalized_ &&
+               "You must call InitDecoding() before AdvanceDecoding");
+  int32 num_frames_ready = decodable->NumFramesReady();
+  // num_frames_ready must be >= num_frames_decoded, or else
+  // the number of frames ready must have decreased (which doesn't
+  // make sense) or the decodable object changed between calls
+  // (which isn't allowed).
+  KALDI_ASSERT(num_frames_ready >= NumFramesDecoded());
+  int32 target_frames_decoded = num_frames_ready;
+  if (max_num_frames >= 0)
+    target_frames_decoded = std::min(target_frames_decoded,
+                                     NumFramesDecoded() + max_num_frames);
+  while (NumFramesDecoded() < target_frames_decoded) {
+    if (NumFramesDecoded() % config_.prune_interval == 0) {
+      PruneActiveTokens(config_.lattice_beam * config_.prune_scale);
+    }
+    BaseFloat cost_cutoff = ProcessEmitting(decodable);
+    ProcessNonemitting(cost_cutoff);
+  }
+}
+
+// FinalizeDecoding() is a version of PruneActiveTokens that we call
+// (optionally) on the final frame.  Takes into account the final-prob of
+// tokens.  This function used to be called PruneActiveTokensFinal().
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::FinalizeDecoding() {
+  int32 final_frame_plus_one = NumFramesDecoded();
+  int32 num_toks_begin = num_toks_;
+  // PruneForwardLinksFinal() prunes final frame (with final-probs), and
+  // sets decoding_finalized_.
+  PruneForwardLinksFinal();
+  for (int32 f = final_frame_plus_one - 1; f >= 0; f--) {
+    bool b1, b2; // values not used.
+    BaseFloat dontcare = 0.0; // delta of zero means we must always update
+    PruneForwardLinks(f, &b1, &b2, dontcare);
+    PruneTokensForFrame(f + 1);
+  }
+  PruneTokensForFrame(0);
+  KALDI_VLOG(4) << "pruned tokens from " << num_toks_begin
+                << " to " << num_toks_;
+}
+
+/// Gets the weight cutoff.  Also counts the active tokens.
+template <typename FST, typename Token>
+BaseFloat LatticeFasterDecoderTpl<FST, Token>::GetCutoff(Elem *list_head, size_t *tok_count,
+                                          BaseFloat *adaptive_beam, Elem **best_elem) {
+  BaseFloat best_weight = std::numeric_limits<BaseFloat>::infinity();
+  // positive == high cost == bad.
+  size_t count = 0;
+  if (config_.max_active == std::numeric_limits<int32>::max() &&
+      config_.min_active == 0) {
+    for (Elem *e = list_head; e != NULL; e = e->tail, count++) {
+      BaseFloat w = static_cast<BaseFloat>(e->val->tot_cost);
+      if (w < best_weight) {
+        best_weight = w;
+        if (best_elem) *best_elem = e;
+      }
+    }
+    if (tok_count != NULL) *tok_count = count;
+    if (adaptive_beam != NULL) *adaptive_beam = config_.beam;
+    return best_weight + config_.beam;
+  } else {
+    tmp_array_.clear();
+    for (Elem *e = list_head; e != NULL; e = e->tail, count++) {
+      BaseFloat w = e->val->tot_cost;
+      tmp_array_.push_back(w);
+      if (w < best_weight) {
+        best_weight = w;
+        if (best_elem) *best_elem = e;
+      }
+    }
+    if (tok_count != NULL) *tok_count = count;
+
+    BaseFloat beam_cutoff = best_weight + config_.beam,
+        min_active_cutoff = std::numeric_limits<BaseFloat>::infinity(),
+        max_active_cutoff = std::numeric_limits<BaseFloat>::infinity();
+
+    KALDI_VLOG(6) << "Number of tokens active on frame " << NumFramesDecoded()
+                  << " is " << tmp_array_.size();
+
+    if (tmp_array_.size() > static_cast<size_t>(config_.max_active)) {
+      std::nth_element(tmp_array_.begin(),
+                       tmp_array_.begin() + config_.max_active,
+                       tmp_array_.end());
+      max_active_cutoff = tmp_array_[config_.max_active];
+    }
+    if (max_active_cutoff < beam_cutoff) { // max_active is tighter than beam.
+      if (adaptive_beam)
+        *adaptive_beam = max_active_cutoff - best_weight + config_.beam_delta;
+      return max_active_cutoff;
+    }
+    if (tmp_array_.size() > static_cast<size_t>(config_.min_active)) {
+      if (config_.min_active == 0) min_active_cutoff = best_weight;
+      else {
+        std::nth_element(tmp_array_.begin(),
+                         tmp_array_.begin() + config_.min_active,
+                         tmp_array_.size() > static_cast<size_t>(config_.max_active) ?
+                         tmp_array_.begin() + config_.max_active :
+                         tmp_array_.end());
+        min_active_cutoff = tmp_array_[config_.min_active];
+      }
+    }
+    if (min_active_cutoff > beam_cutoff) { // min_active is looser than beam.
+      if (adaptive_beam)
+        *adaptive_beam = min_active_cutoff - best_weight + config_.beam_delta;
+      return min_active_cutoff;
+    } else {
+      *adaptive_beam = config_.beam;
+      return beam_cutoff;
+    }
+  }
+}
+
+template <typename FST, typename Token>
+BaseFloat LatticeFasterDecoderTpl<FST, Token>::ProcessEmitting(
+    DecodableInterface *decodable) {
+  KALDI_ASSERT(active_toks_.size() > 0);
+  int32 frame = active_toks_.size() - 1; // frame is the frame-index
+                                         // (zero-based) used to get likelihoods
+                                         // from the decodable object.
+  active_toks_.resize(active_toks_.size() + 1);
+
+  Elem *final_toks = toks_.Clear(); // analogous to swapping prev_toks_ / cur_toks_
+                                   // in simple-decoder.h.   Removes the Elems from
+                                   // being indexed in the hash in toks_.
+  Elem *best_elem = NULL;
+  BaseFloat adaptive_beam;
+  size_t tok_cnt;
+  BaseFloat cur_cutoff = GetCutoff(final_toks, &tok_cnt, &adaptive_beam, &best_elem);
+  KALDI_VLOG(6) << "Adaptive beam on frame " << NumFramesDecoded() << " is "
+                << adaptive_beam;
+
+  PossiblyResizeHash(tok_cnt);  // This makes sure the hash is always big enough.
+
+  BaseFloat next_cutoff = std::numeric_limits<BaseFloat>::infinity();
+  // pruning "online" before having seen all tokens
+
+  BaseFloat cost_offset = 0.0; // Used to keep probabilities in a good
+                               // dynamic range.
+
+
+  // First process the best token to get a hopefully
+  // reasonably tight bound on the next cutoff.  The only
+  // products of the next block are "next_cutoff" and "cost_offset".
+  if (best_elem) {
+    StateId state = best_elem->key;
+    Token *tok = best_elem->val;
+    cost_offset = - tok->tot_cost;
+    for (fst::ArcIterator<FST> aiter(*fst_, state);
+         !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      if (arc.ilabel != 0) {  // propagate..
+        BaseFloat new_weight = arc.weight.Value() + cost_offset -
+            decodable->LogLikelihood(frame, arc.ilabel) + tok->tot_cost;
+        if (new_weight + adaptive_beam < next_cutoff)
+          next_cutoff = new_weight + adaptive_beam;
+      }
+    }
+  }
+
+  // Store the offset on the acoustic likelihoods that we're applying.
+  // Could just do cost_offsets_.push_back(cost_offset), but we
+  // do it this way as it's more robust to future code changes.
+  cost_offsets_.resize(frame + 1, 0.0);
+  cost_offsets_[frame] = cost_offset;
+
+  // the tokens are now owned here, in final_toks, and the hash is empty.
+  // 'owned' is a complex thing here; the point is we need to call DeleteElem
+  // on each elem 'e' to let toks_ know we're done with them.
+  for (Elem *e = final_toks, *e_tail; e != NULL; e = e_tail) {
+    // loop this way because we delete "e" as we go.
+    StateId state = e->key;
+    Token *tok = e->val;
+    if (tok->tot_cost <= cur_cutoff) {
+      for (fst::ArcIterator<FST> aiter(*fst_, state);
+           !aiter.Done();
+           aiter.Next()) {
+        const Arc &arc = aiter.Value();
+        if (arc.ilabel != 0) {  // propagate..
+          BaseFloat ac_cost = cost_offset -
+              decodable->LogLikelihood(frame, arc.ilabel),
+              graph_cost = arc.weight.Value(),
+              cur_cost = tok->tot_cost,
+              tot_cost = cur_cost + ac_cost + graph_cost;
+          if (tot_cost >= next_cutoff) continue;
+          else if (tot_cost + adaptive_beam < next_cutoff)
+            next_cutoff = tot_cost + adaptive_beam; // prune by best current token
+          // Note: the frame indexes into active_toks_ are one-based,
+          // hence the + 1.
+          Elem *e_next = FindOrAddToken(arc.nextstate,
+                                        frame + 1, tot_cost, tok, NULL);
+          // NULL: no change indicator needed
+
+          // Add ForwardLink from tok to next_tok (put on head of list tok->links)
+          tok->links = new (forward_link_pool_.Allocate())
+              ForwardLinkT(e_next->val, arc.ilabel, arc.olabel, graph_cost,
+                           ac_cost, tok->links);
+        }
+      } // for all arcs
+    }
+    e_tail = e->tail;
+    toks_.Delete(e); // delete Elem
+  }
+  return next_cutoff;
+}
+
+// static inline
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::DeleteForwardLinks(Token *tok) {
+  ForwardLinkT *l = tok->links, *m;
+  while (l != NULL) {
+    m = l->next;
+    forward_link_pool_.Free(l);
+    l = m;
+  }
+  tok->links = NULL;
+}
+
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::ProcessNonemitting(BaseFloat cutoff) {
+  KALDI_ASSERT(!active_toks_.empty());
+  int32 frame = static_cast<int32>(active_toks_.size()) - 2;
+  // Note: "frame" is the time-index we just processed, or -1 if
+  // we are processing the nonemitting transitions before the
+  // first frame (called from InitDecoding()).
+
+  // Processes nonemitting arcs for one frame.  Propagates within toks_.
+  // Note-- this queue structure is not very optimal as
+  // it may cause us to process states unnecessarily (e.g. more than once),
+  // but in the baseline code, turning this vector into a set to fix this
+  // problem did not improve overall speed.
+
+  KALDI_ASSERT(queue_.empty());
+
+  if (toks_.GetList() == NULL) {
+    if (!warned_) {
+      KALDI_WARN << "Error, no surviving tokens: frame is " << frame;
+      warned_ = true;
+    }
+  }
+
+  for (const Elem *e = toks_.GetList(); e != NULL;  e = e->tail) {
+    StateId state = e->key;
+    if (fst_->NumInputEpsilons(state) != 0)
+      queue_.push_back(e);
+  }
+
+  while (!queue_.empty()) {
+    const Elem *e = queue_.back();
+    queue_.pop_back();
+
+    StateId state = e->key;
+    Token *tok = e->val;  // would segfault if e is a NULL pointer but this can't happen.
+    BaseFloat cur_cost = tok->tot_cost;
+    if (cur_cost >= cutoff) // Don't bother processing successors.
+      continue;
+    // If "tok" has any existing forward links, delete them,
+    // because we're about to regenerate them.  This is a kind
+    // of non-optimality (remember, this is the simple decoder),
+    // but since most states are emitting it's not a huge issue.
+    DeleteForwardLinks(tok); // necessary when re-visiting
+    tok->links = NULL;
+    for (fst::ArcIterator<FST> aiter(*fst_, state);
+         !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      if (arc.ilabel == 0) {  // propagate nonemitting only...
+        BaseFloat graph_cost = arc.weight.Value(),
+            tot_cost = cur_cost + graph_cost;
+        if (tot_cost < cutoff) {
+          bool changed;
+
+          Elem *e_new = FindOrAddToken(arc.nextstate, frame + 1, tot_cost,
+                                          tok, &changed);
+
+          tok->links = new (forward_link_pool_.Allocate()) ForwardLinkT(
+              e_new->val, 0, arc.olabel, graph_cost, 0, tok->links);
+
+          // "changed" tells us whether the new token has a different
+          // cost from before, or is new [if so, add into queue].
+          if (changed && fst_->NumInputEpsilons(arc.nextstate) != 0)
+            queue_.push_back(e_new);
+        }
+      }
+    } // for all arcs
+  } // while queue not empty
+}
+
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::DeleteElems(Elem *list) {
+  for (Elem *e = list, *e_tail; e != NULL; e = e_tail) {
+    e_tail = e->tail;
+    toks_.Delete(e);
+  }
+}
+
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::ClearActiveTokens() { // a cleanup routine, at utt end/begin
+  for (size_t i = 0; i < active_toks_.size(); i++) {
+    // Delete all tokens alive on this frame, and any forward
+    // links they may have.
+    for (Token *tok = active_toks_[i].toks; tok != NULL; ) {
+      DeleteForwardLinks(tok);
+      Token *next_tok = tok->next;
+      token_pool_.Free(tok);
+      num_toks_--;
+      tok = next_tok;
+    }
+  }
+  active_toks_.clear();
+  KALDI_ASSERT(num_toks_ == 0);
+}
+
+// static
+template <typename FST, typename Token>
+void LatticeFasterDecoderTpl<FST, Token>::TopSortTokens(
+    Token *tok_list, std::vector<Token*> *topsorted_list) {
+  unordered_map<Token*, int32> token2pos;
+  typedef typename unordered_map<Token*, int32>::iterator IterType;
+  int32 num_toks = 0;
+  for (Token *tok = tok_list; tok != NULL; tok = tok->next)
+    num_toks++;
+  int32 cur_pos = 0;
+  // We assign the tokens numbers num_toks - 1, ... , 2, 1, 0.
+  // This is likely to be in closer to topological order than
+  // if we had given them ascending order, because of the way
+  // new tokens are put at the front of the list.
+  for (Token *tok = tok_list; tok != NULL; tok = tok->next)
+    token2pos[tok] = num_toks - ++cur_pos;
+
+  unordered_set<Token*> reprocess;
+
+  for (IterType iter = token2pos.begin(); iter != token2pos.end(); ++iter) {
+    Token *tok = iter->first;
+    int32 pos = iter->second;
+    for (ForwardLinkT *link = tok->links; link != NULL; link = link->next) {
+      if (link->ilabel == 0) {
+        // We only need to consider epsilon links, since non-epsilon links
+        // transition between frames and this function only needs to sort a list
+        // of tokens from a single frame.
+        IterType following_iter = token2pos.find(link->next_tok);
+        if (following_iter != token2pos.end()) { // another token on this frame,
+                                                 // so must consider it.
+          int32 next_pos = following_iter->second;
+          if (next_pos < pos) { // reassign the position of the next Token.
+            following_iter->second = cur_pos++;
+            reprocess.insert(link->next_tok);
+          }
+        }
+      }
+    }
+    // In case we had previously assigned this token to be reprocessed, we can
+    // erase it from that set because it's "happy now" (we just processed it).
+    reprocess.erase(tok);
+  }
+
+  size_t max_loop = 1000000, loop_count; // max_loop is to detect epsilon cycles.
+  for (loop_count = 0;
+       !reprocess.empty() && loop_count < max_loop; ++loop_count) {
+    std::vector<Token*> reprocess_vec;
+    for (typename unordered_set<Token*>::iterator iter = reprocess.begin();
+         iter != reprocess.end(); ++iter)
+      reprocess_vec.push_back(*iter);
+    reprocess.clear();
+    for (typename std::vector<Token*>::iterator iter = reprocess_vec.begin();
+         iter != reprocess_vec.end(); ++iter) {
+      Token *tok = *iter;
+      int32 pos = token2pos[tok];
+      // Repeat the processing we did above (for comments, see above).
+      for (ForwardLinkT *link = tok->links; link != NULL; link = link->next) {
+        if (link->ilabel == 0) {
+          IterType following_iter = token2pos.find(link->next_tok);
+          if (following_iter != token2pos.end()) {
+            int32 next_pos = following_iter->second;
+            if (next_pos < pos) {
+              following_iter->second = cur_pos++;
+              reprocess.insert(link->next_tok);
+            }
+          }
+        }
+      }
+    }
+  }
+  KALDI_ASSERT(loop_count < max_loop && "Epsilon loops exist in your decoding "
+               "graph (this is not allowed!)");
+
+  topsorted_list->clear();
+  topsorted_list->resize(cur_pos, NULL);  // create a list with NULLs in between.
+  for (IterType iter = token2pos.begin(); iter != token2pos.end(); ++iter)
+    (*topsorted_list)[iter->second] = iter->first;
+}
+
+// Instantiate the template for the combination of token types and FST types
+// that we'll need.
+template class LatticeFasterDecoderTpl<fst::Fst<fst::StdArc>, decoder::StdToken>;
+template class LatticeFasterDecoderTpl<fst::VectorFst<fst::StdArc>, decoder::StdToken >;
+template class LatticeFasterDecoderTpl<fst::ConstFst<fst::StdArc>, decoder::StdToken >;
+
+template class LatticeFasterDecoderTpl<fst::ConstGrammarFst, decoder::StdToken>;
+template class LatticeFasterDecoderTpl<fst::VectorGrammarFst, decoder::StdToken>;
+
+template class LatticeFasterDecoderTpl<fst::Fst<fst::StdArc> , decoder::BackpointerToken>;
+template class LatticeFasterDecoderTpl<fst::VectorFst<fst::StdArc>, decoder::BackpointerToken >;
+template class LatticeFasterDecoderTpl<fst::ConstFst<fst::StdArc>, decoder::BackpointerToken >;
+template class LatticeFasterDecoderTpl<fst::ConstGrammarFst, decoder::BackpointerToken>;
+template class LatticeFasterDecoderTpl<fst::VectorGrammarFst, decoder::BackpointerToken>;
+
+
+} // end namespace kaldi.

speechx/speechx/kaldi/decoder/lattice-faster-decoder.h

+// decoder/lattice-faster-decoder.h
+
+// Copyright 2009-2013  Microsoft Corporation;  Mirko Hannemann;
+//           2013-2014  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+//                2018  Zhehuai Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef KALDI_DECODER_LATTICE_FASTER_DECODER_H_
+#define KALDI_DECODER_LATTICE_FASTER_DECODER_H_
+
+#include "decoder/grammar-fst.h"
+#include "fst/fstlib.h"
+#include "fst/memory.h"
+#include "fstext/fstext-lib.h"
+#include "itf/decodable-itf.h"
+#include "lat/determinize-lattice-pruned.h"
+#include "lat/kaldi-lattice.h"
+#include "util/hash-list.h"
+#include "util/stl-utils.h"
+
+namespace kaldi {
+
+struct LatticeFasterDecoderConfig {
+  BaseFloat beam;
+  int32 max_active;
+  int32 min_active;
+  BaseFloat lattice_beam;
+  int32 prune_interval;
+  bool determinize_lattice; // not inspected by this class... used in
+                            // command-line program.
+  BaseFloat beam_delta;
+  BaseFloat hash_ratio;
+  // Note: we don't make prune_scale configurable on the command line, it's not
+  // a very important parameter.  It affects the algorithm that prunes the
+  // tokens as we go.
+  BaseFloat prune_scale;
+
+  // Number of elements in the block for Token and ForwardLink memory
+  // pool allocation.
+  int32 memory_pool_tokens_block_size;
+  int32 memory_pool_links_block_size;
+
+  // Most of the options inside det_opts are not actually queried by the
+  // LatticeFasterDecoder class itself, but by the code that calls it, for
+  // example in the function DecodeUtteranceLatticeFaster.
+  fst::DeterminizeLatticePhonePrunedOptions det_opts;
+
+  LatticeFasterDecoderConfig()
+      : beam(16.0),
+        max_active(std::numeric_limits<int32>::max()),
+        min_active(200),
+        lattice_beam(10.0),
+        prune_interval(25),
+        determinize_lattice(true),
+        beam_delta(0.5),
+        hash_ratio(2.0),
+        prune_scale(0.1),
+        memory_pool_tokens_block_size(1 << 8),
+        memory_pool_links_block_size(1 << 8) {}
+  void Register(OptionsItf *opts) {
+    det_opts.Register(opts);
+    opts->Register("beam", &beam, "Decoding beam.  Larger->slower, more accurate.");
+    opts->Register("max-active", &max_active, "Decoder max active states.  Larger->slower; "
+                   "more accurate");
+    opts->Register("min-active", &min_active, "Decoder minimum #active states.");
+    opts->Register("lattice-beam", &lattice_beam, "Lattice generation beam.  Larger->slower, "
+                   "and deeper lattices");
+    opts->Register("prune-interval", &prune_interval, "Interval (in frames) at "
+                   "which to prune tokens");
+    opts->Register("determinize-lattice", &determinize_lattice, "If true, "
+                   "determinize the lattice (lattice-determinization, keeping only "
+                   "best pdf-sequence for each word-sequence).");
+    opts->Register("beam-delta", &beam_delta, "Increment used in decoding-- this "
+                   "parameter is obscure and relates to a speedup in the way the "
+                   "max-active constraint is applied.  Larger is more accurate.");
+    opts->Register("hash-ratio", &hash_ratio, "Setting used in decoder to "
+                   "control hash behavior");
+    opts->Register("memory-pool-tokens-block-size", &memory_pool_tokens_block_size,
+                   "Memory pool block size suggestion for storing tokens (in elements). "
+                   "Smaller uses less memory but increases cache misses.");
+    opts->Register("memory-pool-links-block-size", &memory_pool_links_block_size,
+                   "Memory pool block size suggestion for storing links (in elements). "
+                   "Smaller uses less memory but increases cache misses.");
+  }
+  void Check() const {
+    KALDI_ASSERT(beam > 0.0 && max_active > 1 && lattice_beam > 0.0
+                 && min_active <= max_active
+                 && prune_interval > 0 && beam_delta > 0.0 && hash_ratio >= 1.0
+                 && prune_scale > 0.0 && prune_scale < 1.0);
+  }
+};
+
+namespace decoder {
+// We will template the decoder on the token type as well as the FST type; this
+// is a mechanism so that we can use the same underlying decoder code for
+// versions of the decoder that support quickly getting the best path
+// (LatticeFasterOnlineDecoder, see lattice-faster-online-decoder.h) and also
+// those that do not (LatticeFasterDecoder).
+
+
+// ForwardLinks are the links from a token to a token on the next frame.
+// or sometimes on the current frame (for input-epsilon links).
+template <typename Token>
+struct ForwardLink {
+  using Label = fst::StdArc::Label;
+
+  Token *next_tok;  // the next token [or NULL if represents final-state]
+  Label ilabel;  // ilabel on arc
+  Label olabel;  // olabel on arc
+  BaseFloat graph_cost;  // graph cost of traversing arc (contains LM, etc.)
+  BaseFloat acoustic_cost;  // acoustic cost (pre-scaled) of traversing arc
+  ForwardLink *next;  // next in singly-linked list of forward arcs (arcs
+                      // in the state-level lattice) from a token.
+  inline ForwardLink(Token *next_tok, Label ilabel, Label olabel,
+                     BaseFloat graph_cost, BaseFloat acoustic_cost,
+                     ForwardLink *next):
+      next_tok(next_tok), ilabel(ilabel), olabel(olabel),
+      graph_cost(graph_cost), acoustic_cost(acoustic_cost),
+      next(next) { }
+};
+
+
+struct StdToken {
+  using ForwardLinkT = ForwardLink<StdToken>;
+  using Token = StdToken;
+
+  // Standard token type for LatticeFasterDecoder.  Each active HCLG
+  // (decoding-graph) state on each frame has one token.
+
+  // tot_cost is the total (LM + acoustic) cost from the beginning of the
+  // utterance up to this point.  (but see cost_offset_, which is subtracted
+  // to keep it in a good numerical range).
+  BaseFloat tot_cost;
+
+  // exta_cost is >= 0.  After calling PruneForwardLinks, this equals the
+  // minimum difference between the cost of the best path that this link is a
+  // part of, and the cost of the absolute best path, under the assumption that
+  // any of the currently active states at the decoding front may eventually
+  // succeed (e.g. if you were to take the currently active states one by one
+  // and compute this difference, and then take the minimum).
+  BaseFloat extra_cost;
+
+  // 'links' is the head of singly-linked list of ForwardLinks, which is what we
+  // use for lattice generation.
+  ForwardLinkT *links;
+
+  //'next' is the next in the singly-linked list of tokens for this frame.
+  Token *next;
+
+  // This function does nothing and should be optimized out; it's needed
+  // so we can share the regular LatticeFasterDecoderTpl code and the code
+  // for LatticeFasterOnlineDecoder that supports fast traceback.
+  inline void SetBackpointer (Token *backpointer) { }
+
+  // This constructor just ignores the 'backpointer' argument.  That argument is
+  // needed so that we can use the same decoder code for LatticeFasterDecoderTpl
+  // and LatticeFasterOnlineDecoderTpl (which needs backpointers to support a
+  // fast way to obtain the best path).
+  inline StdToken(BaseFloat tot_cost, BaseFloat extra_cost, ForwardLinkT *links,
+                  Token *next, Token *backpointer):
+      tot_cost(tot_cost), extra_cost(extra_cost), links(links), next(next) { }
+};
+
+struct BackpointerToken {
+  using ForwardLinkT = ForwardLink<BackpointerToken>;
+  using Token = BackpointerToken;
+
+  // BackpointerToken is like Token but also
+  // Standard token type for LatticeFasterDecoder.  Each active HCLG
+  // (decoding-graph) state on each frame has one token.
+
+  // tot_cost is the total (LM + acoustic) cost from the beginning of the
+  // utterance up to this point.  (but see cost_offset_, which is subtracted
+  // to keep it in a good numerical range).
+  BaseFloat tot_cost;
+
+  // exta_cost is >= 0.  After calling PruneForwardLinks, this equals
+  // the minimum difference between the cost of the best path, and the cost of
+  // this is on, and the cost of the absolute best path, under the assumption
+  // that any of the currently active states at the decoding front may
+  // eventually succeed (e.g. if you were to take the currently active states
+  // one by one and compute this difference, and then take the minimum).
+  BaseFloat extra_cost;
+
+  // 'links' is the head of singly-linked list of ForwardLinks, which is what we
+  // use for lattice generation.
+  ForwardLinkT *links;
+
+  //'next' is the next in the singly-linked list of tokens for this frame.
+  BackpointerToken *next;
+
+  // Best preceding BackpointerToken (could be a on this frame, connected to
+  // this via an epsilon transition, or on a previous frame).  This is only
+  // required for an efficient GetBestPath function in
+  // LatticeFasterOnlineDecoderTpl; it plays no part in the lattice generation
+  // (the "links" list is what stores the forward links, for that).
+  Token *backpointer;
+
+  inline void SetBackpointer (Token *backpointer) {
+    this->backpointer = backpointer;
+  }
+
+  inline BackpointerToken(BaseFloat tot_cost, BaseFloat extra_cost, ForwardLinkT *links,
+                          Token *next, Token *backpointer):
+      tot_cost(tot_cost), extra_cost(extra_cost), links(links), next(next),
+      backpointer(backpointer) { }
+};
+
+}  // namespace decoder
+
+
+/** This is the "normal" lattice-generating decoder.
+    See \ref lattices_generation \ref decoders_faster and \ref decoders_simple
+     for more information.
+
+   The decoder is templated on the FST type and the token type.  The token type
+   will normally be StdToken, but also may be BackpointerToken which is to support
+   quick lookup of the current best path (see lattice-faster-online-decoder.h)
+
+   The FST you invoke this decoder which is expected to equal
+   Fst::Fst<fst::StdArc>, a.k.a. StdFst, or GrammarFst.  If you invoke it with
+   FST == StdFst and it notices that the actual FST type is
+   fst::VectorFst<fst::StdArc> or fst::ConstFst<fst::StdArc>, the decoder object
+   will internally cast itself to one that is templated on those more specific
+   types; this is an optimization for speed.
+ */
+template <typename FST, typename Token = decoder::StdToken>
+class LatticeFasterDecoderTpl {
+ public:
+  using Arc = typename FST::Arc;
+  using Label = typename Arc::Label;
+  using StateId = typename Arc::StateId;
+  using Weight = typename Arc::Weight;
+  using ForwardLinkT = decoder::ForwardLink<Token>;
+
+  // Instantiate this class once for each thing you have to decode.
+  // This version of the constructor does not take ownership of
+  // 'fst'.
+  LatticeFasterDecoderTpl(const FST &fst,
+                          const LatticeFasterDecoderConfig &config);
+
+  // This version of the constructor takes ownership of the fst, and will delete
+  // it when this object is destroyed.
+  LatticeFasterDecoderTpl(const LatticeFasterDecoderConfig &config,
+                          FST *fst);
+
+  void SetOptions(const LatticeFasterDecoderConfig &config) {
+    config_ = config;
+  }
+
+  const LatticeFasterDecoderConfig &GetOptions() const {
+    return config_;
+  }
+
+  ~LatticeFasterDecoderTpl();
+
+  /// Decodes until there are no more frames left in the "decodable" object..
+  /// note, this may block waiting for input if the "decodable" object blocks.
+  /// Returns true if any kind of traceback is available (not necessarily from a
+  /// final state).
+  bool Decode(DecodableInterface *decodable);
+
+
+  /// says whether a final-state was active on the last frame.  If it was not, the
+  /// lattice (or traceback) will end with states that are not final-states.
+  bool ReachedFinal() const {
+    return FinalRelativeCost() != std::numeric_limits<BaseFloat>::infinity();
+  }
+
+  /// Outputs an FST corresponding to the single best path through the lattice.
+  /// Returns true if result is nonempty (using the return status is deprecated,
+  /// it will become void).  If "use_final_probs" is true AND we reached the
+  /// final-state of the graph then it will include those as final-probs, else
+  /// it will treat all final-probs as one.  Note: this just calls GetRawLattice()
+  /// and figures out the shortest path.
+  bool GetBestPath(Lattice *ofst,
+                   bool use_final_probs = true) const;
+
+  /// Outputs an FST corresponding to the raw, state-level
+  /// tracebacks.  Returns true if result is nonempty.
+  /// If "use_final_probs" is true AND we reached the final-state
+  /// of the graph then it will include those as final-probs, else
+  /// it will treat all final-probs as one.
+  /// The raw lattice will be topologically sorted.
+  ///
+  /// See also GetRawLatticePruned in lattice-faster-online-decoder.h,
+  /// which also supports a pruning beam, in case for some reason
+  /// you want it pruned tighter than the regular lattice beam.
+  /// We could put that here in future needed.
+  bool GetRawLattice(Lattice *ofst, bool use_final_probs = true) const;
+
+
+
+  /// [Deprecated, users should now use GetRawLattice and determinize it
+  /// themselves, e.g. using DeterminizeLatticePhonePrunedWrapper].
+  /// Outputs an FST corresponding to the lattice-determinized
+  /// lattice (one path per word sequence).   Returns true if result is nonempty.
+  /// If "use_final_probs" is true AND we reached the final-state of the graph
+  /// then it will include those as final-probs, else it will treat all
+  /// final-probs as one.
+  bool GetLattice(CompactLattice *ofst,
+                  bool use_final_probs = true) const;
+
+  /// InitDecoding initializes the decoding, and should only be used if you
+  /// intend to call AdvanceDecoding().  If you call Decode(), you don't need to
+  /// call this.  You can also call InitDecoding if you have already decoded an
+  /// utterance and want to start with a new utterance.
+  void InitDecoding();
+
+  /// This will decode until there are no more frames ready in the decodable
+  /// object.  You can keep calling it each time more frames become available.
+  /// If max_num_frames is specified, it specifies the maximum number of frames
+  /// the function will decode before returning.
+  void AdvanceDecoding(DecodableInterface *decodable,
+                       int32 max_num_frames = -1);
+
+  /// This function may be optionally called after AdvanceDecoding(), when you
+  /// do not plan to decode any further.  It does an extra pruning step that
+  /// will help to prune the lattices output by GetLattice and (particularly)
+  /// GetRawLattice more completely, particularly toward the end of the
+  /// utterance.  If you call this, you cannot call AdvanceDecoding again (it
+  /// will fail), and you cannot call GetLattice() and related functions with
+  /// use_final_probs = false.  Used to be called PruneActiveTokensFinal().
+  void FinalizeDecoding();
+
+  /// FinalRelativeCost() serves the same purpose as ReachedFinal(), but gives
+  /// more information.  It returns the difference between the best (final-cost
+  /// plus cost) of any token on the final frame, and the best cost of any token
+  /// on the final frame.  If it is infinity it means no final-states were
+  /// present on the final frame.  It will usually be nonnegative.  If it not
+  /// too positive (e.g. < 5 is my first guess, but this is not tested) you can
+  /// take it as a good indication that we reached the final-state with
+  /// reasonable likelihood.
+  BaseFloat FinalRelativeCost() const;
+
+
+  // Returns the number of frames decoded so far.  The value returned changes
+  // whenever we call ProcessEmitting().
+  inline int32 NumFramesDecoded() const { return active_toks_.size() - 1; }
+
+ protected:
+  // we make things protected instead of private, as code in
+  // LatticeFasterOnlineDecoderTpl, which inherits from this, also uses the
+  // internals.
+
+  // Deletes the elements of the singly linked list tok->links.
+  void DeleteForwardLinks(Token *tok);
+
+  // head of per-frame list of Tokens (list is in topological order),
+  // and something saying whether we ever pruned it using PruneForwardLinks.
+  struct TokenList {
+    Token *toks;
+    bool must_prune_forward_links;
+    bool must_prune_tokens;
+    TokenList(): toks(NULL), must_prune_forward_links(true),
+                 must_prune_tokens(true) { }
+  };
+
+  using Elem = typename HashList<StateId, Token*>::Elem;
+  // Equivalent to:
+  //  struct Elem {
+  //    StateId key;
+  //    Token *val;
+  //    Elem *tail;
+  //  };
+
+  void PossiblyResizeHash(size_t num_toks);
+
+  // FindOrAddToken either locates a token in hash of toks_, or if necessary
+  // inserts a new, empty token (i.e. with no forward links) for the current
+  // frame.  [note: it's inserted if necessary into hash toks_ and also into the
+  // singly linked list of tokens active on this frame (whose head is at
+  // active_toks_[frame]).  The frame_plus_one argument is the acoustic frame
+  // index plus one, which is used to index into the active_toks_ array.
+  // Returns the Token pointer.  Sets "changed" (if non-NULL) to true if the
+  // token was newly created or the cost changed.
+  // If Token == StdToken, the 'backpointer' argument has no purpose (and will
+  // hopefully be optimized out).
+  inline Elem *FindOrAddToken(StateId state, int32 frame_plus_one,
+                              BaseFloat tot_cost, Token *backpointer,
+                              bool *changed);
+
+  // prunes outgoing links for all tokens in active_toks_[frame]
+  // it's called by PruneActiveTokens
+  // all links, that have link_extra_cost > lattice_beam are pruned
+  // delta is the amount by which the extra_costs must change
+  // before we set *extra_costs_changed = true.
+  // If delta is larger,  we'll tend to go back less far
+  //    toward the beginning of the file.
+  // extra_costs_changed is set to true if extra_cost was changed for any token
+  // links_pruned is set to true if any link in any token was pruned
+  void PruneForwardLinks(int32 frame_plus_one, bool *extra_costs_changed,
+                         bool *links_pruned,
+                         BaseFloat delta);
+
+  // This function computes the final-costs for tokens active on the final
+  // frame.  It outputs to final-costs, if non-NULL, a map from the Token*
+  // pointer to the final-prob of the corresponding state, for all Tokens
+  // that correspond to states that have final-probs.  This map will be
+  // empty if there were no final-probs.  It outputs to
+  // final_relative_cost, if non-NULL, the difference between the best
+  // forward-cost including the final-prob cost, and the best forward-cost
+  // without including the final-prob cost (this will usually be positive), or
+  // infinity if there were no final-probs.  [c.f. FinalRelativeCost(), which
+  // outputs this quanitity].  It outputs to final_best_cost, if
+  // non-NULL, the lowest for any token t active on the final frame, of
+  // forward-cost[t] + final-cost[t], where final-cost[t] is the final-cost in
+  // the graph of the state corresponding to token t, or the best of
+  // forward-cost[t] if there were no final-probs active on the final frame.
+  // You cannot call this after FinalizeDecoding() has been called; in that
+  // case you should get the answer from class-member variables.
+  void ComputeFinalCosts(unordered_map<Token*, BaseFloat> *final_costs,
+                         BaseFloat *final_relative_cost,
+                         BaseFloat *final_best_cost) const;
+
+  // PruneForwardLinksFinal is a version of PruneForwardLinks that we call
+  // on the final frame.  If there are final tokens active, it uses
+  // the final-probs for pruning, otherwise it treats all tokens as final.
+  void PruneForwardLinksFinal();
+
+  // Prune away any tokens on this frame that have no forward links.
+  // [we don't do this in PruneForwardLinks because it would give us
+  // a problem with dangling pointers].
+  // It's called by PruneActiveTokens if any forward links have been pruned
+  void PruneTokensForFrame(int32 frame_plus_one);
+
+
+  // Go backwards through still-alive tokens, pruning them if the
+  // forward+backward cost is more than lat_beam away from the best path.  It's
+  // possible to prove that this is "correct" in the sense that we won't lose
+  // anything outside of lat_beam, regardless of what happens in the future.
+  // delta controls when it considers a cost to have changed enough to continue
+  // going backward and propagating the change.  larger delta -> will recurse
+  // less far.
+  void PruneActiveTokens(BaseFloat delta);
+
+  /// Gets the weight cutoff.  Also counts the active tokens.
+  BaseFloat GetCutoff(Elem *list_head, size_t *tok_count,
+                      BaseFloat *adaptive_beam, Elem **best_elem);
+
+  /// Processes emitting arcs for one frame.  Propagates from prev_toks_ to
+  /// cur_toks_.  Returns the cost cutoff for subsequent ProcessNonemitting() to
+  /// use.
+  BaseFloat ProcessEmitting(DecodableInterface *decodable);
+
+  /// Processes nonemitting (epsilon) arcs for one frame.  Called after
+  /// ProcessEmitting() on each frame.  The cost cutoff is computed by the
+  /// preceding ProcessEmitting().
+  void ProcessNonemitting(BaseFloat cost_cutoff);
+
+  // HashList defined in ../util/hash-list.h.  It actually allows us to maintain
+  // more than one list (e.g. for current and previous frames), but only one of
+  // them at a time can be indexed by StateId.  It is indexed by frame-index
+  // plus one, where the frame-index is zero-based, as used in decodable object.
+  // That is, the emitting probs of frame t are accounted for in tokens at
+  // toks_[t+1].  The zeroth frame is for nonemitting transition at the start of
+  // the graph.
+  HashList<StateId, Token*> toks_;
+
+  std::vector<TokenList> active_toks_; // Lists of tokens, indexed by
+  // frame (members of TokenList are toks, must_prune_forward_links,
+  // must_prune_tokens).
+  std::vector<const Elem* > queue_;  // temp variable used in ProcessNonemitting,
+  std::vector<BaseFloat> tmp_array_;  // used in GetCutoff.
+
+  // fst_ is a pointer to the FST we are decoding from.
+  const FST *fst_;
+  // delete_fst_ is true if the pointer fst_ needs to be deleted when this
+  // object is destroyed.
+  bool delete_fst_;
+
+  std::vector<BaseFloat> cost_offsets_; // This contains, for each
+  // frame, an offset that was added to the acoustic log-likelihoods on that
+  // frame in order to keep everything in a nice dynamic range i.e.  close to
+  // zero, to reduce roundoff errors.
+  LatticeFasterDecoderConfig config_;
+  int32 num_toks_; // current total #toks allocated...
+  bool warned_;
+
+  /// decoding_finalized_ is true if someone called FinalizeDecoding().  [note,
+  /// calling this is optional].  If true, it's forbidden to decode more.  Also,
+  /// if this is set, then the output of ComputeFinalCosts() is in the next
+  /// three variables.  The reason we need to do this is that after
+  /// FinalizeDecoding() calls PruneTokensForFrame() for the final frame, some
+  /// of the tokens on the last frame are freed, so we free the list from toks_
+  /// to avoid having dangling pointers hanging around.
+  bool decoding_finalized_;
+  /// For the meaning of the next 3 variables, see the comment for
+  /// decoding_finalized_ above., and ComputeFinalCosts().
+  unordered_map<Token*, BaseFloat> final_costs_;
+  BaseFloat final_relative_cost_;
+  BaseFloat final_best_cost_;
+
+  // Memory pools for storing tokens and forward links.
+  // We use it to decrease the work put on allocator and to move some of data
+  // together. Too small block sizes will result in more work to allocator but
+  // bigger ones increase the memory usage.
+  fst::MemoryPool<Token> token_pool_;
+  fst::MemoryPool<ForwardLinkT> forward_link_pool_;
+
+  // There are various cleanup tasks... the toks_ structure contains
+  // singly linked lists of Token pointers, where Elem is the list type.
+  // It also indexes them in a hash, indexed by state (this hash is only
+  // maintained for the most recent frame).  toks_.Clear()
+  // deletes them from the hash and returns the list of Elems.  The
+  // function DeleteElems calls toks_.Delete(elem) for each elem in
+  // the list, which returns ownership of the Elem to the toks_ structure
+  // for reuse, but does not delete the Token pointer.  The Token pointers
+  // are reference-counted and are ultimately deleted in PruneTokensForFrame,
+  // but are also linked together on each frame by their own linked-list,
+  // using the "next" pointer.  We delete them manually.
+  void DeleteElems(Elem *list);
+
+  // This function takes a singly linked list of tokens for a single frame, and
+  // outputs a list of them in topological order (it will crash if no such order
+  // can be found, which will typically be due to decoding graphs with epsilon
+  // cycles, which are not allowed).  Note: the output list may contain NULLs,
+  // which the caller should pass over; it just happens to be more efficient for
+  // the algorithm to output a list that contains NULLs.
+  static void TopSortTokens(Token *tok_list,
+                            std::vector<Token*> *topsorted_list);
+
+  void ClearActiveTokens();
+
+  KALDI_DISALLOW_COPY_AND_ASSIGN(LatticeFasterDecoderTpl);
+};
+
+typedef LatticeFasterDecoderTpl<fst::StdFst, decoder::StdToken> LatticeFasterDecoder;
+
+
+
+} // end namespace kaldi.
+
+#endif

speechx/speechx/kaldi/decoder/lattice-faster-online-decoder.cc

+// decoder/lattice-faster-online-decoder.cc
+
+// Copyright 2009-2012  Microsoft Corporation  Mirko Hannemann
+//           2013-2014  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+//                2014  IMSL, PKU-HKUST (author: Wei Shi)
+//                2018  Zhehuai Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+// see note at the top of lattice-faster-decoder.cc, about how to maintain this
+// file in sync with lattice-faster-decoder.cc
+
+#include "decoder/lattice-faster-online-decoder.h"
+#include "lat/lattice-functions.h"
+
+namespace kaldi {
+
+template <typename FST>
+bool LatticeFasterOnlineDecoderTpl<FST>::TestGetBestPath(
+    bool use_final_probs) const {
+  Lattice lat1;
+  {
+    Lattice raw_lat;
+    this->GetRawLattice(&raw_lat, use_final_probs);
+    ShortestPath(raw_lat, &lat1);
+  }
+  Lattice lat2;
+  GetBestPath(&lat2, use_final_probs);
+  BaseFloat delta = 0.1;
+  int32 num_paths = 1;
+  if (!fst::RandEquivalent(lat1, lat2, num_paths, delta, rand())) {
+    KALDI_WARN << "Best-path test failed";
+    return false;
+  } else {
+    return true;
+  }
+}
+
+
+// Outputs an FST corresponding to the single best path through the lattice.
+template <typename FST>
+bool LatticeFasterOnlineDecoderTpl<FST>::GetBestPath(Lattice *olat,
+                                                     bool use_final_probs) const {
+  olat->DeleteStates();
+  BaseFloat final_graph_cost;
+  BestPathIterator iter = BestPathEnd(use_final_probs, &final_graph_cost);
+  if (iter.Done())
+    return false;  // would have printed warning.
+  StateId state = olat->AddState();
+  olat->SetFinal(state, LatticeWeight(final_graph_cost, 0.0));
+  while (!iter.Done()) {
+    LatticeArc arc;
+    iter = TraceBackBestPath(iter, &arc);
+    arc.nextstate = state;
+    StateId new_state = olat->AddState();
+    olat->AddArc(new_state, arc);
+    state = new_state;
+  }
+  olat->SetStart(state);
+  return true;
+}
+
+template <typename FST>
+typename LatticeFasterOnlineDecoderTpl<FST>::BestPathIterator LatticeFasterOnlineDecoderTpl<FST>::BestPathEnd(
+    bool use_final_probs,
+    BaseFloat *final_cost_out) const {
+  if (this->decoding_finalized_ && !use_final_probs)
+    KALDI_ERR << "You cannot call FinalizeDecoding() and then call "
+              << "BestPathEnd() with use_final_probs == false";
+  KALDI_ASSERT(this->NumFramesDecoded() > 0 &&
+               "You cannot call BestPathEnd if no frames were decoded.");
+
+  unordered_map<Token*, BaseFloat> final_costs_local;
+
+  const unordered_map<Token*, BaseFloat> &final_costs =
+      (this->decoding_finalized_ ? this->final_costs_ :final_costs_local);
+  if (!this->decoding_finalized_ && use_final_probs)
+    this->ComputeFinalCosts(&final_costs_local, NULL, NULL);
+
+  // Singly linked list of tokens on last frame (access list through "next"
+  // pointer).
+  BaseFloat best_cost = std::numeric_limits<BaseFloat>::infinity();
+  BaseFloat best_final_cost = 0;
+  Token *best_tok = NULL;
+  for (Token *tok = this->active_toks_.back().toks;
+       tok != NULL; tok = tok->next) {
+    BaseFloat cost = tok->tot_cost, final_cost = 0.0;
+    if (use_final_probs && !final_costs.empty()) {
+      // if we are instructed to use final-probs, and any final tokens were
+      // active on final frame, include the final-prob in the cost of the token.
+      typename unordered_map<Token*, BaseFloat>::const_iterator
+          iter = final_costs.find(tok);
+      if (iter != final_costs.end()) {
+        final_cost = iter->second;
+        cost += final_cost;
+      } else {
+        cost = std::numeric_limits<BaseFloat>::infinity();
+      }
+    }
+    if (cost < best_cost) {
+      best_cost = cost;
+      best_tok = tok;
+      best_final_cost = final_cost;
+    }
+  }
+  if (best_tok == NULL) {  // this should not happen, and is likely a code error or
+    // caused by infinities in likelihoods, but I'm not making
+    // it a fatal error for now.
+    KALDI_WARN << "No final token found.";
+  }
+  if (final_cost_out)
+    *final_cost_out = best_final_cost;
+  return BestPathIterator(best_tok, this->NumFramesDecoded() - 1);
+}
+
+
+template <typename FST>
+typename LatticeFasterOnlineDecoderTpl<FST>::BestPathIterator LatticeFasterOnlineDecoderTpl<FST>::TraceBackBestPath(
+    BestPathIterator iter, LatticeArc *oarc) const {
+  KALDI_ASSERT(!iter.Done() && oarc != NULL);
+  Token *tok = static_cast<Token*>(iter.tok);
+  int32 cur_t = iter.frame, step_t = 0;
+  if (tok->backpointer != NULL) {
+    // retrieve the correct forward link(with the best link cost)
+    BaseFloat best_cost = std::numeric_limits<BaseFloat>::infinity();
+    ForwardLinkT *link;
+    for (link = tok->backpointer->links;
+         link != NULL; link = link->next) {
+      if (link->next_tok == tok) { // this is a link to "tok"
+        BaseFloat graph_cost = link->graph_cost, 
+                  acoustic_cost = link->acoustic_cost;
+        BaseFloat cost = graph_cost + acoustic_cost;
+        if (cost < best_cost) {
+          oarc->ilabel = link->ilabel;
+          oarc->olabel = link->olabel;
+          if (link->ilabel != 0) {
+            KALDI_ASSERT(static_cast<size_t>(cur_t) < this->cost_offsets_.size());
+            acoustic_cost -= this->cost_offsets_[cur_t];
+            step_t = -1;
+          } else {
+            step_t = 0;
+          }
+          oarc->weight = LatticeWeight(graph_cost, acoustic_cost);
+          best_cost = cost;
+        }
+      }
+    }
+    if (link == NULL &&
+        best_cost == std::numeric_limits<BaseFloat>::infinity()) { // Did not find correct link.
+      KALDI_ERR << "Error tracing best-path back (likely "
+                << "bug in token-pruning algorithm)";
+    }
+  } else {
+    oarc->ilabel = 0;
+    oarc->olabel = 0;
+    oarc->weight = LatticeWeight::One(); // zero costs.
+  }
+  return BestPathIterator(tok->backpointer, cur_t + step_t);
+}
+
+template <typename FST>
+bool LatticeFasterOnlineDecoderTpl<FST>::GetRawLatticePruned(
+    Lattice *ofst,
+    bool use_final_probs,
+    BaseFloat beam) const {
+  typedef LatticeArc Arc;
+  typedef Arc::StateId StateId;
+  typedef Arc::Weight Weight;
+  typedef Arc::Label Label;
+
+  // Note: you can't use the old interface (Decode()) if you want to
+  // get the lattice with use_final_probs = false.  You'd have to do
+  // InitDecoding() and then AdvanceDecoding().
+  if (this->decoding_finalized_ && !use_final_probs)
+    KALDI_ERR << "You cannot call FinalizeDecoding() and then call "
+              << "GetRawLattice() with use_final_probs == false";
+
+  unordered_map<Token*, BaseFloat> final_costs_local;
+
+  const unordered_map<Token*, BaseFloat> &final_costs =
+      (this->decoding_finalized_ ? this->final_costs_ : final_costs_local);
+  if (!this->decoding_finalized_ && use_final_probs)
+    this->ComputeFinalCosts(&final_costs_local, NULL, NULL);
+
+  ofst->DeleteStates();
+  // num-frames plus one (since frames are one-based, and we have
+  // an extra frame for the start-state).
+  int32 num_frames = this->active_toks_.size() - 1;
+  KALDI_ASSERT(num_frames > 0);
+  for (int32 f = 0; f <= num_frames; f++) {
+    if (this->active_toks_[f].toks == NULL) {
+      KALDI_WARN << "No tokens active on frame " << f
+                 << ": not producing lattice.\n";
+      return false;
+    }
+  }
+  unordered_map<Token*, StateId> tok_map;
+  std::queue<std::pair<Token*, int32> > tok_queue;
+  // First initialize the queue and states.  Put the initial state on the queue;
+  // this is the last token in the list active_toks_[0].toks.
+  for (Token *tok = this->active_toks_[0].toks;
+       tok != NULL; tok = tok->next) {
+    if (tok->next == NULL) {
+      tok_map[tok] = ofst->AddState();
+      ofst->SetStart(tok_map[tok]);
+      std::pair<Token*, int32> tok_pair(tok, 0);  // #frame = 0
+      tok_queue.push(tok_pair);
+    }
+  }
+
+  // Next create states for "good" tokens
+  while (!tok_queue.empty()) {
+    std::pair<Token*, int32> cur_tok_pair = tok_queue.front();
+    tok_queue.pop();
+    Token *cur_tok = cur_tok_pair.first;
+    int32 cur_frame = cur_tok_pair.second;
+    KALDI_ASSERT(cur_frame >= 0 &&
+                 cur_frame <= this->cost_offsets_.size());
+
+    typename unordered_map<Token*, StateId>::const_iterator iter =
+        tok_map.find(cur_tok);
+    KALDI_ASSERT(iter != tok_map.end());
+    StateId cur_state = iter->second;
+
+    for (ForwardLinkT *l = cur_tok->links;
+         l != NULL;
+         l = l->next) {
+      Token *next_tok = l->next_tok;
+      if (next_tok->extra_cost < beam) {
+        // so both the current and the next token are good; create the arc
+        int32 next_frame = l->ilabel == 0 ? cur_frame : cur_frame + 1;
+        StateId nextstate;
+        if (tok_map.find(next_tok) == tok_map.end()) {
+          nextstate = tok_map[next_tok] = ofst->AddState();
+          tok_queue.push(std::pair<Token*, int32>(next_tok, next_frame));
+        } else {
+          nextstate = tok_map[next_tok];
+        }
+        BaseFloat cost_offset = (l->ilabel != 0 ?
+                                 this->cost_offsets_[cur_frame] : 0);
+        Arc arc(l->ilabel, l->olabel,
+                Weight(l->graph_cost, l->acoustic_cost - cost_offset),
+                nextstate);
+        ofst->AddArc(cur_state, arc);
+      }
+    }
+    if (cur_frame == num_frames) {
+      if (use_final_probs && !final_costs.empty()) {
+        typename unordered_map<Token*, BaseFloat>::const_iterator iter =
+            final_costs.find(cur_tok);
+        if (iter != final_costs.end())
+          ofst->SetFinal(cur_state, LatticeWeight(iter->second, 0));
+      } else {
+        ofst->SetFinal(cur_state, LatticeWeight::One());
+      }
+    }
+  }
+  return (ofst->NumStates() != 0);
+}
+
+
+
+// Instantiate the template for the FST types that we'll need.
+template class LatticeFasterOnlineDecoderTpl<fst::Fst<fst::StdArc> >;
+template class LatticeFasterOnlineDecoderTpl<fst::VectorFst<fst::StdArc> >;
+template class LatticeFasterOnlineDecoderTpl<fst::ConstFst<fst::StdArc> >;
+template class LatticeFasterOnlineDecoderTpl<fst::ConstGrammarFst >;
+template class LatticeFasterOnlineDecoderTpl<fst::VectorGrammarFst >;
+
+
+} // end namespace kaldi.

speechx/speechx/kaldi/decoder/lattice-faster-online-decoder.h

+// decoder/lattice-faster-online-decoder.h
+
+// Copyright 2009-2013  Microsoft Corporation;  Mirko Hannemann;
+//           2013-2014  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+//                2018  Zhehuai Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+// see note at the top of lattice-faster-decoder.h, about how to maintain this
+// file in sync with lattice-faster-decoder.h
+
+
+#ifndef KALDI_DECODER_LATTICE_FASTER_ONLINE_DECODER_H_
+#define KALDI_DECODER_LATTICE_FASTER_ONLINE_DECODER_H_
+
+#include "util/stl-utils.h"
+#include "util/hash-list.h"
+#include "fst/fstlib.h"
+#include "itf/decodable-itf.h"
+#include "fstext/fstext-lib.h"
+#include "lat/determinize-lattice-pruned.h"
+#include "lat/kaldi-lattice.h"
+#include "decoder/lattice-faster-decoder.h"
+
+namespace kaldi {
+
+
+
+/** LatticeFasterOnlineDecoderTpl is as LatticeFasterDecoderTpl but also
+    supports an efficient way to get the best path (see the function
+    BestPathEnd()), which is useful in endpointing and in situations where you
+    might want to frequently access the best path.
+
+    This is only templated on the FST type, since the Token type is required to
+    be BackpointerToken.  Actually it only makes sense to instantiate
+    LatticeFasterDecoderTpl with Token == BackpointerToken if you do so indirectly via
+    this child class.
+ */
+template <typename FST>
+class LatticeFasterOnlineDecoderTpl:
+      public LatticeFasterDecoderTpl<FST, decoder::BackpointerToken> {
+ public:
+  using Arc = typename FST::Arc;
+  using Label = typename Arc::Label;
+  using StateId = typename Arc::StateId;
+  using Weight = typename Arc::Weight;
+  using Token = decoder::BackpointerToken;
+  using ForwardLinkT = decoder::ForwardLink<Token>;
+
+  // Instantiate this class once for each thing you have to decode.
+  // This version of the constructor does not take ownership of
+  // 'fst'.
+  LatticeFasterOnlineDecoderTpl(const FST &fst,
+                                const LatticeFasterDecoderConfig &config):
+      LatticeFasterDecoderTpl<FST, Token>(fst, config) { }
+
+  // This version of the initializer takes ownership of 'fst', and will delete
+  // it when this object is destroyed.
+  LatticeFasterOnlineDecoderTpl(const LatticeFasterDecoderConfig &config,
+                                FST *fst):
+      LatticeFasterDecoderTpl<FST, Token>(config, fst) { }
+
+
+  struct BestPathIterator {
+    void *tok;
+    int32 frame;
+    // note, "frame" is the frame-index of the frame you'll get the
+    // transition-id for next time, if you call TraceBackBestPath on this
+    // iterator (assuming it's not an epsilon transition).  Note that this
+    // is one less than you might reasonably expect, e.g. it's -1 for
+    // the nonemitting transitions before the first frame.
+    BestPathIterator(void *t, int32 f): tok(t), frame(f) { }
+    bool Done() const { return tok == NULL; }
+  };
+
+
+  /// Outputs an FST corresponding to the single best path through the lattice.
+  /// This is quite efficient because it doesn't get the entire raw lattice and find
+  /// the best path through it; instead, it uses the BestPathEnd and BestPathIterator
+  /// so it basically traces it back through the lattice.
+  /// Returns true if result is nonempty (using the return status is deprecated,
+  /// it will become void).  If "use_final_probs" is true AND we reached the
+  /// final-state of the graph then it will include those as final-probs, else
+  /// it will treat all final-probs as one.
+  bool GetBestPath(Lattice *ofst,
+                   bool use_final_probs = true) const;
+
+
+  /// This function does a self-test of GetBestPath().  Returns true on
+  /// success; returns false and prints a warning on failure.
+  bool TestGetBestPath(bool use_final_probs = true) const;
+
+
+  /// This function returns an iterator that can be used to trace back
+  /// the best path.  If use_final_probs == true and at least one final state
+  /// survived till the end, it will use the final-probs in working out the best
+  /// final Token, and will output the final cost to *final_cost (if non-NULL),
+  /// else it will use only the forward likelihood, and will put zero in
+  /// *final_cost (if non-NULL).
+  /// Requires that NumFramesDecoded() > 0.
+  BestPathIterator BestPathEnd(bool use_final_probs,
+                               BaseFloat *final_cost = NULL) const;
+
+
+  /// This function can be used in conjunction with BestPathEnd() to trace back
+  /// the best path one link at a time (e.g. this can be useful in endpoint
+  /// detection).  By "link" we mean a link in the graph; not all links cross
+  /// frame boundaries, but each time you see a nonzero ilabel you can interpret
+  /// that as a frame.  The return value is the updated iterator.  It outputs
+  /// the ilabel and olabel, and the (graph and acoustic) weight to the "arc" pointer,
+  /// while leaving its "nextstate" variable unchanged.
+  BestPathIterator TraceBackBestPath(
+      BestPathIterator iter, LatticeArc *arc) const;
+
+
+  /// Behaves the same as GetRawLattice but only processes tokens whose
+  /// extra_cost is smaller than the best-cost plus the specified beam.
+  /// It is only worthwhile to call this function if beam is less than
+  /// the lattice_beam specified in the config; otherwise, it would
+  /// return essentially the same thing as GetRawLattice, but more slowly.
+  bool GetRawLatticePruned(Lattice *ofst,
+                           bool use_final_probs,
+                           BaseFloat beam) const;
+
+  KALDI_DISALLOW_COPY_AND_ASSIGN(LatticeFasterOnlineDecoderTpl);
+};
+
+typedef LatticeFasterOnlineDecoderTpl<fst::StdFst> LatticeFasterOnlineDecoder;
+
+
+} // end namespace kaldi.
+
+#endif

speechx/speechx/kaldi/lat/determinize-lattice-pruned-test.cc

+// lat/determinize-lattice-pruned-test.cc
+
+// Copyright 2009-2012  Microsoft Corporation
+//           2012-2013  Johns Hopkins University (Author: Daniel Povey)
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#include "lat/determinize-lattice-pruned.h"
+#include "fstext/lattice-utils.h"
+#include "fstext/fst-test-utils.h"
+#include "lat/kaldi-lattice.h"
+#include "lat/lattice-functions.h"
+
+namespace fst {
+// Caution: these tests are not as generic as you might think from all the
+// templates in the code.  They are basically only valid for LatticeArc.
+// This is partly due to the fact that certain templates need to be instantiated
+// in other .cc files in this directory.
+
+// test that determinization proceeds correctly on general
+// FSTs (not guaranteed determinzable, but we use the
+// max-states option to stop it getting out of control).
+template<class Arc> void TestDeterminizeLatticePruned() {
+  typedef kaldi::int32 Int;
+  typedef typename Arc::Weight Weight;
+  typedef ArcTpl<CompactLatticeWeightTpl<Weight, Int> > CompactArc;
+
+  for(int i = 0; i < 100; i++) {
+    RandFstOptions opts;
+    opts.n_states = 4;
+    opts.n_arcs = 10;
+    opts.n_final = 2;
+    opts.allow_empty = false;
+    opts.weight_multiplier = 0.5; // impt for the randomly generated weights
+    opts.acyclic = true;
+    // to be exactly representable in float,
+    // or this test fails because numerical differences can cause symmetry in
+    // weights to be broken, which causes the wrong path to be chosen as far
+    // as the string part is concerned.
+
+    VectorFst<Arc> *fst = RandPairFst<Arc>(opts);
+
+    bool sorted = TopSort(fst);
+    KALDI_ASSERT(sorted);
+
+    ILabelCompare<Arc> ilabel_comp;
+    if (kaldi::Rand() % 2 == 0)
+      ArcSort(fst, ilabel_comp);
+
+    std::cout << "FST before lattice-determinizing is:\n";
+    {
+      FstPrinter<Arc> fstprinter(*fst, NULL, NULL, NULL, false, true, "\t");
+      fstprinter.Print(&std::cout, "standard output");
+    }
+    VectorFst<Arc> det_fst;
+    try {
+      DeterminizeLatticePrunedOptions lat_opts;
+      lat_opts.max_mem = ((kaldi::Rand() % 2 == 0) ? 100 : 1000);
+      lat_opts.max_states = ((kaldi::Rand() % 2 == 0) ? -1 : 20);
+      lat_opts.max_arcs = ((kaldi::Rand() % 2 == 0) ? -1 : 30);
+      bool ans = DeterminizeLatticePruned<Weight>(*fst, 10.0, &det_fst, lat_opts);
+
+      std::cout << "FST after lattice-determinizing is:\n";
+      {
+        FstPrinter<Arc> fstprinter(det_fst, NULL, NULL, NULL, false, true, "\t");
+        fstprinter.Print(&std::cout, "standard output");
+      }
+      KALDI_ASSERT(det_fst.Properties(kIDeterministic, true) & kIDeterministic);
+      // OK, now determinize it a different way and check equivalence.
+      // [note: it's not normal determinization, it's taking the best path
+      // for any input-symbol sequence....
+
+
+      VectorFst<Arc> pruned_fst(*fst);
+      if (pruned_fst.NumStates() != 0)
+        kaldi::PruneLattice(10.0, &pruned_fst);
+
+      VectorFst<CompactArc> compact_pruned_fst, compact_pruned_det_fst;
+      ConvertLattice<Weight, Int>(pruned_fst, &compact_pruned_fst, false);
+      std::cout << "Compact pruned FST is:\n";
+      {
+        FstPrinter<CompactArc> fstprinter(compact_pruned_fst, NULL, NULL, NULL, false, true, "\t");
+        fstprinter.Print(&std::cout, "standard output");
+      }
+      ConvertLattice<Weight, Int>(det_fst, &compact_pruned_det_fst, false);
+
+      std::cout << "Compact version of determinized FST is:\n";
+      {
+        FstPrinter<CompactArc> fstprinter(compact_pruned_det_fst, NULL, NULL, NULL, false, true, "\t");
+        fstprinter.Print(&std::cout, "standard output");
+      }
+
+      if (ans)
+        KALDI_ASSERT(RandEquivalent(compact_pruned_det_fst, compact_pruned_fst, 5/*paths*/, 0.01/*delta*/, kaldi::Rand()/*seed*/, 100/*path length, max*/));
+    } catch (...) {
+      std::cout << "Failed to lattice-determinize this FST (probably not determinizable)\n";
+    }
+    delete fst;
+  }
+}
+
+// test that determinization proceeds without crash on acyclic FSTs
+// (guaranteed determinizable in this sense).
+template<class Arc> void TestDeterminizeLatticePruned2() {
+  typedef typename Arc::Weight Weight;
+  RandFstOptions opts;
+  opts.acyclic = true;
+  for(int i = 0; i < 100; i++) {
+    VectorFst<Arc> *fst = RandPairFst<Arc>(opts);
+    std::cout << "FST before lattice-determinizing is:\n";
+    {
+      FstPrinter<Arc> fstprinter(*fst, NULL, NULL, NULL, false, true, "\t");
+      fstprinter.Print(&std::cout, "standard output");
+    }
+    VectorFst<Arc> ofst;
+    DeterminizeLatticePruned<Weight>(*fst, 10.0, &ofst);
+    std::cout << "FST after lattice-determinizing is:\n";
+    {
+      FstPrinter<Arc> fstprinter(ofst, NULL, NULL, NULL, false, true, "\t");
+      fstprinter.Print(&std::cout, "standard output");
+    }
+    delete fst;
+  }
+}
+
+
+} // end namespace fst
+
+int main() {
+  using namespace fst;
+  TestDeterminizeLatticePruned<kaldi::LatticeArc>();
+  TestDeterminizeLatticePruned2<kaldi::LatticeArc>();
+  std::cout << "Tests succeeded\n";
+}

speechx/speechx/kaldi/lat/determinize-lattice-pruned.cc

+// lat/determinize-lattice-pruned.cc
+
+// Copyright 2009-2012  Microsoft Corporation
+//           2012-2013  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#include <vector>
+#include <climits>
+#include "fstext/determinize-lattice.h" // for LatticeStringRepository
+#include "fstext/fstext-utils.h"
+#include "lat/lattice-functions.h"  // for PruneLattice
+#include "lat/minimize-lattice.h"   // for minimization
+#include "lat/push-lattice.h"       // for minimization
+#include "lat/determinize-lattice-pruned.h"
+
+namespace fst {
+
+using std::vector;
+using std::pair;
+using std::greater;
+
+// class LatticeDeterminizerPruned is templated on the same types that
+// CompactLatticeWeight is templated on: the base weight (Weight), typically
+// LatticeWeightTpl<float> etc. but could also be e.g. TropicalWeight, and the
+// IntType, typically int32, used for the output symbols in the compact
+// representation of strings [note: the output symbols would usually be
+// p.d.f. id's in the anticipated use of this code] It has a special requirement
+// on the Weight type: that there should be a Compare function on the weights
+// such that Compare(w1, w2) returns -1 if w1 < w2, 0 if w1 == w2, and +1 if w1 >
+// w2.  This requires that there be a total order on the weights.
+
+template<class Weight, class IntType> class LatticeDeterminizerPruned {
+ public:
+  // Output to Gallic acceptor (so the strings go on weights, and there is a 1-1 correspondence
+  // between our states and the states in ofst.  If destroy == true, release memory as we go
+  // (but we cannot output again).
+
+  typedef CompactLatticeWeightTpl<Weight, IntType> CompactWeight;
+  typedef ArcTpl<CompactWeight> CompactArc; // arc in compact, acceptor form of lattice
+  typedef ArcTpl<Weight> Arc; // arc in non-compact version of lattice
+
+  // Output to standard FST with CompactWeightTpl<Weight> as its weight type (the
+  // weight stores the original output-symbol strings).  If destroy == true,
+  // release memory as we go (but we cannot output again).
+  void Output(MutableFst<CompactArc>  *ofst, bool destroy = true) {
+    KALDI_ASSERT(determinized_);
+    typedef typename Arc::StateId StateId;
+    StateId nStates = static_cast<StateId>(output_states_.size());
+    if (destroy)
+      FreeMostMemory();
+    ofst->DeleteStates();
+    ofst->SetStart(kNoStateId);
+    if (nStates == 0) {
+      return;
+    }
+    for (StateId s = 0;s < nStates;s++) {
+      OutputStateId news = ofst->AddState();
+      KALDI_ASSERT(news == s);
+    }
+    ofst->SetStart(0);
+    // now process transitions.
+    for (StateId this_state_id = 0; this_state_id < nStates; this_state_id++) {
+      OutputState &this_state = *(output_states_[this_state_id]);
+      vector<TempArc> &this_vec(this_state.arcs);
+      typename vector<TempArc>::const_iterator iter = this_vec.begin(), end = this_vec.end();
+
+      for (;iter != end; ++iter) {
+        const TempArc &temp_arc(*iter);
+        CompactArc new_arc;
+        vector<Label> olabel_seq;
+        repository_.ConvertToVector(temp_arc.string, &olabel_seq);
+        CompactWeight weight(temp_arc.weight, olabel_seq);
+        if (temp_arc.nextstate == kNoStateId) {  // is really final weight.
+          ofst->SetFinal(this_state_id, weight);
+        } else {  // is really an arc.
+          new_arc.nextstate = temp_arc.nextstate;
+          new_arc.ilabel = temp_arc.ilabel;
+          new_arc.olabel = temp_arc.ilabel;  // acceptor.  input == output.
+          new_arc.weight = weight;  // includes string and weight.
+          ofst->AddArc(this_state_id, new_arc);
+        }
+      }
+      // Free up memory.  Do this inside the loop as ofst is also allocating memory,
+      // and we want to reduce the maximum amount ever allocated.
+      if (destroy) { vector<TempArc> temp; temp.swap(this_vec); }
+    }
+    if (destroy) {
+      FreeOutputStates();
+      repository_.Destroy();
+    }
+  }
+
+  // Output to standard FST with Weight as its weight type.  We will create extra
+  // states to handle sequences of symbols on the output.  If destroy == true,
+  // release memory as we go (but we cannot output again).
+  void  Output(MutableFst<Arc> *ofst, bool destroy = true) {
+    // Outputs to standard fst.
+    OutputStateId nStates = static_cast<OutputStateId>(output_states_.size());
+    ofst->DeleteStates();
+    if (nStates == 0) {
+      ofst->SetStart(kNoStateId);
+      return;
+    }
+    if (destroy)
+      FreeMostMemory();
+    // Add basic states-- but we will add extra ones to account for strings on output.
+    for (OutputStateId s = 0; s< nStates;s++) {
+      OutputStateId news = ofst->AddState();
+      KALDI_ASSERT(news == s);
+    }
+    ofst->SetStart(0);
+    for (OutputStateId this_state_id = 0; this_state_id < nStates; this_state_id++) {
+      OutputState &this_state = *(output_states_[this_state_id]);
+      vector<TempArc> &this_vec(this_state.arcs);
+
+      typename vector<TempArc>::const_iterator iter = this_vec.begin(), end = this_vec.end();
+      for (; iter != end; ++iter) {
+        const TempArc &temp_arc(*iter);
+        vector<Label> seq;
+        repository_.ConvertToVector(temp_arc.string, &seq);
+
+        if (temp_arc.nextstate == kNoStateId) {  // Really a final weight.
+          // Make a sequence of states going to a final state, with the strings
+          // as labels.  Put the weight on the first arc.
+          OutputStateId cur_state = this_state_id;
+          for (size_t i = 0; i < seq.size(); i++) {
+            OutputStateId next_state = ofst->AddState();
+            Arc arc;
+            arc.nextstate = next_state;
+            arc.weight = (i == 0 ? temp_arc.weight : Weight::One());
+            arc.ilabel = 0;  // epsilon.
+            arc.olabel = seq[i];
+            ofst->AddArc(cur_state, arc);
+            cur_state = next_state;
+          }
+          ofst->SetFinal(cur_state, (seq.size() == 0 ? temp_arc.weight : Weight::One()));
+        } else {  // Really an arc.
+          OutputStateId cur_state = this_state_id;
+          // Have to be careful with this integer comparison (i+1 < seq.size()) because unsigned.
+          // i < seq.size()-1 could fail for zero-length sequences.
+          for (size_t i = 0; i+1 < seq.size();i++) {
+            // for all but the last element of seq, create new state.
+            OutputStateId next_state = ofst->AddState();
+            Arc arc;
+            arc.nextstate = next_state;
+            arc.weight = (i == 0 ? temp_arc.weight : Weight::One());
+            arc.ilabel = (i == 0 ? temp_arc.ilabel : 0);  // put ilabel on first element of seq.
+            arc.olabel = seq[i];
+            ofst->AddArc(cur_state, arc);
+            cur_state = next_state;
+          }
+          // Add the final arc in the sequence.
+          Arc arc;
+          arc.nextstate = temp_arc.nextstate;
+          arc.weight = (seq.size() <= 1 ? temp_arc.weight : Weight::One());
+          arc.ilabel = (seq.size() <= 1 ? temp_arc.ilabel : 0);
+          arc.olabel = (seq.size() > 0 ? seq.back() : 0);
+          ofst->AddArc(cur_state, arc);
+        }
+      }
+      // Free up memory.  Do this inside the loop as ofst is also allocating memory
+      if (destroy) { vector<TempArc> temp; temp.swap(this_vec); }
+    }
+    if (destroy) {
+      FreeOutputStates();
+      repository_.Destroy();
+    }
+  }
+
+
+  // Initializer.  After initializing the object you will typically
+  // call Determinize() and then call one of the Output functions.
+  // Note: ifst.Copy() will generally do a
+  // shallow copy.  We do it like this for memory safety, rather than
+  // keeping a reference or pointer to ifst_.
+  LatticeDeterminizerPruned(const ExpandedFst<Arc> &ifst,
+                            double beam,
+                            DeterminizeLatticePrunedOptions opts):
+      num_arcs_(0), num_elems_(0), ifst_(ifst.Copy()), beam_(beam), opts_(opts),
+      equal_(opts_.delta), determinized_(false),
+      minimal_hash_(3, hasher_, equal_), initial_hash_(3, hasher_, equal_) {
+    KALDI_ASSERT(Weight::Properties() & kIdempotent); // this algorithm won't
+    // work correctly otherwise.
+  }
+
+  void FreeOutputStates() {
+    for (size_t i = 0; i < output_states_.size(); i++)
+      delete output_states_[i];
+    vector<OutputState*> temp;
+    temp.swap(output_states_);
+  }
+
+  // frees all memory except the info (in output_states_[ ]->arcs)
+  // that we need to output the FST.
+  void FreeMostMemory() {
+    if (ifst_) {
+      delete ifst_;
+      ifst_ = NULL;
+    }
+    { MinimalSubsetHash tmp; tmp.swap(minimal_hash_); }
+
+    for (size_t i = 0; i < output_states_.size(); i++) {
+      vector<Element> empty_subset;
+      empty_subset.swap(output_states_[i]->minimal_subset);
+    }
+
+    for (typename InitialSubsetHash::iterator iter = initial_hash_.begin();
+         iter != initial_hash_.end(); ++iter)
+      delete iter->first;
+    { InitialSubsetHash tmp; tmp.swap(initial_hash_); }
+    { vector<char> tmp;  tmp.swap(isymbol_or_final_); }
+    { // Free up the queue.  I'm not sure how to make sure all
+      // the memory is really freed (no swap() function)... doesn't really
+      // matter much though.
+      while (!queue_.empty()) {
+        Task *t = queue_.top();
+        delete t;
+        queue_.pop();
+      }
+    }
+    { vector<pair<Label, Element> > tmp; tmp.swap(all_elems_tmp_); }
+  }
+
+  ~LatticeDeterminizerPruned() {
+    FreeMostMemory();
+    FreeOutputStates();
+    // rest is deleted by destructors.
+  }
+
+  void RebuildRepository() { // rebuild the string repository,
+    // freeing stuff we don't need.. we call this when memory usage
+    // passes a supplied threshold.  We need to accumulate all the
+    // strings we need the repository to "remember", then tell it
+    // to clean the repository.
+    std::vector<StringId> needed_strings;
+    for (size_t i = 0; i < output_states_.size(); i++) {
+      AddStrings(output_states_[i]->minimal_subset, &needed_strings);
+      for (size_t j = 0; j < output_states_[i]->arcs.size(); j++)
+        needed_strings.push_back(output_states_[i]->arcs[j].string);
+    }
+
+    { // the queue doesn't allow us access to the underlying vector,
+      // so we have to resort to a temporary collection.
+      std::vector<Task*> tasks;
+      while (!queue_.empty()) {
+        Task *task = queue_.top();
+        queue_.pop();
+        tasks.push_back(task);
+        AddStrings(task->subset, &needed_strings);
+      }
+      for (size_t i = 0; i < tasks.size(); i++)
+        queue_.push(tasks[i]);
+    }
+
+    // the following loop covers strings present in initial_hash_.
+    for (typename InitialSubsetHash::const_iterator
+             iter = initial_hash_.begin();
+         iter != initial_hash_.end(); ++iter) {
+      const vector<Element> &vec = *(iter->first);
+      Element elem = iter->second;
+      AddStrings(vec, &needed_strings);
+      needed_strings.push_back(elem.string);
+    }
+    std::sort(needed_strings.begin(), needed_strings.end());
+    needed_strings.erase(std::unique(needed_strings.begin(),
+                                     needed_strings.end()),
+                         needed_strings.end()); // uniq the strings.
+    KALDI_LOG << "Rebuilding repository.";
+
+    repository_.Rebuild(needed_strings);
+  }
+
+  bool CheckMemoryUsage() {
+    int32 repo_size = repository_.MemSize(),
+        arcs_size = num_arcs_ * sizeof(TempArc),
+        elems_size = num_elems_ * sizeof(Element),
+        total_size = repo_size + arcs_size + elems_size;
+    if (opts_.max_mem > 0 && total_size > opts_.max_mem) { // We passed the memory threshold.
+      // This is usually due to the repository getting large, so we
+      // clean this out.
+      RebuildRepository();
+      int32 new_repo_size = repository_.MemSize(),
+          new_total_size = new_repo_size + arcs_size + elems_size;
+
+      KALDI_VLOG(2) << "Rebuilt repository in determinize-lattice: repository shrank from "
+                    << repo_size << " to " << new_repo_size << " bytes (approximately)";
+
+      if (new_total_size > static_cast<int32>(opts_.max_mem * 0.8)) {
+        // Rebuilding didn't help enough-- we need a margin to stop
+        // having to rebuild too often.  We'll just return to the user at
+        // this point, with a partial lattice that's pruned tighter than
+        // the specified beam.  Here we figure out what the effective
+        // beam was.
+        double effective_beam = beam_;
+        if (!queue_.empty()) { // Note: queue should probably not be empty; we're
+          // just being paranoid here.
+          Task *task = queue_.top();
+          double total_weight = backward_costs_[ifst_->Start()]; // best weight of FST.
+          effective_beam = task->priority_cost - total_weight;
+        }
+        KALDI_WARN << "Did not reach requested beam in determinize-lattice: "
+                   << "size exceeds maximum " << opts_.max_mem
+                   << " bytes; (repo,arcs,elems) = (" << repo_size << ","
+                   << arcs_size << "," << elems_size
+                   << "), after rebuilding, repo size was " << new_repo_size
+                   << ", effective beam was " << effective_beam
+                   << " vs. requested beam " << beam_;
+        return false;
+      }
+    }
+    return true;
+  }
+
+  bool Determinize(double *effective_beam) {
+    KALDI_ASSERT(!determinized_);
+    // This determinizes the input fst but leaves it in the "special format"
+    // in "output_arcs_".  Must be called after Initialize().  To get the
+    // output, call one of the Output routines.
+
+    InitializeDeterminization(); // some start-up tasks.
+    while (!queue_.empty()) {
+      Task *task = queue_.top();
+      // Note: the queue contains only tasks that are "within the beam".
+      // We also have to check whether we have reached one of the user-specified
+      // maximums, of estimated memory, arcs, or states.  The condition for
+      // ending is:
+      // num-states is more than user specified, OR
+      // num-arcs is more than user specified, OR
+      // memory passed a user-specified threshold and cleanup failed
+      //  to get it below that threshold.
+      size_t num_states = output_states_.size();
+      if ((opts_.max_states > 0 && num_states > opts_.max_states) ||
+          (opts_.max_arcs > 0 && num_arcs_ > opts_.max_arcs) ||
+          (num_states % 10 == 0 && !CheckMemoryUsage())) { // note: at some point
+        // it was num_states % 100, not num_states % 10, but I encountered an example
+        // where memory was exhausted before we reached state #100.
+        KALDI_VLOG(1) << "Lattice determinization terminated but not "
+                      << " because of lattice-beam.  (#states, #arcs) is ( "
+                      << output_states_.size() << ", " << num_arcs_
+                      << " ), versus limits ( " << opts_.max_states << ", "
+                      << opts_.max_arcs << " ) (else, may be memory limit).";
+        break;
+        // we terminate the determinization here-- whatever we already expanded is
+        // what we'll return...  because we expanded stuff in order of total
+        // (forward-backward) weight, the stuff we returned first is the most
+        // important.
+      }
+      queue_.pop();
+      ProcessTransition(task->state, task->label, &(task->subset));
+      delete task;
+    }
+    determinized_ = true;
+    if (effective_beam != NULL) {
+      if (queue_.empty()) *effective_beam = beam_;
+      else
+        *effective_beam = queue_.top()->priority_cost -
+            backward_costs_[ifst_->Start()];
+    }
+    return (queue_.empty()); // return success if queue was empty, i.e. we processed
+    // all tasks and did not break out of the loop early due to reaching a memory,
+    // arc or state limit.
+  }
+ private:
+
+  typedef typename Arc::Label Label;
+  typedef typename Arc::StateId StateId;  // use this when we don't know if it's input or output.
+  typedef typename Arc::StateId InputStateId;  // state in the input FST.
+  typedef typename Arc::StateId OutputStateId;  // same as above but distinguish
+                                                // states in output Fst.
+
+  typedef LatticeStringRepository<IntType> StringRepositoryType;
+  typedef const typename StringRepositoryType::Entry* StringId;
+
+  // Element of a subset [of original states]
+  struct Element {
+    StateId state; // use StateId as this is usually InputStateId but in one case
+                   // OutputStateId.
+    StringId string;
+    Weight weight;
+    bool operator != (const Element &other) const {
+      return (state != other.state || string != other.string ||
+              weight != other.weight);
+    }
+    // This operator is only intended for the priority_queue in the function
+    // EpsilonClosure().
+    bool operator > (const Element &other) const {
+      return state > other.state;
+    }
+    // This operator is only intended to support sorting in EpsilonClosure()
+    bool operator < (const Element &other) const {
+      return state < other.state;
+    }
+  };
+
+  // Arcs in the format we temporarily create in this class (a representation, essentially of
+  // a Gallic Fst).
+  struct TempArc {
+    Label ilabel;
+    StringId string;  // Look it up in the StringRepository, it's a sequence of Labels.
+    OutputStateId nextstate;  // or kNoState for final weights.
+    Weight weight;
+  };
+
+  // Hashing function used in hash of subsets.
+  // A subset is a pointer to vector<Element>.
+  // The Elements are in sorted order on state id, and without repeated states.
+  // Because the order of Elements is fixed, we can use a hashing function that is
+  // order-dependent.  However the weights are not included in the hashing function--
+  // we hash subsets that differ only in weight to the same key.  This is not optimal
+  // in terms of the O(N) performance but typically if we have a lot of determinized
+  // states that differ only in weight then the input probably was pathological in some way,
+  // or even non-determinizable.
+  //   We don't quantize the weights, in order to avoid inexactness in simple cases.
+  // Instead we apply the delta when comparing subsets for equality, and allow a small
+  // difference.
+
+  class SubsetKey {
+   public:
+    size_t operator ()(const vector<Element> * subset) const {  // hashes only the state and string.
+      size_t hash = 0, factor = 1;
+      for (typename vector<Element>::const_iterator iter= subset->begin(); iter != subset->end(); ++iter) {
+        hash *= factor;
+        hash += iter->state + reinterpret_cast<size_t>(iter->string);
+        factor *= 23531;  // these numbers are primes.
+      }
+      return hash;
+    }
+  };
+
+  // This is the equality operator on subsets.  It checks for exact match on state-id
+  // and string, and approximate match on weights.
+  class SubsetEqual {
+   public:
+    bool operator ()(const vector<Element> * s1, const vector<Element> * s2) const {
+      size_t sz = s1->size();
+      KALDI_ASSERT(sz>=0);
+      if (sz != s2->size()) return false;
+      typename vector<Element>::const_iterator iter1 = s1->begin(),
+          iter1_end = s1->end(), iter2=s2->begin();
+      for (; iter1 < iter1_end; ++iter1, ++iter2) {
+        if (iter1->state != iter2->state ||
+           iter1->string != iter2->string ||
+            ! ApproxEqual(iter1->weight, iter2->weight, delta_)) return false;
+      }
+      return true;
+    }
+    float delta_;
+    SubsetEqual(float delta): delta_(delta) {}
+    SubsetEqual(): delta_(kDelta) {}
+  };
+
+  // Operator that says whether two Elements have the same states.
+  // Used only for debug.
+  class SubsetEqualStates {
+   public:
+    bool operator ()(const vector<Element> * s1, const vector<Element> * s2) const {
+      size_t sz = s1->size();
+      KALDI_ASSERT(sz>=0);
+      if (sz != s2->size()) return false;
+      typename vector<Element>::const_iterator iter1 = s1->begin(),
+          iter1_end = s1->end(), iter2=s2->begin();
+      for (; iter1 < iter1_end; ++iter1, ++iter2) {
+        if (iter1->state != iter2->state) return false;
+      }
+      return true;
+    }
+  };
+
+  // Define the hash type we use to map subsets (in minimal
+  // representation) to OutputStateId.
+  typedef unordered_map<const vector<Element>*, OutputStateId,
+                        SubsetKey, SubsetEqual> MinimalSubsetHash;
+
+  // Define the hash type we use to map subsets (in initial
+  // representation) to OutputStateId, together with an
+  // extra weight. [note: we interpret the Element.state in here
+  // as an OutputStateId even though it's declared as InputStateId;
+  // these types are the same anyway].
+  typedef unordered_map<const vector<Element>*, Element,
+                        SubsetKey, SubsetEqual> InitialSubsetHash;
+
+
+  // converts the representation of the subset from canonical (all states) to
+  // minimal (only states with output symbols on arcs leaving them, and final
+  // states).  Output is not necessarily normalized, even if input_subset was.
+  void ConvertToMinimal(vector<Element> *subset) {
+    KALDI_ASSERT(!subset->empty());
+    typename vector<Element>::iterator cur_in = subset->begin(),
+        cur_out = subset->begin(), end = subset->end();
+    while (cur_in != end) {
+      if(IsIsymbolOrFinal(cur_in->state)) {  // keep it...
+        *cur_out = *cur_in;
+        cur_out++;
+      }
+      cur_in++;
+    }
+    subset->resize(cur_out - subset->begin());
+  }
+
+  // Takes a minimal, normalized subset, and converts it to an OutputStateId.
+  // Involves a hash lookup, and possibly adding a new OutputStateId.
+  // If it creates a new OutputStateId, it creates a new record for it, works
+  // out its final-weight, and puts stuff on the queue relating to its
+  // transitions.
+  OutputStateId MinimalToStateId(const vector<Element> &subset,
+                                 const double forward_cost) {
+    typename MinimalSubsetHash::const_iterator iter
+        = minimal_hash_.find(&subset);
+    if (iter != minimal_hash_.end()) { // Found a matching subset.
+      OutputStateId state_id = iter->second;
+      const OutputState &state = *(output_states_[state_id]);
+      // Below is just a check that the algorithm is working...
+      if (forward_cost < state.forward_cost - 0.1) {
+        // for large weights, this check could fail due to roundoff.
+        KALDI_WARN << "New cost is less (check the difference is small) "
+                   << forward_cost << ", "
+                   << state.forward_cost;
+      }
+      return state_id;
+    }
+    OutputStateId state_id = static_cast<OutputStateId>(output_states_.size());
+    OutputState *new_state = new OutputState(subset, forward_cost);
+    minimal_hash_[&(new_state->minimal_subset)] = state_id;
+    output_states_.push_back(new_state);
+    num_elems_ += subset.size();
+    // Note: in the previous algorithm, we pushed the new state-id onto the queue
+    // at this point.  Here, the queue happens elsewhere, and we directly process
+    // the state (which result in stuff getting added to the queue).
+    ProcessFinal(state_id); // will work out the final-prob.
+    ProcessTransitions(state_id); // will process transitions and add stuff to the queue.
+    return state_id;
+  }
+
+
+  // Given a normalized initial subset of elements (i.e. before epsilon closure),
+  // compute the corresponding output-state.
+  OutputStateId InitialToStateId(const vector<Element> &subset_in,
+                                 double forward_cost,
+                                 Weight *remaining_weight,
+                                 StringId *common_prefix) {
+    typename InitialSubsetHash::const_iterator iter
+        = initial_hash_.find(&subset_in);
+    if (iter != initial_hash_.end()) { // Found a matching subset.
+      const Element &elem = iter->second;
+      *remaining_weight = elem.weight;
+      *common_prefix = elem.string;
+      if (elem.weight == Weight::Zero())
+        KALDI_WARN << "Zero weight!";
+      return elem.state;
+    }
+    // else no matching subset-- have to work it out.
+    vector<Element> subset(subset_in);
+    // Follow through epsilons.  Will add no duplicate states.  note: after
+    // EpsilonClosure, it is the same as "canonical" subset, except not
+    // normalized (actually we never compute the normalized canonical subset,
+    // only the normalized minimal one).
+    EpsilonClosure(&subset); // follow epsilons.
+    ConvertToMinimal(&subset); // remove all but emitting and final states.
+
+    Element elem; // will be used to store remaining weight and string, and
+                 // OutputStateId, in initial_hash_;
+    NormalizeSubset(&subset, &elem.weight, &elem.string); // normalize subset; put
+    // common string and weight in "elem".  The subset is now a minimal,
+    // normalized subset.
+
+    forward_cost += ConvertToCost(elem.weight);
+    OutputStateId ans = MinimalToStateId(subset, forward_cost);
+    *remaining_weight = elem.weight;
+    *common_prefix = elem.string;
+    if (elem.weight == Weight::Zero())
+      KALDI_WARN << "Zero weight!";
+
+    // Before returning "ans", add the initial subset to the hash,
+    // so that we can bypass the epsilon-closure etc., next time
+    // we process the same initial subset.
+    vector<Element> *initial_subset_ptr = new vector<Element>(subset_in);
+    elem.state = ans;
+    initial_hash_[initial_subset_ptr] = elem;
+    num_elems_ += initial_subset_ptr->size(); // keep track of memory usage.
+    return ans;
+  }
+
+  // returns the Compare value (-1 if a < b, 0 if a == b, 1 if a > b) according
+  // to the ordering we defined on strings for the CompactLatticeWeightTpl.
+  // see function
+  // inline int Compare (const CompactLatticeWeightTpl<WeightType,IntType> &w1,
+  //                     const CompactLatticeWeightTpl<WeightType,IntType> &w2)
+  // in lattice-weight.h.
+  // this is the same as that, but optimized for our data structures.
+  inline int Compare(const Weight &a_w, StringId a_str,
+                     const Weight &b_w, StringId b_str) const {
+    int weight_comp = fst::Compare(a_w, b_w);
+    if (weight_comp != 0) return weight_comp;
+    // now comparing strings.
+    if (a_str == b_str) return 0;
+    vector<IntType> a_vec, b_vec;
+    repository_.ConvertToVector(a_str, &a_vec);
+    repository_.ConvertToVector(b_str, &b_vec);
+    // First compare their lengths.
+    int a_len = a_vec.size(), b_len = b_vec.size();
+    // use opposite order on the string lengths (c.f. Compare in
+    // lattice-weight.h)
+    if (a_len > b_len) return -1;
+    else if (a_len < b_len) return 1;
+    for(int i = 0; i < a_len; i++) {
+      if (a_vec[i] < b_vec[i]) return -1;
+      else if (a_vec[i] > b_vec[i]) return 1;
+    }
+    KALDI_ASSERT(0); // because we checked if a_str == b_str above, shouldn't reach here
+    return 0;
+  }
+
+  // This function computes epsilon closure of subset of states by following epsilon links.
+  // Called by InitialToStateId and Initialize.
+  // Has no side effects except on the string repository.  The "output_subset" is not
+  // necessarily normalized (in the sense of there being no common substring), unless
+  // input_subset was.
+  void EpsilonClosure(vector<Element> *subset) {
+    // at input, subset must have only one example of each StateId.  [will still
+    // be so at output].  This function follows input-epsilons, and augments the
+    // subset accordingly.
+
+    std::priority_queue<Element, vector<Element>, greater<Element> > queue;
+    unordered_map<InputStateId, Element> cur_subset;
+    typedef typename unordered_map<InputStateId, Element>::iterator MapIter;
+    typedef typename vector<Element>::const_iterator VecIter;
+
+    for (VecIter iter = subset->begin(); iter != subset->end(); ++iter) {
+      queue.push(*iter);
+      cur_subset[iter->state] = *iter;
+    }
+
+    // find whether input fst is known to be sorted on input label.
+    bool sorted = ((ifst_->Properties(kILabelSorted, false) & kILabelSorted) != 0);
+    bool replaced_elems = false; // relates to an optimization, see below.
+    int counter = 0; // stops infinite loops here for non-lattice-determinizable input
+    // (e.g. input with negative-cost epsilon loops); useful in testing.
+    while (queue.size() != 0) {
+      Element elem = queue.top();
+      queue.pop();
+
+      // The next if-statement is a kind of optimization.  It's to prevent us
+      // unnecessarily repeating the processing of a state.  "cur_subset" always
+      // contains only one Element with a particular state.  The issue is that
+      // whenever we modify the Element corresponding to that state in "cur_subset",
+      // both the new (optimal) and old (less-optimal) Element will still be in
+      // "queue".  The next if-statement stops us from wasting compute by
+      // processing the old Element.
+      if (replaced_elems && cur_subset[elem.state] != elem)
+        continue;
+      if (opts_.max_loop > 0 && counter++ > opts_.max_loop) {
+        KALDI_ERR << "Lattice determinization aborted since looped more than "
+                  << opts_.max_loop << " times during epsilon closure.";
+      }
+      for (ArcIterator<ExpandedFst<Arc> > aiter(*ifst_, elem.state); !aiter.Done(); aiter.Next()) {
+        const Arc &arc = aiter.Value();
+        if (sorted && arc.ilabel != 0) break;  // Break from the loop: due to sorting there will be no
+        // more transitions with epsilons as input labels.
+        if (arc.ilabel == 0
+            && arc.weight != Weight::Zero()) {  // Epsilon transition.
+          Element next_elem;
+          next_elem.state = arc.nextstate;
+          next_elem.weight = Times(elem.weight, arc.weight);
+          // next_elem.string is not set up yet... create it only
+          // when we know we need it (this is an optimization)
+
+          MapIter iter = cur_subset.find(next_elem.state);
+          if (iter == cur_subset.end()) {
+            // was no such StateId: insert and add to queue.
+            next_elem.string = (arc.olabel == 0 ? elem.string :
+                                repository_.Successor(elem.string, arc.olabel));
+            cur_subset[next_elem.state] = next_elem;
+            queue.push(next_elem);
+          } else {
+            // was not inserted because one already there.  In normal
+            // determinization we'd add the weights.  Here, we find which one
+            // has the better weight, and keep its corresponding string.
+            int comp = fst::Compare(next_elem.weight, iter->second.weight);
+            if (comp == 0) { // A tie on weights.  This should be a rare case;
+                             // we don't optimize for it.
+              next_elem.string = (arc.olabel == 0 ? elem.string :
+                                  repository_.Successor(elem.string,
+                                                        arc.olabel));
+              comp = Compare(next_elem.weight, next_elem.string,
+                             iter->second.weight, iter->second.string);
+            }
+            if(comp == 1) { // next_elem is better, so use its (weight, string)
+              next_elem.string = (arc.olabel == 0 ? elem.string :
+                                  repository_.Successor(elem.string, arc.olabel));
+              iter->second.string = next_elem.string;
+              iter->second.weight = next_elem.weight;
+              queue.push(next_elem);
+              replaced_elems = true;
+            }
+            // else it is the same or worse, so use original one.
+          }
+        }
+      }
+    }
+
+    { // copy cur_subset to subset.
+      subset->clear();
+      subset->reserve(cur_subset.size());
+      MapIter iter = cur_subset.begin(), end = cur_subset.end();
+      for (; iter != end; ++iter) subset->push_back(iter->second);
+      // sort by state ID, because the subset hash function is order-dependent(see SubsetKey)
+      std::sort(subset->begin(), subset->end());
+    }
+  }
+
+
+  // This function works out the final-weight of the determinized state.
+  // called by ProcessSubset.
+  // Has no side effects except on the variable repository_, and
+  // output_states_[output_state_id].arcs
+
+  void ProcessFinal(OutputStateId output_state_id) {
+    OutputState &state = *(output_states_[output_state_id]);
+    const vector<Element> &minimal_subset = state.minimal_subset;
+    // processes final-weights for this subset.  state.minimal_subset_ may be
+    // empty if the graphs is not connected/trimmed, I think, do don't check
+    // that it's nonempty.
+    StringId final_string = repository_.EmptyString();  // set it to keep the
+    // compiler happy; if it doesn't get set in the loop, we won't use the value anyway.
+    Weight final_weight = Weight::Zero();
+    bool is_final = false;
+    typename vector<Element>::const_iterator iter = minimal_subset.begin(), end = minimal_subset.end();
+    for (; iter != end; ++iter) {
+      const Element &elem = *iter;
+      Weight this_final_weight = Times(elem.weight, ifst_->Final(elem.state));
+      StringId this_final_string = elem.string;
+      if (this_final_weight != Weight::Zero() &&
+         (!is_final || Compare(this_final_weight, this_final_string,
+                               final_weight, final_string) == 1)) { // the new
+        // (weight, string) pair is more in semiring than our current
+        // one.
+        is_final = true;
+        final_weight = this_final_weight;
+        final_string = this_final_string;
+      }
+    }
+    if (is_final &&
+        ConvertToCost(final_weight) + state.forward_cost <= cutoff_) {
+      // store final weights in TempArc structure, just like a transition.
+      // Note: we only store the final-weight if it's inside the pruning beam, hence
+      // the stuff with Compare.
+      TempArc temp_arc;
+      temp_arc.ilabel = 0;
+      temp_arc.nextstate = kNoStateId;  // special marker meaning "final weight".
+      temp_arc.string = final_string;
+      temp_arc.weight = final_weight;
+      state.arcs.push_back(temp_arc);
+      num_arcs_++;
+    }
+  }
+
+  // NormalizeSubset normalizes the subset "elems" by
+  // removing any common string prefix (putting it in common_str),
+  // and dividing by the total weight (putting it in tot_weight).
+  void NormalizeSubset(vector<Element> *elems,
+                       Weight *tot_weight,
+                       StringId *common_str) {
+    if(elems->empty()) { // just set common_str, tot_weight
+      // to defaults and return...
+      KALDI_WARN << "empty subset";
+      *common_str = repository_.EmptyString();
+      *tot_weight = Weight::Zero();
+      return;
+    }
+    size_t size = elems->size();
+    vector<IntType> common_prefix;
+    repository_.ConvertToVector((*elems)[0].string, &common_prefix);
+    Weight weight = (*elems)[0].weight;
+    for(size_t i = 1; i < size; i++) {
+      weight = Plus(weight, (*elems)[i].weight);
+      repository_.ReduceToCommonPrefix((*elems)[i].string, &common_prefix);
+    }
+    KALDI_ASSERT(weight != Weight::Zero()); // we made sure to ignore arcs with zero
+    // weights on them, so we shouldn't have zero here.
+    size_t prefix_len = common_prefix.size();
+    for(size_t i = 0; i < size; i++) {
+      (*elems)[i].weight = Divide((*elems)[i].weight, weight, DIVIDE_LEFT);
+      (*elems)[i].string =
+          repository_.RemovePrefix((*elems)[i].string, prefix_len);
+    }
+    *common_str = repository_.ConvertFromVector(common_prefix);
+    *tot_weight = weight;
+  }
+
+  // Take a subset of Elements that is sorted on state, and
+  // merge any Elements that have the same state (taking the best
+  // (weight, string) pair in the semiring).
+  void MakeSubsetUnique(vector<Element> *subset) {
+    typedef typename vector<Element>::iterator IterType;
+
+    // This KALDI_ASSERT is designed to fail (usually) if the subset is not sorted on
+    // state.
+    KALDI_ASSERT(subset->size() < 2 || (*subset)[0].state <= (*subset)[1].state);
+
+    IterType cur_in = subset->begin(), cur_out = cur_in, end = subset->end();
+    size_t num_out = 0;
+    // Merge elements with same state-id
+    while (cur_in != end) {  // while we have more elements to process.
+      // At this point, cur_out points to location of next place we want to put an element,
+      // cur_in points to location of next element we want to process.
+      if (cur_in != cur_out) *cur_out = *cur_in;
+      cur_in++;
+      while (cur_in != end && cur_in->state == cur_out->state) {
+        if (Compare(cur_in->weight, cur_in->string,
+                   cur_out->weight, cur_out->string) == 1) {
+          // if *cur_in > *cur_out in semiring, then take *cur_in.
+          cur_out->string = cur_in->string;
+          cur_out->weight = cur_in->weight;
+        }
+        cur_in++;
+      }
+      cur_out++;
+      num_out++;
+    }
+    subset->resize(num_out);
+  }
+
+  // ProcessTransition was called from "ProcessTransitions" in the non-pruned
+  // code, but now we in effect put the calls to ProcessTransition on a priority
+  // queue, and it now gets called directly from Determinize().  This function
+  // processes a transition from state "ostate_id".  The set "subset" of Elements
+  // represents a set of next-states with associated weights and strings, each
+  // one arising from an arc from some state in a determinized-state; the
+  // next-states are unique (there is only one Entry assocated with each)
+  void ProcessTransition(OutputStateId ostate_id, Label ilabel, vector<Element> *subset) {
+
+    double forward_cost = output_states_[ostate_id]->forward_cost;
+    StringId common_str;
+    Weight tot_weight;
+    NormalizeSubset(subset, &tot_weight, &common_str);
+    forward_cost += ConvertToCost(tot_weight);
+
+    OutputStateId nextstate;
+    {
+      Weight next_tot_weight;
+      StringId next_common_str;
+      nextstate = InitialToStateId(*subset,
+                                   forward_cost,
+                                   &next_tot_weight,
+                                   &next_common_str);
+      common_str = repository_.Concatenate(common_str, next_common_str);
+      tot_weight = Times(tot_weight, next_tot_weight);
+    }
+
+    // Now add an arc to the next state (would have been created if necessary by
+    // InitialToStateId).
+    TempArc temp_arc;
+    temp_arc.ilabel = ilabel;
+    temp_arc.nextstate = nextstate;
+    temp_arc.string = common_str;
+    temp_arc.weight = tot_weight;
+    output_states_[ostate_id]->arcs.push_back(temp_arc);  // record the arc.
+    num_arcs_++;
+  }
+
+
+  // "less than" operator for pair<Label, Element>.   Used in ProcessTransitions.
+  // Lexicographical order, which only compares the state when ordering the
+  // "Element" member of the pair.
+
+  class PairComparator {
+   public:
+    inline bool operator () (const pair<Label, Element> &p1, const pair<Label, Element> &p2) {
+      if (p1.first < p2.first) return true;
+      else if (p1.first > p2.first) return false;
+      else {
+        return p1.second.state < p2.second.state;
+      }
+    }
+  };
+
+
+  // ProcessTransitions processes emitting transitions (transitions with
+  // ilabels) out of this subset of states.  It actualy only creates records
+  // ("Task") that get added to the queue.  The transitions will be processed in
+  // priority order from Determinize().  This function soes not consider final
+  // states.  Partitions the emitting transitions up by ilabel (by sorting on
+  // ilabel), and for each unique ilabel, it creates a Task record that contains
+  // the information we need to process the transition.
+
+  void ProcessTransitions(OutputStateId output_state_id) {
+    const vector<Element> &minimal_subset = output_states_[output_state_id]->minimal_subset;
+    // it's possible that minimal_subset could be empty if there are
+    // unreachable parts of the graph, so don't check that it's nonempty.
+    vector<pair<Label, Element> > &all_elems(all_elems_tmp_); // use class member
+    // to avoid memory allocation/deallocation.
+    {
+      // Push back into "all_elems", elements corresponding to all
+      // non-epsilon-input transitions out of all states in "minimal_subset".
+      typename vector<Element>::const_iterator iter = minimal_subset.begin(), end = minimal_subset.end();
+      for (;iter != end; ++iter) {
+        const Element &elem = *iter;
+        for (ArcIterator<ExpandedFst<Arc> > aiter(*ifst_, elem.state); ! aiter.Done(); aiter.Next()) {
+          const Arc &arc = aiter.Value();
+          if (arc.ilabel != 0
+              && arc.weight != Weight::Zero()) {  // Non-epsilon transition -- ignore epsilons here.
+            pair<Label, Element> this_pr;
+            this_pr.first = arc.ilabel;
+            Element &next_elem(this_pr.second);
+            next_elem.state = arc.nextstate;
+            next_elem.weight = Times(elem.weight, arc.weight);
+            if (arc.olabel == 0) // output epsilon
+              next_elem.string = elem.string;
+            else
+              next_elem.string = repository_.Successor(elem.string, arc.olabel);
+            all_elems.push_back(this_pr);
+          }
+        }
+      }
+    }
+    PairComparator pc;
+    std::sort(all_elems.begin(), all_elems.end(), pc);
+    // now sorted first on input label, then on state.
+    typedef typename vector<pair<Label, Element> >::const_iterator PairIter;
+    PairIter cur = all_elems.begin(), end = all_elems.end();
+    while (cur != end) {
+      // The old code (non-pruned) called ProcessTransition; here, instead,
+      // we'll put the calls into a priority queue.
+      Task *task = new Task;
+      // Process ranges that share the same input symbol.
+      Label ilabel = cur->first;
+      task->state = output_state_id;
+      task->priority_cost = std::numeric_limits<double>::infinity();
+      task->label = ilabel;
+      while (cur != end && cur->first == ilabel) {
+        task->subset.push_back(cur->second);
+        const Element &element = cur->second;
+        // Note: we'll later include the term "forward_cost" in the
+        // priority_cost.
+        task->priority_cost = std::min(task->priority_cost,
+                                       ConvertToCost(element.weight) +
+                                       backward_costs_[element.state]);
+        cur++;
+      }
+
+      // After the command below, the "priority_cost" is a value comparable to
+      // the total-weight of the input FST, like a total-path weight... of
+      // course, it will typically be less (in the semiring) than that.
+      // note: we represent it just as a double.
+      task->priority_cost += output_states_[output_state_id]->forward_cost;
+
+      if (task->priority_cost > cutoff_) {
+        // This task would never get done as it's past the pruning cutoff.
+        delete task;
+      } else {
+        MakeSubsetUnique(&(task->subset)); // remove duplicate Elements with the same state.
+        queue_.push(task); // Push the task onto the queue.  The queue keeps it
+        // in prioritized order, so we always process the one with the "best"
+        // weight (highest in the semiring).
+
+        { // this is a check.
+          double best_cost = backward_costs_[ifst_->Start()],
+              tolerance = 0.01 + 1.0e-04 * std::abs(best_cost);
+          if (task->priority_cost < best_cost - tolerance) {
+            KALDI_WARN << "Cost below best cost was encountered:"
+                       << task->priority_cost << " < " << best_cost;
+          }
+        }
+      }
+    }
+    all_elems.clear(); // as it's a reference to a class variable; we want it to stay
+    // empty.
+  }
+
+
+  bool IsIsymbolOrFinal(InputStateId state) { // returns true if this state
+    // of the input FST either is final or has an osymbol on an arc out of it.
+    // Uses the vector isymbol_or_final_ as a cache for this info.
+    KALDI_ASSERT(state >= 0);
+    if (isymbol_or_final_.size() <= state)
+      isymbol_or_final_.resize(state+1, static_cast<char>(OSF_UNKNOWN));
+    if (isymbol_or_final_[state] == static_cast<char>(OSF_NO))
+      return false;
+    else if (isymbol_or_final_[state] == static_cast<char>(OSF_YES))
+      return true;
+    // else work it out...
+    isymbol_or_final_[state] = static_cast<char>(OSF_NO);
+    if (ifst_->Final(state) != Weight::Zero())
+      isymbol_or_final_[state] = static_cast<char>(OSF_YES);
+    for (ArcIterator<ExpandedFst<Arc> > aiter(*ifst_, state);
+         !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      if (arc.ilabel != 0 && arc.weight != Weight::Zero()) {
+        isymbol_or_final_[state] = static_cast<char>(OSF_YES);
+        return true;
+      }
+    }
+    return IsIsymbolOrFinal(state); // will only recurse once.
+  }
+
+  void ComputeBackwardWeight() {
+    // Sets up the backward_costs_ array, and the cutoff_ variable.
+    KALDI_ASSERT(beam_ > 0);
+
+    // Only handle the toplogically sorted case.
+    backward_costs_.resize(ifst_->NumStates());
+    for (StateId s = ifst_->NumStates() - 1; s >= 0; s--) {
+      double &cost = backward_costs_[s];
+      cost = ConvertToCost(ifst_->Final(s));
+      for (ArcIterator<ExpandedFst<Arc> > aiter(*ifst_, s);
+           !aiter.Done(); aiter.Next()) {
+        const Arc &arc = aiter.Value();
+        cost = std::min(cost,
+                        ConvertToCost(arc.weight) + backward_costs_[arc.nextstate]);
+      }
+    }
+
+    if (ifst_->Start() == kNoStateId) return; // we'll be returning
+    // an empty FST.
+
+    double best_cost = backward_costs_[ifst_->Start()];
+    if (best_cost == std::numeric_limits<double>::infinity())
+      KALDI_WARN << "Total weight of input lattice is zero.";
+    cutoff_ = best_cost + beam_;
+  }
+
+  void InitializeDeterminization() {
+    // We insist that the input lattice be topologically sorted.  This is not a
+    // fundamental limitation of the algorithm (which in principle should be
+    // applicable to even cyclic FSTs), but it helps us more efficiently
+    // compute the backward_costs_ array.  There may be some other reason we
+    // require this, that escapes me at the moment.
+    KALDI_ASSERT(ifst_->Properties(kTopSorted, true) != 0);
+    ComputeBackwardWeight();
+#if !(__GNUC__ == 4 && __GNUC_MINOR__ == 0)
+    if(ifst_->Properties(kExpanded, false) != 0) { // if we know the number of
+      // states in ifst_, it might be a bit more efficient
+      // to pre-size the hashes so we're not constantly rebuilding them.
+      StateId num_states =
+          down_cast<const ExpandedFst<Arc>*, const Fst<Arc> >(ifst_)->NumStates();
+      minimal_hash_.rehash(num_states/2 + 3);
+      initial_hash_.rehash(num_states/2 + 3);
+    }
+#endif
+    InputStateId start_id = ifst_->Start();
+    if (start_id != kNoStateId) {
+      /* Create determinized-state corresponding to the start state....
+         Unlike all the other states, we don't "normalize" the representation
+         of this determinized-state before we put it into minimal_hash_.  This is actually
+         what we want, as otherwise we'd have problems dealing with any extra weight
+         and string and might have to create a "super-initial" state which would make
+         the output nondeterministic.  Normalization is only needed to make the
+         determinized output more minimal anyway, it's not needed for correctness.
+         Note, we don't put anything in the initial_hash_.  The initial_hash_ is only
+         a lookaside buffer anyway, so this isn't a problem-- it will get populated
+         later if it needs to be.
+      */
+      vector<Element> subset(1);
+      subset[0].state = start_id;
+      subset[0].weight = Weight::One();
+      subset[0].string = repository_.EmptyString();  // Id of empty sequence.
+      EpsilonClosure(&subset); // follow through epsilon-input links
+      ConvertToMinimal(&subset); // remove all but final states and
+      // states with input-labels on arcs out of them.
+      // Weight::One() is the "forward-weight" of this determinized state...
+      // i.e. the minimal cost from the start of the determinized FST to this
+      // state [One() because it's the start state].
+      OutputState *initial_state = new OutputState(subset, 0);
+      KALDI_ASSERT(output_states_.empty());
+      output_states_.push_back(initial_state);
+      num_elems_ += subset.size();
+      OutputStateId initial_state_id = 0;
+      minimal_hash_[&(initial_state->minimal_subset)] = initial_state_id;
+      ProcessFinal(initial_state_id);
+      ProcessTransitions(initial_state_id); // this will add tasks to
+      // the queue, which we'll start processing in Determinize().
+    }
+  }
+
+  KALDI_DISALLOW_COPY_AND_ASSIGN(LatticeDeterminizerPruned);
+
+  struct OutputState {
+    vector<Element> minimal_subset;
+    vector<TempArc> arcs; // arcs out of the state-- those that have been processed.
+    // Note: the final-weight is included here with kNoStateId as the state id.  We
+    // always process the final-weight regardless of the beam; when producing the
+    // output we may have to ignore some of these.
+    double forward_cost; // Represents minimal cost from start-state
+    // to this state.  Used in prioritization of tasks, and pruning.
+    // Note: we know this minimal cost from when we first create the OutputState;
+    // this is because of the priority-queue we use, that ensures that the
+    // "best" path into the state will be expanded first.
+    OutputState(const vector<Element> &minimal_subset,
+                double forward_cost): minimal_subset(minimal_subset),
+                                      forward_cost(forward_cost) { }
+  };
+
+  vector<OutputState*> output_states_; // All the info about the output states.
+
+  int num_arcs_; // keep track of memory usage: number of arcs in output_states_[ ]->arcs
+  int num_elems_; // keep track of memory usage: number of elems in output_states_ and
+  // the keys of initial_hash_
+
+  const ExpandedFst<Arc> *ifst_;
+  std::vector<double> backward_costs_; // This vector stores, for every state in ifst_,
+  // the minimal cost to the end-state (i.e. the sum of weights; they are guaranteed to
+  // have "take-the-minimum" semantics).  We get the double from the ConvertToCost()
+  // function on the lattice weights.
+
+  double beam_;
+  double cutoff_; // beam plus total-weight of input (and note, the weight is
+  // guaranteed to be "tropical-like" so the sum does represent a min-cost.
+
+  DeterminizeLatticePrunedOptions opts_;
+  SubsetKey hasher_;  // object that computes keys-- has no data members.
+  SubsetEqual equal_;  // object that compares subsets-- only data member is delta_.
+  bool determinized_; // set to true when user called Determinize(); used to make
+  // sure this object is used correctly.
+  MinimalSubsetHash minimal_hash_;  // hash from Subset to OutputStateId.  Subset is "minimal
+                                    // representation" (only include final and states and states with
+                                    // nonzero ilabel on arc out of them.  Owns the pointers
+                                    // in its keys.
+  InitialSubsetHash initial_hash_;   // hash from Subset to Element, which
+                                     // represents the OutputStateId together
+                                     // with an extra weight and string.  Subset
+                                     // is "initial representation".  The extra
+                                     // weight and string is needed because after
+                                     // we convert to minimal representation and
+                                     // normalize, there may be an extra weight
+                                     // and string.  Owns the pointers
+                                     // in its keys.
+
+  struct Task {
+    OutputStateId state; // State from which we're processing the transition.
+    Label label; // Label on the transition we're processing out of this state.
+    vector<Element> subset; // Weighted subset of states (with strings)-- not normalized.
+    double priority_cost; // Cost used in deciding priority of tasks.  Note:
+    // we assume there is a ConvertToCost() function that converts the semiring to double.
+  };
+
+  struct TaskCompare {
+    inline int operator() (const Task *t1, const Task *t2) {
+      // view this like operator <, which is the default template parameter
+      // to std::priority_queue.
+      // returns true if t1 is worse than t2.
+      return (t1->priority_cost > t2->priority_cost);
+    }
+  };
+
+  // This priority queue contains "Task"s to be processed; these correspond
+  // to transitions out of determinized states.  We process these in priority
+  // order according to the best weight of any path passing through these
+  // determinized states... it's possible to work this out.
+  std::priority_queue<Task*, vector<Task*>, TaskCompare> queue_;
+
+  vector<pair<Label, Element> > all_elems_tmp_; // temporary vector used in ProcessTransitions.
+
+  enum IsymbolOrFinal { OSF_UNKNOWN = 0, OSF_NO = 1, OSF_YES = 2 };
+
+  vector<char> isymbol_or_final_; // A kind of cache; it says whether
+  // each state is (emitting or final) where emitting means it has at least one
+  // non-epsilon output arc.  Only accessed by IsIsymbolOrFinal()
+
+  LatticeStringRepository<IntType> repository_;  // defines a compact and fast way of
+  // storing sequences of labels.
+
+  void AddStrings(const vector<Element> &vec,
+                  vector<StringId> *needed_strings) {
+    for (typename std::vector<Element>::const_iterator iter = vec.begin();
+         iter != vec.end(); ++iter)
+      needed_strings->push_back(iter->string);
+  }
+};
+
+
+// normally Weight would be LatticeWeight<float> (which has two floats),
+// or possibly TropicalWeightTpl<float>, and IntType would be int32.
+// Caution: there are two versions of the function DeterminizeLatticePruned,
+// with identical code but different output FST types.
+template<class Weight, class IntType>
+bool DeterminizeLatticePruned(
+    const ExpandedFst<ArcTpl<Weight> >&ifst,
+    double beam,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > >*ofst,
+    DeterminizeLatticePrunedOptions opts) {
+  ofst->SetInputSymbols(ifst.InputSymbols());
+  ofst->SetOutputSymbols(ifst.OutputSymbols());
+  if (ifst.NumStates() == 0) {
+    ofst->DeleteStates();
+    return true;
+  }
+  KALDI_ASSERT(opts.retry_cutoff >= 0.0 && opts.retry_cutoff < 1.0);
+  int32 max_num_iters = 10;  // avoid the potential for infinite loops if
+                             // retrying.
+  VectorFst<ArcTpl<Weight> > temp_fst;
+
+  for (int32 iter = 0; iter < max_num_iters; iter++) {
+    LatticeDeterminizerPruned<Weight, IntType> det(iter == 0 ? ifst : temp_fst,
+                                                   beam, opts);
+    double effective_beam;
+    bool ans = det.Determinize(&effective_beam);
+    // if it returns false it will typically still produce reasonable output,
+    // just with a narrower beam than "beam".  If the user specifies an infinite
+    // beam we don't do this beam-narrowing.
+    if (effective_beam >= beam * opts.retry_cutoff ||
+        beam == std::numeric_limits<double>::infinity() ||
+        iter + 1 == max_num_iters) {
+      det.Output(ofst);
+      return ans;
+    } else {
+      // The code below to set "beam" is a heuristic.
+      // If effective_beam is very small, we want to reduce by a lot.
+      // But never change the beam by more than a factor of two.
+      if (effective_beam < 0.0) effective_beam = 0.0;
+      double new_beam = beam * sqrt(effective_beam / beam);
+      if (new_beam < 0.5 * beam) new_beam = 0.5 * beam;
+      beam = new_beam;
+      if (iter == 0) temp_fst = ifst;
+      kaldi::PruneLattice(beam, &temp_fst);
+      KALDI_LOG << "Pruned state-level lattice with beam " << beam
+                << " and retrying determinization with that beam.";
+    }
+  }
+  return false; // Suppress compiler warning; this code is unreachable.
+}
+
+
+// normally Weight would be LatticeWeight<float> (which has two floats),
+// or possibly TropicalWeightTpl<float>, and IntType would be int32.
+// Caution: there are two versions of the function DeterminizeLatticePruned,
+// with identical code but different output FST types.
+template<class Weight>
+bool DeterminizeLatticePruned(const ExpandedFst<ArcTpl<Weight> > &ifst,
+                              double beam,
+                              MutableFst<ArcTpl<Weight> > *ofst,
+                              DeterminizeLatticePrunedOptions opts) {
+  typedef int32 IntType;
+  ofst->SetInputSymbols(ifst.InputSymbols());
+  ofst->SetOutputSymbols(ifst.OutputSymbols());
+  KALDI_ASSERT(opts.retry_cutoff >= 0.0 && opts.retry_cutoff < 1.0);
+  if (ifst.NumStates() == 0) {
+    ofst->DeleteStates();
+    return true;
+  }
+  int32 max_num_iters = 10;  // avoid the potential for infinite loops if
+                             // retrying.
+  VectorFst<ArcTpl<Weight> > temp_fst;
+
+  for (int32 iter = 0; iter < max_num_iters; iter++) {
+    LatticeDeterminizerPruned<Weight, IntType> det(iter == 0 ? ifst : temp_fst,
+                                                   beam, opts);
+    double effective_beam;
+    bool ans = det.Determinize(&effective_beam);
+    // if it returns false it will typically still
+    // produce reasonable output, just with a
+    // narrower beam than "beam".
+    if (effective_beam >= beam * opts.retry_cutoff ||
+        iter + 1 == max_num_iters) {
+      det.Output(ofst);
+      return ans;
+    } else {
+      // The code below to set "beam" is a heuristic.
+      // If effective_beam is very small, we want to reduce by a lot.
+      // But never change the beam by more than a factor of two.
+      if (effective_beam < 0)
+        effective_beam = 0;
+      double new_beam = beam * sqrt(effective_beam / beam);
+      if (new_beam < 0.5 * beam) new_beam = 0.5 * beam;
+      KALDI_WARN << "Effective beam " << effective_beam << " was less than beam "
+                 << beam << " * cutoff " << opts.retry_cutoff << ", pruning raw "
+                 << "lattice with new beam " << new_beam << " and retrying.";
+      beam = new_beam;
+      if (iter == 0) temp_fst = ifst;
+      kaldi::PruneLattice(beam, &temp_fst);
+    }
+  }
+  return false; // Suppress compiler warning; this code is unreachable.
+}
+
+template<class Weight>
+typename ArcTpl<Weight>::Label DeterminizeLatticeInsertPhones(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<ArcTpl<Weight> > *fst) {
+  // Define some types.
+  typedef ArcTpl<Weight> Arc;
+  typedef typename Arc::StateId StateId;
+  typedef typename Arc::Label Label;
+
+  // Work out the first phone symbol. This is more related to the phone
+  // insertion function, so we put it here and make it the returning value of
+  // DeterminizeLatticeInsertPhones().
+  Label first_phone_label = HighestNumberedInputSymbol(*fst) + 1;
+
+  // Insert phones here.
+  for (StateIterator<MutableFst<Arc> > siter(*fst);
+       !siter.Done(); siter.Next()) {
+    StateId state = siter.Value();
+    if (state == fst->Start())
+      continue;
+    for (MutableArcIterator<MutableFst<Arc> > aiter(fst, state);
+         !aiter.Done(); aiter.Next()) {
+      Arc arc = aiter.Value();
+
+      // Note: the words are on the input symbol side and transition-id's are on
+      // the output symbol side.
+      if ((arc.olabel != 0)
+          && (trans_model.TransitionIdIsStartOfPhone(arc.olabel))
+          && (!trans_model.IsSelfLoop(arc.olabel))) {
+        Label phone =
+            static_cast<Label>(trans_model.TransitionIdToPhone(arc.olabel));
+
+        // Skips <eps>.
+        KALDI_ASSERT(phone != 0);
+
+        if (arc.ilabel == 0) {
+          // If there is no word on the arc, insert the phone directly.
+          arc.ilabel = first_phone_label + phone;
+        } else {
+          // Otherwise, add an additional arc.
+          StateId additional_state = fst->AddState();
+          StateId next_state = arc.nextstate;
+          arc.nextstate = additional_state;
+          fst->AddArc(additional_state,
+                      Arc(first_phone_label + phone, 0,
+                          Weight::One(), next_state));
+        }
+      }
+
+      aiter.SetValue(arc);
+    }
+  }
+
+  return first_phone_label;
+}
+
+template<class Weight>
+void DeterminizeLatticeDeletePhones(
+    typename ArcTpl<Weight>::Label first_phone_label,
+    MutableFst<ArcTpl<Weight> > *fst) {
+  // Define some types.
+  typedef ArcTpl<Weight> Arc;
+  typedef typename Arc::StateId StateId;
+  typedef typename Arc::Label Label;
+
+  // Delete phones here.
+  for (StateIterator<MutableFst<Arc> > siter(*fst);
+       !siter.Done(); siter.Next()) {
+    StateId state = siter.Value();
+    for (MutableArcIterator<MutableFst<Arc> > aiter(fst, state);
+         !aiter.Done(); aiter.Next()) {
+      Arc arc = aiter.Value();
+
+      if (arc.ilabel >= first_phone_label)
+        arc.ilabel = 0;
+
+      aiter.SetValue(arc);
+    }
+  }
+}
+// instantiate for type LatticeWeight
+template
+void DeterminizeLatticeDeletePhones(
+    ArcTpl<kaldi::LatticeWeight>::Label first_phone_label,
+    MutableFst<ArcTpl<kaldi::LatticeWeight> > *fst);
+
+/** This function does a first pass determinization with phone symbols inserted
+    at phone boundary. It uses a transition model to work out the transition-id
+    to phone map. First, phones will be inserted into the word level lattice.
+    Second, determinization will be applied on top of the phone + word lattice.
+    Finally, the inserted phones will be removed, converting the lattice back to
+    a word level lattice. The output lattice of this pass is not deterministic,
+    since we remove the phone symbols as a last step. It is supposed to be
+    followed by another pass of determinization at the word level. It could also
+    be useful for some other applications such as fMLLR estimation, confidence
+    estimation, discriminative training, etc.
+*/
+template<class Weight, class IntType>
+bool DeterminizeLatticePhonePrunedFirstPass(
+    const kaldi::TransitionInformation &trans_model,
+    double beam,
+    MutableFst<ArcTpl<Weight> > *fst,
+    const DeterminizeLatticePrunedOptions &opts) {
+  // First, insert the phones.
+  typename ArcTpl<Weight>::Label first_phone_label =
+      DeterminizeLatticeInsertPhones(trans_model, fst);
+  TopSort(fst);
+
+  // Second, do determinization with phone inserted.
+  bool ans = DeterminizeLatticePruned<Weight>(*fst, beam, fst, opts);
+
+  // Finally, remove the inserted phones.
+  DeterminizeLatticeDeletePhones(first_phone_label, fst);
+  TopSort(fst);
+
+  return ans;
+}
+
+// "Destructive" version of DeterminizeLatticePhonePruned() where the input
+// lattice might be modified.
+template<class Weight, class IntType>
+bool DeterminizeLatticePhonePruned(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<ArcTpl<Weight> > *ifst,
+    double beam,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
+    DeterminizeLatticePhonePrunedOptions opts) {
+  // Returning status.
+  bool ans = true;
+
+  // Make sure at least one of opts.phone_determinize and opts.word_determinize
+  // is not false, otherwise calling this function doesn't make any sense.
+  if ((opts.phone_determinize || opts.word_determinize) == false) {
+    KALDI_WARN << "Both --phone-determinize and --word-determinize are set to "
+               << "false, copying lattice without determinization.";
+    // We are expecting the words on the input side.
+    ConvertLattice<Weight, IntType>(*ifst, ofst, false);
+    return ans;
+  }
+
+  // Determinization options.
+  DeterminizeLatticePrunedOptions det_opts;
+  det_opts.delta = opts.delta;
+  det_opts.max_mem = opts.max_mem;
+
+  // If --phone-determinize is true, do the determinization on phone + word
+  // lattices.
+  if (opts.phone_determinize) {
+    KALDI_VLOG(3) << "Doing first pass of determinization on phone + word "
+                  << "lattices.";
+    ans = DeterminizeLatticePhonePrunedFirstPass<Weight, IntType>(
+        trans_model, beam, ifst, det_opts) && ans;
+
+    // If --word-determinize is false, we've finished the job and return here.
+    if (!opts.word_determinize) {
+      // We are expecting the words on the input side.
+      ConvertLattice<Weight, IntType>(*ifst, ofst, false);
+      return ans;
+    }
+  }
+
+  // If --word-determinize is true, do the determinization on word lattices.
+  if (opts.word_determinize) {
+    KALDI_VLOG(3) << "Doing second pass of determinization on word lattices.";
+    ans = DeterminizeLatticePruned<Weight, IntType>(
+        *ifst, beam, ofst, det_opts) && ans;
+  }
+
+  // If --minimize is true, push and minimize after determinization.
+  if (opts.minimize) {
+    KALDI_VLOG(3) << "Pushing and minimizing on word lattices.";
+    ans = PushCompactLatticeStrings<Weight, IntType>(ofst) && ans;
+    ans = PushCompactLatticeWeights<Weight, IntType>(ofst) && ans;
+    ans = MinimizeCompactLattice<Weight, IntType>(ofst) && ans;
+  }
+
+  return ans;
+}
+
+// Normal verson of DeterminizeLatticePhonePruned(), where the input lattice
+// will be kept as unchanged.
+template<class Weight, class IntType>
+bool DeterminizeLatticePhonePruned(
+    const kaldi::TransitionInformation &trans_model,
+    const ExpandedFst<ArcTpl<Weight> > &ifst,
+    double beam,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
+    DeterminizeLatticePhonePrunedOptions opts) {
+  VectorFst<ArcTpl<Weight> > temp_fst(ifst);
+  return DeterminizeLatticePhonePruned(trans_model, &temp_fst,
+                                       beam, ofst, opts);
+}
+
+bool DeterminizeLatticePhonePrunedWrapper(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<kaldi::LatticeArc> *ifst,
+    double beam,
+    MutableFst<kaldi::CompactLatticeArc> *ofst,
+    DeterminizeLatticePhonePrunedOptions opts) {
+  bool ans = true;
+  Invert(ifst);
+  if (ifst->Properties(fst::kTopSorted, true) == 0) {
+    if (!TopSort(ifst)) {
+      // Cannot topologically sort the lattice -- determinization will fail.
+      KALDI_ERR << "Topological sorting of state-level lattice failed (probably"
+                << " your lexicon has empty words or your LM has epsilon cycles"
+                << ").";
+    }
+  }
+  ILabelCompare<kaldi::LatticeArc> ilabel_comp;
+  ArcSort(ifst, ilabel_comp);
+  ans = DeterminizeLatticePhonePruned<kaldi::LatticeWeight, kaldi::int32>(
+      trans_model, ifst, beam, ofst, opts);
+  Connect(ofst);
+  return ans;
+}
+
+// Instantiate the templates for the types we might need.
+// Note: there are actually four templates, each of which
+// we instantiate for a single type.
+template
+bool DeterminizeLatticePruned<kaldi::LatticeWeight>(
+    const ExpandedFst<kaldi::LatticeArc> &ifst,
+    double prune,
+    MutableFst<kaldi::CompactLatticeArc> *ofst,
+    DeterminizeLatticePrunedOptions opts);
+
+template
+bool DeterminizeLatticePruned<kaldi::LatticeWeight>(
+    const ExpandedFst<kaldi::LatticeArc> &ifst,
+    double prune,
+    MutableFst<kaldi::LatticeArc> *ofst,
+    DeterminizeLatticePrunedOptions opts);
+
+template
+bool DeterminizeLatticePhonePruned<kaldi::LatticeWeight, kaldi::int32>(
+    const kaldi::TransitionInformation &trans_model,
+    const ExpandedFst<kaldi::LatticeArc> &ifst,
+    double prune,
+    MutableFst<kaldi::CompactLatticeArc> *ofst,
+    DeterminizeLatticePhonePrunedOptions opts);
+
+template
+bool DeterminizeLatticePhonePruned<kaldi::LatticeWeight, kaldi::int32>(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<kaldi::LatticeArc> *ifst,
+    double prune,
+    MutableFst<kaldi::CompactLatticeArc> *ofst,
+    DeterminizeLatticePhonePrunedOptions opts);
+
+}

speechx/speechx/kaldi/lat/determinize-lattice-pruned.h

+// lat/determinize-lattice-pruned.h
+
+// Copyright 2009-2012  Microsoft Corporation
+//           2012-2013  Johns Hopkins University (Author: Daniel Povey)
+//                2014  Guoguo Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef KALDI_LAT_DETERMINIZE_LATTICE_PRUNED_H_
+#define KALDI_LAT_DETERMINIZE_LATTICE_PRUNED_H_
+#include <fst/fstlib.h>
+#include <fst/fst-decl.h>
+#include <algorithm>
+#include <map>
+#include <set>
+#include <vector>
+#include "fstext/lattice-weight.h"
+#include "itf/transition-information.h"
+#include "itf/options-itf.h"
+#include "lat/kaldi-lattice.h"
+
+namespace fst {
+
+/// \addtogroup fst_extensions
+///  @{
+
+
+// For example of usage, see test-determinize-lattice-pruned.cc
+
+/*
+   DeterminizeLatticePruned implements a special form of determinization with
+   epsilon removal, optimized for a phase of lattice generation.  This algorithm
+   also does pruning at the same time-- the combination is more efficient as it
+   somtimes prevents us from creating a lot of states that would later be pruned
+   away.  This allows us to increase the lattice-beam and not have the algorithm
+   blow up.  Also, because our algorithm processes states in order from those
+   that appear on high-scoring paths down to those that appear on low-scoring
+   paths, we can easily terminate the algorithm after a certain specified number
+   of states or arcs.
+
+   The input is an FST with weight-type BaseWeightType (usually a pair of floats,
+   with a lexicographical type of order, such as LatticeWeightTpl<float>).
+   Typically this would be a state-level lattice, with input symbols equal to
+   words, and output-symbols equal to p.d.f's (so like the inverse of HCLG).  Imagine representing this as an
+   acceptor of type CompactLatticeWeightTpl<float>, in which the input/output
+   symbols are words, and the weights contain the original weights together with
+   strings (with zero or one symbol in them) containing the original output labels
+   (the p.d.f.'s).  We determinize this using acceptor determinization with
+   epsilon removal.  Remember (from lattice-weight.h) that
+   CompactLatticeWeightTpl has a special kind of semiring where we always take
+   the string corresponding to the best cost (of type BaseWeightType), and
+   discard the other.  This corresponds to taking the best output-label sequence
+   (of p.d.f.'s) for each input-label sequence (of words).  We couldn't use the
+   Gallic weight for this, or it would die as soon as it detected that the input
+   FST was non-functional.  In our case, any acyclic FST (and many cyclic ones)
+   can be determinized.
+   We assume that there is a function
+      Compare(const BaseWeightType &a, const BaseWeightType &b)
+   that returns (-1, 0, 1) according to whether (a < b, a == b, a > b) in the
+   total order on the BaseWeightType... this information should be the
+   same as NaturalLess would give, but it's more efficient to do it this way.
+   You can define this for things like TropicalWeight if you need to instantiate
+   this class for that weight type.
+
+   We implement this determinization in a special way to make it efficient for
+   the types of FSTs that we will apply it to.  One issue is that if we
+   explicitly represent the strings (in CompactLatticeWeightTpl) as vectors of
+   type vector<IntType>, the algorithm takes time quadratic in the length of
+   words (in states), because propagating each arc involves copying a whole
+   vector (of integers representing p.d.f.'s).  Instead we use a hash structure
+   where each string is a pointer (Entry*), and uses a hash from (Entry*,
+   IntType), to the successor string (and a way to get the latest IntType and the
+   ancestor Entry*).  [this is the class LatticeStringRepository].
+
+   Another issue is that rather than representing a determinized-state as a
+   collection of (state, weight), we represent it in a couple of reduced forms.
+   Suppose a determinized-state is a collection of (state, weight) pairs; call
+   this the "canonical representation".  Note: these collections are always
+   normalized to remove any common weight and string part.  Define end-states as
+   the subset of states that have an arc out of them with a label on, or are
+   final.  If we represent a determinized-state a the set of just its (end-state,
+   weight) pairs, this will be a valid and more compact representation, and will
+   lead to a smaller set of determinized states (like early minimization).  Call
+   this collection of (end-state, weight) pairs the "minimal representation".  As
+   a mechanism to reduce compute, we can also consider another representation.
+   In the determinization algorithm, we start off with a set of (begin-state,
+   weight) pairs (where the "begin-states" are initial or have a label on the
+   transition into them), and the "canonical representation" consists of the
+   epsilon-closure of this set (i.e. follow epsilons).  Call this set of
+   (begin-state, weight) pairs, appropriately normalized, the "initial
+   representation".  If two initial representations are the same, the "canonical
+   representation" and hence the "minimal representation" will be the same.  We
+   can use this to reduce compute.  Note that if two initial representations are
+   different, this does not preclude the other representations from being the same.
+
+*/
+
+
+struct DeterminizeLatticePrunedOptions {
+  float delta; // A small offset used to measure equality of weights.
+  int max_mem; // If >0, determinization will fail and return false
+  // when the algorithm's (approximate) memory consumption crosses this threshold.
+  int max_loop; // If >0, can be used to detect non-determinizable input
+  // (a case that wouldn't be caught by max_mem).
+  int max_states;
+  int max_arcs;
+  float retry_cutoff;
+  DeterminizeLatticePrunedOptions(): delta(kDelta),
+                                     max_mem(-1),
+                                     max_loop(-1),
+                                     max_states(-1),
+                                     max_arcs(-1),
+                                     retry_cutoff(0.5) { }
+  void Register (kaldi::OptionsItf *opts) {
+    opts->Register("delta", &delta, "Tolerance used in determinization");
+    opts->Register("max-mem", &max_mem, "Maximum approximate memory usage in "
+                   "determinization (real usage might be many times this)");
+    opts->Register("max-arcs", &max_arcs, "Maximum number of arcs in "
+                   "output FST (total, not per state");
+    opts->Register("max-states", &max_states, "Maximum number of arcs in output "
+                   "FST (total, not per state");
+    opts->Register("max-loop", &max_loop, "Option used to detect a particular "
+                   "type of determinization failure, typically due to invalid input "
+                   "(e.g., negative-cost loops)");
+    opts->Register("retry-cutoff", &retry_cutoff, "Controls pruning un-determinized "
+                   "lattice and retrying determinization: if effective-beam < "
+                   "retry-cutoff * beam, we prune the raw lattice and retry.  Avoids "
+                   "ever getting empty output for long segments.");
+  }
+};
+
+struct DeterminizeLatticePhonePrunedOptions {
+  // delta: a small offset used to measure equality of weights.
+  float delta;
+  // max_mem: if > 0, determinization will fail and return false when the
+  // algorithm's (approximate) memory consumption crosses this threshold.
+  int max_mem;
+  // phone_determinize: if true, do a first pass determinization on both phones
+  // and words.
+  bool phone_determinize;
+  // word_determinize: if true, do a second pass determinization on words only.
+  bool word_determinize;
+  // minimize: if true, push and minimize after determinization.
+  bool minimize;
+  DeterminizeLatticePhonePrunedOptions(): delta(kDelta),
+                                          max_mem(50000000),
+                                          phone_determinize(true),
+                                          word_determinize(true),
+                                          minimize(false) {}
+  void Register (kaldi::OptionsItf *opts) {
+    opts->Register("delta", &delta, "Tolerance used in determinization");
+    opts->Register("max-mem", &max_mem, "Maximum approximate memory usage in "
+                   "determinization (real usage might be many times this).");
+    opts->Register("phone-determinize", &phone_determinize, "If true, do an "
+                   "initial pass of determinization on both phones and words (see"
+                   " also --word-determinize)");
+    opts->Register("word-determinize", &word_determinize, "If true, do a second "
+                   "pass of determinization on words only (see also "
+                   "--phone-determinize)");
+    opts->Register("minimize", &minimize, "If true, push and minimize after "
+                   "determinization.");
+  }
+};
+
+/**
+    This function implements the normal version of DeterminizeLattice, in which the
+    output strings are represented using sequences of arcs, where all but the
+    first one has an epsilon on the input side.  It also prunes using the beam
+    in the "prune" parameter.  The input FST must be topologically sorted in order
+    for the algorithm to work. For efficiency it is recommended to sort ilabel as well.
+    Returns true on success, and false if it had to terminate the determinization
+    earlier than specified by the "prune" beam-- that is, if it terminated because
+    of the max_mem, max_loop or max_arcs constraints in the options.
+    CAUTION: you may want to use the version below which outputs to CompactLattice.
+*/
+template<class Weight>
+bool DeterminizeLatticePruned(
+    const ExpandedFst<ArcTpl<Weight> > &ifst,
+    double prune,
+    MutableFst<ArcTpl<Weight> > *ofst,
+    DeterminizeLatticePrunedOptions opts = DeterminizeLatticePrunedOptions());
+
+
+/*  This is a version of DeterminizeLattice with a slightly more "natural" output format,
+    where the output sequences are encoded using the CompactLatticeArcTpl template
+    (i.e. the sequences of output symbols are represented directly as strings The input
+    FST must be topologically sorted in order for the algorithm to work. For efficiency
+    it is recommended to sort the ilabel for the input FST as well.
+    Returns true on normal success, and false if it had to terminate the determinization
+    earlier than specified by the "prune" beam-- that is, if it terminated because
+    of the max_mem, max_loop or max_arcs constraints in the options.
+    CAUTION: if Lattice is the input, you need to Invert() before calling this,
+    so words are on the input side.
+*/
+template<class Weight, class IntType>
+bool DeterminizeLatticePruned(
+    const ExpandedFst<ArcTpl<Weight> >&ifst,
+    double prune,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
+    DeterminizeLatticePrunedOptions opts = DeterminizeLatticePrunedOptions());
+
+/** This function takes in lattices and inserts phones at phone boundaries. It
+    uses the transition model to work out the transition_id to phone map. The
+    returning value is the starting index of the phone label. Typically we pick
+    (maximum_output_label_index + 1) as this value. The inserted phones are then
+    mapped to (returning_value + original_phone_label) in the new lattice. The
+    returning value will be used by DeterminizeLatticeDeletePhones() where it
+    works out the phones according to this value.
+*/
+template<class Weight>
+typename ArcTpl<Weight>::Label DeterminizeLatticeInsertPhones(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<ArcTpl<Weight> > *fst);
+
+/** This function takes in lattices and deletes "phones" from them. The "phones"
+    here are actually any label that is larger than first_phone_label because
+    when we insert phones into the lattice, we map the original phone label to
+    (first_phone_label + original_phone_label). It is supposed to be used
+    together with DeterminizeLatticeInsertPhones()
+*/
+template<class Weight>
+void DeterminizeLatticeDeletePhones(
+    typename ArcTpl<Weight>::Label first_phone_label,
+    MutableFst<ArcTpl<Weight> > *fst);
+
+/** This function is a wrapper of DeterminizeLatticePhonePrunedFirstPass() and
+    DeterminizeLatticePruned(). If --phone-determinize is set to true, it first
+    calls DeterminizeLatticePhonePrunedFirstPass() to do the initial pass of
+    determinization on the phone + word lattices. If --word-determinize is set
+    true, it then does a second pass of determinization on the word lattices by
+    calling DeterminizeLatticePruned(). If both are set to false, then it gives
+    a warning and copying the lattices without determinization.
+
+    Note: the point of doing first a phone-level determinization pass and then
+    a word-level determinization pass is that it allows us to determinize
+    deeper lattices without "failing early" and returning a too-small lattice
+    due to the max-mem constraint.  The result should be the same as word-level
+    determinization in general, but for deeper lattices it is a bit faster,
+    despite the fact that we now have two passes of determinization by default.
+*/
+template<class Weight, class IntType>
+bool DeterminizeLatticePhonePruned(
+    const kaldi::TransitionInformation &trans_model,
+    const ExpandedFst<ArcTpl<Weight> > &ifst,
+    double prune,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
+    DeterminizeLatticePhonePrunedOptions opts
+      = DeterminizeLatticePhonePrunedOptions());
+
+/** "Destructive" version of DeterminizeLatticePhonePruned() where the input
+    lattice might be changed.
+*/
+template<class Weight, class IntType>
+bool DeterminizeLatticePhonePruned(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<ArcTpl<Weight> > *ifst,
+    double prune,
+    MutableFst<ArcTpl<CompactLatticeWeightTpl<Weight, IntType> > > *ofst,
+    DeterminizeLatticePhonePrunedOptions opts
+      = DeterminizeLatticePhonePrunedOptions());
+
+/** This function is a wrapper of DeterminizeLatticePhonePruned() that works for
+    Lattice type FSTs.  It simplifies the calling process by calling
+    TopSort() Invert() and ArcSort() for you.
+    Unlike other determinization routines, the function
+    requires "ifst" to have transition-id's on the input side and words on the
+    output side.
+    This function can be used as the top-level interface to all the determinization
+    code.
+*/
+bool DeterminizeLatticePhonePrunedWrapper(
+    const kaldi::TransitionInformation &trans_model,
+    MutableFst<kaldi::LatticeArc> *ifst,
+    double prune,
+    MutableFst<kaldi::CompactLatticeArc> *ofst,
+    DeterminizeLatticePhonePrunedOptions opts
+      = DeterminizeLatticePhonePrunedOptions());
+
+/// @} end "addtogroup fst_extensions"
+
+} // end namespace fst
+
+#endif

speechx/speechx/kaldi/lat/kaldi-lattice.cc

+// lat/kaldi-lattice.cc
+
+// Copyright 2009-2011     Microsoft Corporation
+//                2013     Johns Hopkins University (author: Daniel Povey)
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+
+#include "lat/kaldi-lattice.h"
+#include "fst/script/print-impl.h"
+
+namespace kaldi {
+
+/// Converts lattice types if necessary, deleting its input.
+template<class OrigWeightType>
+CompactLattice* ConvertToCompactLattice(fst::VectorFst<OrigWeightType> *ifst) {
+  if (!ifst) return NULL;
+  CompactLattice *ofst = new CompactLattice();
+  ConvertLattice(*ifst, ofst);
+  delete ifst;
+  return ofst;
+}
+
+// This overrides the template if there is no type conversion going on
+// (for efficiency).
+template<>
+CompactLattice* ConvertToCompactLattice(CompactLattice *ifst) {
+  return ifst;
+}
+
+/// Converts lattice types if necessary, deleting its input.
+template<class OrigWeightType>
+Lattice* ConvertToLattice(fst::VectorFst<OrigWeightType> *ifst) {
+  if (!ifst) return NULL;
+  Lattice *ofst = new Lattice();
+  ConvertLattice(*ifst, ofst);
+  delete ifst;
+  return ofst;
+}
+
+// This overrides the template if there is no type conversion going on
+// (for efficiency).
+template<>
+Lattice* ConvertToLattice(Lattice *ifst) {
+  return ifst;
+}
+
+
+bool WriteCompactLattice(std::ostream &os, bool binary,
+                         const CompactLattice &t) {
+  if (binary) {
+    fst::FstWriteOptions opts;
+    // Leave all the options default.  Normally these lattices wouldn't have any
+    // osymbols/isymbols so no point directing it not to write them (who knows what
+    // we'd want to if we had them).
+    return t.Write(os, opts);
+  } else {
+    // Text-mode output.  Note: we expect that t.InputSymbols() and
+    // t.OutputSymbols() would always return NULL.  The corresponding input
+    // routine would not work if the FST actually had symbols attached.
+    // Write a newline after the key, so the first line of the FST appears
+    // on its own line.
+    os << '\n';
+    bool acceptor = true, write_one = false;
+    fst::FstPrinter<CompactLatticeArc> printer(t, t.InputSymbols(),
+                                               t.OutputSymbols(),
+                                               NULL, acceptor, write_one, "\t");
+    printer.Print(&os, "<unknown>");
+    if (os.fail())
+      KALDI_WARN << "Stream failure detected.";
+    // Write another newline as a terminating character.  The read routine will
+    // detect this [this is a Kaldi mechanism, not somethig in the original
+    // OpenFst code].
+    os << '\n';
+    return os.good();
+  }
+}
+
+/// LatticeReader provides (static) functions for reading both Lattice
+/// and CompactLattice, in text form.
+class LatticeReader {
+  typedef LatticeArc Arc;
+  typedef LatticeWeight Weight;
+  typedef CompactLatticeArc CArc;
+  typedef CompactLatticeWeight CWeight;
+  typedef Arc::Label Label;
+  typedef Arc::StateId StateId;
+ public:
+  // everything is static in this class.
+
+  /** This function reads from the FST text format; it does not know in advance
+      whether it's a Lattice or CompactLattice in the stream so it tries to
+      read both formats until it becomes clear which is the correct one.
+  */
+  static std::pair<Lattice*, CompactLattice*> ReadText(
+      std::istream &is) {
+    typedef std::pair<Lattice*, CompactLattice*> PairT;
+    using std::string;
+    using std::vector;
+    Lattice *fst = new Lattice();
+    CompactLattice *cfst = new CompactLattice();
+    string line;
+    size_t nline = 0;
+    string separator = FLAGS_fst_field_separator + "\r\n";
+    while (std::getline(is, line)) {
+      nline++;
+      vector<string> col;
+      // on Windows we'll write in text and read in binary mode.
+      SplitStringToVector(line, separator.c_str(), true, &col);
+      if (col.size() == 0) break; // Empty line is a signal to stop, in our
+      // archive format.
+      if (col.size() > 5) {
+        KALDI_WARN << "Reading lattice: bad line in FST: " << line;
+        delete fst;
+        delete cfst;
+        return PairT(static_cast<Lattice*>(NULL),
+                     static_cast<CompactLattice*>(NULL));
+      }
+      StateId s;
+      if (!ConvertStringToInteger(col[0], &s)) {
+        KALDI_WARN << "FstCompiler: bad line in FST: " << line;
+        delete fst;
+        delete cfst;
+        return PairT(static_cast<Lattice*>(NULL),
+                     static_cast<CompactLattice*>(NULL));
+      }
+      if (fst)
+        while (s >= fst->NumStates())
+          fst->AddState();
+      if (cfst)
+        while (s >= cfst->NumStates())
+          cfst->AddState();
+      if (nline == 1) {
+        if (fst) fst->SetStart(s);
+        if (cfst) cfst->SetStart(s);
+      }
+
+      if (fst) { // we still have fst; try to read that arc.
+        bool ok = true;
+        Arc arc;
+        Weight w;
+        StateId d = s;
+        switch (col.size()) {
+          case 1 :
+            fst->SetFinal(s, Weight::One());
+            break;
+          case 2:
+            if (!StrToWeight(col[1], true, &w)) ok = false;
+            else fst->SetFinal(s, w);
+            break;
+          case 3: // 3 columns not ok for Lattice format; it's not an acceptor.
+            ok = false;
+            break;
+          case 4:
+            ok = ConvertStringToInteger(col[1], &arc.nextstate) &&
+                ConvertStringToInteger(col[2], &arc.ilabel) &&
+                ConvertStringToInteger(col[3], &arc.olabel);
+            if (ok) {
+              d = arc.nextstate;
+              arc.weight = Weight::One();
+              fst->AddArc(s, arc);
+            }
+            break;
+          case 5:
+            ok = ConvertStringToInteger(col[1], &arc.nextstate) &&
+                ConvertStringToInteger(col[2], &arc.ilabel) &&
+                ConvertStringToInteger(col[3], &arc.olabel) &&
+                StrToWeight(col[4], false, &arc.weight);
+            if (ok) {
+              d = arc.nextstate;
+              fst->AddArc(s, arc);
+            }
+            break;
+          default:
+            ok = false;
+        }
+        while (d >= fst->NumStates())
+          fst->AddState();
+        if (!ok) {
+          delete fst;
+          fst = NULL;
+        }
+      }
+      if (cfst) {
+        bool ok = true;
+        CArc arc;
+        CWeight w;
+        StateId d = s;
+        switch (col.size()) {
+          case 1 :
+            cfst->SetFinal(s, CWeight::One());
+            break;
+          case 2:
+            if (!StrToCWeight(col[1], true, &w)) ok = false;
+            else cfst->SetFinal(s, w);
+            break;
+          case 3: // compact-lattice is acceptor format: state, next-state, label.
+            ok = ConvertStringToInteger(col[1], &arc.nextstate) &&
+                ConvertStringToInteger(col[2], &arc.ilabel);
+            if (ok) {
+              d = arc.nextstate;
+              arc.olabel = arc.ilabel;
+              arc.weight = CWeight::One();
+              cfst->AddArc(s, arc);
+            }
+            break;
+          case 4:
+            ok = ConvertStringToInteger(col[1], &arc.nextstate) &&
+                ConvertStringToInteger(col[2], &arc.ilabel) &&
+                StrToCWeight(col[3], false, &arc.weight);
+            if (ok) {
+              d = arc.nextstate;
+              arc.olabel = arc.ilabel;
+              cfst->AddArc(s, arc);
+            }
+            break;
+          case 5: default:
+            ok = false;
+        }
+        while (d >= cfst->NumStates())
+          cfst->AddState();
+        if (!ok) {
+          delete cfst;
+          cfst = NULL;
+        }
+      }
+      if (!fst && !cfst) {
+        KALDI_WARN << "Bad line in lattice text format: " << line;
+        // read until we get an empty line, so at least we
+        // have a chance to read the next one (although this might
+        // be a bit futile since the calling code will get unhappy
+        // about failing to read this one.
+        while (std::getline(is, line)) {
+          SplitStringToVector(line, separator.c_str(), true, &col);
+          if (col.empty()) break;
+        }
+        return PairT(static_cast<Lattice*>(NULL),
+                     static_cast<CompactLattice*>(NULL));
+      }
+    }
+    return PairT(fst, cfst);
+  }
+
+  static bool StrToWeight(const std::string &s, bool allow_zero, Weight *w) {
+    std::istringstream strm(s);
+    strm >> *w;
+    if (!strm || (!allow_zero && *w == Weight::Zero())) {
+      return false;
+    }
+    return true;
+  }
+
+  static  bool StrToCWeight(const std::string &s, bool allow_zero, CWeight *w) {
+    std::istringstream strm(s);
+    strm >> *w;
+    if (!strm || (!allow_zero && *w == CWeight::Zero())) {
+      return false;
+    }
+    return true;
+  }
+};
+
+
+CompactLattice *ReadCompactLatticeText(std::istream &is) {
+  std::pair<Lattice*, CompactLattice*> lat_pair = LatticeReader::ReadText(is);
+  if (lat_pair.second != NULL) {
+    delete lat_pair.first;
+    return lat_pair.second;
+  } else if (lat_pair.first != NULL) {
+    // note: ConvertToCompactLattice frees its input.
+    return ConvertToCompactLattice(lat_pair.first);
+  } else {
+    return NULL;
+  }
+}
+
+
+Lattice *ReadLatticeText(std::istream &is) {
+  std::pair<Lattice*, CompactLattice*> lat_pair = LatticeReader::ReadText(is);
+  if (lat_pair.first != NULL) {
+    delete lat_pair.second;
+    return lat_pair.first;
+  } else if (lat_pair.second != NULL) {
+    // note: ConvertToLattice frees its input.
+    return ConvertToLattice(lat_pair.second);
+  } else {
+    return NULL;
+  }
+}
+
+bool ReadCompactLattice(std::istream &is, bool binary,
+                        CompactLattice **clat) {
+  KALDI_ASSERT(*clat == NULL);
+  if (binary) {
+    fst::FstHeader hdr;
+    if (!hdr.Read(is, "<unknown>")) {
+      KALDI_WARN << "Reading compact lattice: error reading FST header.";
+      return false;
+    }
+    if (hdr.FstType() != "vector") {
+      KALDI_WARN << "Reading compact lattice: unsupported FST type: "
+                 << hdr.FstType();
+      return false;
+    }
+    fst::FstReadOptions ropts("<unspecified>",
+                              &hdr);
+
+    typedef fst::CompactLatticeWeightTpl<fst::LatticeWeightTpl<float>, int32> T1;
+    typedef fst::CompactLatticeWeightTpl<fst::LatticeWeightTpl<double>, int32> T2;
+    typedef fst::LatticeWeightTpl<float> T3;
+    typedef fst::LatticeWeightTpl<double> T4;
+    typedef fst::VectorFst<fst::ArcTpl<T1> > F1;
+    typedef fst::VectorFst<fst::ArcTpl<T2> > F2;
+    typedef fst::VectorFst<fst::ArcTpl<T3> > F3;
+    typedef fst::VectorFst<fst::ArcTpl<T4> > F4;
+
+    CompactLattice *ans = NULL;
+    if (hdr.ArcType() == T1::Type()) {
+      ans = ConvertToCompactLattice(F1::Read(is, ropts));
+    } else if (hdr.ArcType() == T2::Type()) {
+      ans = ConvertToCompactLattice(F2::Read(is, ropts));
+    } else if (hdr.ArcType() == T3::Type()) {
+      ans = ConvertToCompactLattice(F3::Read(is, ropts));
+    } else if (hdr.ArcType() == T4::Type()) {
+      ans = ConvertToCompactLattice(F4::Read(is, ropts));
+    } else {
+      KALDI_WARN << "FST with arc type " << hdr.ArcType()
+                 << " cannot be converted to CompactLattice.\n";
+      return false;
+    }
+    if (ans == NULL) {
+      KALDI_WARN << "Error reading compact lattice (after reading header).";
+      return false;
+    }
+    *clat = ans;
+    return true;
+  } else {
+    // The next line would normally consume the \r on Windows, plus any
+    // extra spaces that might have got in there somehow.
+    while (std::isspace(is.peek()) && is.peek() != '\n') is.get();
+    if (is.peek() == '\n') is.get(); // consume the newline.
+    else { // saw spaces but no newline.. this is not expected.
+      KALDI_WARN << "Reading compact lattice: unexpected sequence of spaces "
+                 << " at file position " << is.tellg();
+      return false;
+    }
+    *clat = ReadCompactLatticeText(is); // that routine will warn on error.
+    return (*clat != NULL);
+  }
+}
+
+
+bool CompactLatticeHolder::Read(std::istream &is) {
+  Clear(); // in case anything currently stored.
+  int c = is.peek();
+  if (c == -1) {
+    KALDI_WARN << "End of stream detected reading CompactLattice.";
+    return false;
+  } else if (isspace(c)) { // The text form of the lattice begins
+    // with space (normally, '\n'), so this means it's text (the binary form
+    // cannot begin with space because it starts with the FST Type() which is not
+    // space).
+    return ReadCompactLattice(is, false, &t_);
+  } else if (c != 214) { // 214 is first char of FST magic number,
+    // on little-endian machines which is all we support (\326 octal)
+    KALDI_WARN << "Reading compact lattice: does not appear to be an FST "
+               << " [non-space but no magic number detected], file pos is "
+               << is.tellg();
+    return false;
+  } else {
+    return ReadCompactLattice(is, true, &t_);
+  }
+}
+
+bool WriteLattice(std::ostream &os, bool binary, const Lattice &t) {
+  if (binary) {
+    fst::FstWriteOptions opts;
+    // Leave all the options default.  Normally these lattices wouldn't have any
+    // osymbols/isymbols so no point directing it not to write them (who knows what
+    // we'd want to do if we had them).
+    return t.Write(os, opts);
+  } else {
+    // Text-mode output.  Note: we expect that t.InputSymbols() and
+    // t.OutputSymbols() would always return NULL.  The corresponding input
+    // routine would not work if the FST actually had symbols attached.
+    // Write a newline after the key, so the first line of the FST appears
+    // on its own line.
+    os << '\n';
+    bool acceptor = false, write_one = false;
+    fst::FstPrinter<LatticeArc> printer(t, t.InputSymbols(),
+                                        t.OutputSymbols(),
+                                        NULL, acceptor, write_one, "\t");
+    printer.Print(&os, "<unknown>");
+    if (os.fail())
+      KALDI_WARN << "Stream failure detected.";
+    // Write another newline as a terminating character.  The read routine will
+    // detect this [this is a Kaldi mechanism, not somethig in the original
+    // OpenFst code].
+    os << '\n';
+    return os.good();
+  }
+}
+
+bool ReadLattice(std::istream &is, bool binary,
+                 Lattice **lat) {
+  KALDI_ASSERT(*lat == NULL);
+  if (binary) {
+    fst::FstHeader hdr;
+    if (!hdr.Read(is, "<unknown>")) {
+      KALDI_WARN << "Reading lattice: error reading FST header.";
+      return false;
+    }
+    if (hdr.FstType() != "vector") {
+      KALDI_WARN << "Reading lattice: unsupported FST type: "
+                 << hdr.FstType();
+      return false;
+    }
+    fst::FstReadOptions ropts("<unspecified>",
+                              &hdr);
+
+    typedef fst::CompactLatticeWeightTpl<fst::LatticeWeightTpl<float>, int32> T1;
+    typedef fst::CompactLatticeWeightTpl<fst::LatticeWeightTpl<double>, int32> T2;
+    typedef fst::LatticeWeightTpl<float> T3;
+    typedef fst::LatticeWeightTpl<double> T4;
+    typedef fst::VectorFst<fst::ArcTpl<T1> > F1;
+    typedef fst::VectorFst<fst::ArcTpl<T2> > F2;
+    typedef fst::VectorFst<fst::ArcTpl<T3> > F3;
+    typedef fst::VectorFst<fst::ArcTpl<T4> > F4;
+
+    Lattice *ans = NULL;
+    if (hdr.ArcType() == T1::Type()) {
+      ans = ConvertToLattice(F1::Read(is, ropts));
+    } else if (hdr.ArcType() == T2::Type()) {
+      ans = ConvertToLattice(F2::Read(is, ropts));
+    } else if (hdr.ArcType() == T3::Type()) {
+      ans = ConvertToLattice(F3::Read(is, ropts));
+    } else if (hdr.ArcType() == T4::Type()) {
+      ans = ConvertToLattice(F4::Read(is, ropts));
+    } else {
+      KALDI_WARN << "FST with arc type " << hdr.ArcType()
+                 << " cannot be converted to Lattice.\n";
+      return false;
+    }
+    if (ans == NULL) {
+      KALDI_WARN << "Error reading lattice (after reading header).";
+      return false;
+    }
+    *lat = ans;
+    return true;
+  } else {
+    // The next line would normally consume the \r on Windows, plus any
+    // extra spaces that might have got in there somehow.
+    while (std::isspace(is.peek()) && is.peek() != '\n') is.get();
+    if (is.peek() == '\n') is.get(); // consume the newline.
+    else { // saw spaces but no newline.. this is not expected.
+      KALDI_WARN << "Reading compact lattice: unexpected sequence of spaces "
+                 << " at file position " << is.tellg();
+      return false;
+    }
+    *lat = ReadLatticeText(is); // that routine will warn on error.
+    return (*lat != NULL);
+  }
+}
+
+
+/* Since we don't write the binary headers for this type of holder,
+   we use a different method to work out whether we're in binary mode.
+ */
+bool LatticeHolder::Read(std::istream &is) {
+  Clear(); // in case anything currently stored.
+  int c = is.peek();
+  if (c == -1) {
+    KALDI_WARN << "End of stream detected reading Lattice.";
+    return false;
+  } else if (isspace(c)) { // The text form of the lattice begins
+    // with space (normally, '\n'), so this means it's text (the binary form
+    // cannot begin with space because it starts with the FST Type() which is not
+    // space).
+    return ReadLattice(is, false, &t_);
+  } else if (c != 214) { // 214 is first char of FST magic number,
+    // on little-endian machines which is all we support (\326 octal)
+    KALDI_WARN << "Reading compact lattice: does not appear to be an FST "
+               << " [non-space but no magic number detected], file pos is "
+               << is.tellg();
+    return false;
+  } else {
+    return ReadLattice(is, true, &t_);
+  }
+}
+
+
+
+} // end namespace kaldi

speechx/speechx/kaldi/lat/kaldi-lattice.h

+// lat/kaldi-lattice.h
+
+// Copyright 2009-2011  Microsoft Corporation
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+
+#ifndef KALDI_LAT_KALDI_LATTICE_H_
+#define KALDI_LAT_KALDI_LATTICE_H_
+
+#include "fstext/fstext-lib.h"
+#include "base/kaldi-common.h"
+#include "util/common-utils.h"
+
+
+namespace kaldi {
+// will import some things above...
+
+typedef fst::LatticeWeightTpl<BaseFloat> LatticeWeight;
+
+// careful: kaldi::int32 is not always the same C type as fst::int32
+typedef fst::CompactLatticeWeightTpl<LatticeWeight, int32> CompactLatticeWeight;
+
+typedef fst::CompactLatticeWeightCommonDivisorTpl<LatticeWeight, int32>
+  CompactLatticeWeightCommonDivisor;
+
+typedef fst::ArcTpl<LatticeWeight> LatticeArc;
+
+typedef fst::ArcTpl<CompactLatticeWeight> CompactLatticeArc;
+
+typedef fst::VectorFst<LatticeArc> Lattice;
+
+typedef fst::VectorFst<CompactLatticeArc> CompactLattice;
+
+// The following functions for writing and reading lattices in binary or text
+// form are provided here in case you need to include lattices in larger,
+// Kaldi-type objects with their own Read and Write functions.  Caution: these
+// functions return false on stream failure rather than throwing an exception as
+// most similar Kaldi functions would do.
+
+bool WriteCompactLattice(std::ostream &os, bool binary,
+                         const CompactLattice &clat);
+bool WriteLattice(std::ostream &os, bool binary,
+                  const Lattice &lat);
+
+// the following function requires that *clat be
+// NULL when called.
+bool ReadCompactLattice(std::istream &is, bool binary,
+                        CompactLattice **clat);
+// the following function requires that *lat be
+// NULL when called.
+bool ReadLattice(std::istream &is, bool binary,
+                 Lattice **lat);
+
+
+class CompactLatticeHolder {
+ public:
+  typedef CompactLattice T;
+
+  CompactLatticeHolder() { t_ = NULL; }
+
+  static bool Write(std::ostream &os, bool binary, const T &t) {
+    // Note: we don't include the binary-mode header when writing
+    // this object to disk; this ensures that if we write to single
+    // files, the result can be read by OpenFst.
+    return WriteCompactLattice(os, binary, t);
+  }
+
+  bool Read(std::istream &is);
+
+  static bool IsReadInBinary() { return true; }
+
+  T &Value() {
+    KALDI_ASSERT(t_ != NULL && "Called Value() on empty CompactLatticeHolder");
+    return *t_;
+  }
+
+  void Clear() { delete t_; t_ = NULL; }
+
+  void Swap(CompactLatticeHolder *other) {
+    std::swap(t_, other->t_);
+  }
+
+  bool ExtractRange(const CompactLatticeHolder &other, const std::string &range) {
+    KALDI_ERR << "ExtractRange is not defined for this type of holder.";
+    return false;
+  }
+
+  ~CompactLatticeHolder() { Clear(); }
+ private:
+  T *t_;
+};
+
+class LatticeHolder {
+ public:
+  typedef Lattice T;
+
+  LatticeHolder() { t_ = NULL; }
+
+  static bool Write(std::ostream &os, bool binary, const T &t) {
+    // Note: we don't include the binary-mode header when writing
+    // this object to disk; this ensures that if we write to single
+    // files, the result can be read by OpenFst.
+    return WriteLattice(os, binary, t);
+  }
+
+  bool Read(std::istream &is);
+
+  static bool IsReadInBinary() { return true; }
+
+  T &Value() {
+    KALDI_ASSERT(t_ != NULL && "Called Value() on empty LatticeHolder");
+    return *t_;
+  }
+
+  void Clear() {  delete t_; t_ = NULL; }
+
+  void Swap(LatticeHolder *other) {
+    std::swap(t_, other->t_);
+  }
+
+  bool ExtractRange(const LatticeHolder &other, const std::string &range) {
+    KALDI_ERR << "ExtractRange is not defined for this type of holder.";
+    return false;
+  }
+
+  ~LatticeHolder() { Clear(); }
+ private:
+  T *t_;
+};
+
+typedef TableWriter<LatticeHolder> LatticeWriter;
+typedef SequentialTableReader<LatticeHolder> SequentialLatticeReader;
+typedef RandomAccessTableReader<LatticeHolder> RandomAccessLatticeReader;
+
+typedef TableWriter<CompactLatticeHolder> CompactLatticeWriter;
+typedef SequentialTableReader<CompactLatticeHolder> SequentialCompactLatticeReader;
+typedef RandomAccessTableReader<CompactLatticeHolder> RandomAccessCompactLatticeReader;
+
+
+} // namespace kaldi
+
+#endif  // KALDI_LAT_KALDI_LATTICE_H_

speechx/speechx/kaldi/lat/lattice-functions.cc

+// lat/lattice-functions.cc
+
+// Copyright 2009-2011  Saarland University (Author: Arnab Ghoshal)
+//           2012-2013  Johns Hopkins University (Author: Daniel Povey);  Chao Weng;
+//                      Bagher BabaAli
+//                2013  Cisco Systems (author: Neha Agrawal) [code modified
+//                      from original code in ../gmmbin/gmm-rescore-lattice.cc]
+//                2014  Guoguo Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+
+#include "base/kaldi-math.h"
+#include "lat/lattice-functions.h"
+
+namespace kaldi {
+using std::map;
+using std::vector;
+
+void GetPerFrameAcousticCosts(const Lattice &nbest,
+                              Vector<BaseFloat> *per_frame_loglikes) {
+  using namespace fst;
+  typedef Lattice::Arc::Weight Weight;
+  vector<BaseFloat> loglikes;
+
+  int32 cur_state = nbest.Start();
+  int32 prev_frame = -1;
+  BaseFloat eps_acwt = 0.0;
+  while(1) {
+    Weight w = nbest.Final(cur_state);
+    if (w != Weight::Zero()) {
+      KALDI_ASSERT(nbest.NumArcs(cur_state) == 0);
+      if (per_frame_loglikes != NULL)  {
+        SubVector<BaseFloat> subvec(&(loglikes[0]), loglikes.size());
+        Vector<BaseFloat> vec(subvec);
+        *per_frame_loglikes = vec;
+      }
+      break;
+    } else {
+      KALDI_ASSERT(nbest.NumArcs(cur_state) == 1);
+      fst::ArcIterator<Lattice> iter(nbest, cur_state);
+      const Lattice::Arc &arc = iter.Value();
+      BaseFloat acwt = arc.weight.Value2();
+      if (arc.ilabel != 0) {
+        if (eps_acwt > 0) {
+          acwt += eps_acwt;
+          eps_acwt = 0.0;
+        }
+        loglikes.push_back(acwt);
+        prev_frame++;
+      } else if (acwt == acwt){
+        if (prev_frame > -1) {
+          loglikes[prev_frame] += acwt;
+        } else {
+          eps_acwt += acwt;
+        }
+      }
+      cur_state = arc.nextstate;
+    }
+  }
+}
+
+int32 LatticeStateTimes(const Lattice &lat, vector<int32> *times) {
+  if (!lat.Properties(fst::kTopSorted, true))
+    KALDI_ERR << "Input lattice must be topologically sorted.";
+  KALDI_ASSERT(lat.Start() == 0);
+  int32 num_states = lat.NumStates();
+  times->clear();
+  times->resize(num_states, -1);
+  (*times)[0] = 0;
+  for (int32 state = 0; state < num_states; state++) {
+    int32 cur_time = (*times)[state];
+    for (fst::ArcIterator<Lattice> aiter(lat, state); !aiter.Done();
+        aiter.Next()) {
+      const LatticeArc &arc = aiter.Value();
+
+      if (arc.ilabel != 0) {  // Non-epsilon input label on arc
+        // next time instance
+        if ((*times)[arc.nextstate] == -1) {
+          (*times)[arc.nextstate] = cur_time + 1;
+        } else {
+          KALDI_ASSERT((*times)[arc.nextstate] == cur_time + 1);
+        }
+      } else {  // epsilon input label on arc
+        // Same time instance
+        if ((*times)[arc.nextstate] == -1)
+          (*times)[arc.nextstate] = cur_time;
+        else
+          KALDI_ASSERT((*times)[arc.nextstate] == cur_time);
+      }
+    }
+  }
+  return (*std::max_element(times->begin(), times->end()));
+}
+
+int32 CompactLatticeStateTimes(const CompactLattice &lat,
+                               vector<int32> *times) {
+  if (!lat.Properties(fst::kTopSorted, true))
+    KALDI_ERR << "Input lattice must be topologically sorted.";
+  KALDI_ASSERT(lat.Start() == 0);
+  int32 num_states = lat.NumStates();
+  times->clear();
+  times->resize(num_states, -1);
+  (*times)[0] = 0;
+  int32 utt_len = -1;
+  for (int32 state = 0; state < num_states; state++) {
+    int32 cur_time = (*times)[state];
+    for (fst::ArcIterator<CompactLattice> aiter(lat, state); !aiter.Done();
+        aiter.Next()) {
+      const CompactLatticeArc &arc = aiter.Value();
+      int32 arc_len = static_cast<int32>(arc.weight.String().size());
+      if ((*times)[arc.nextstate] == -1)
+        (*times)[arc.nextstate] = cur_time + arc_len;
+      else
+        KALDI_ASSERT((*times)[arc.nextstate] == cur_time + arc_len);
+    }
+    if (lat.Final(state) != CompactLatticeWeight::Zero()) {
+      int32 this_utt_len = (*times)[state] + lat.Final(state).String().size();
+      if (utt_len == -1) utt_len = this_utt_len;
+      else {
+        if (this_utt_len != utt_len) {
+          KALDI_WARN << "Utterance does not "
+              "seem to have a consistent length.";
+          utt_len = std::max(utt_len, this_utt_len);
+        }
+      }
+    }
+  }
+  if (utt_len == -1) {
+    KALDI_WARN << "Utterance does not have a final-state.";
+    return 0;
+  }
+  return utt_len;
+}
+
+bool ComputeCompactLatticeAlphas(const CompactLattice &clat,
+                                 vector<double> *alpha) {
+  using namespace fst;
+
+  // typedef the arc, weight types
+  typedef CompactLattice::Arc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  //Make sure the lattice is topologically sorted.
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    KALDI_WARN << "Input lattice must be topologically sorted.";
+    return false;
+  }
+  if (clat.Start() != 0) {
+    KALDI_WARN << "Input lattice must start from state 0.";
+    return false;
+  }
+
+  int32 num_states = clat.NumStates();
+  (*alpha).resize(0);
+  (*alpha).resize(num_states, kLogZeroDouble);
+
+  // Now propagate alphas forward. Note that we don't acount the weight of the
+  // final state to alpha[final_state] -- we acount it to beta[final_state];
+  (*alpha)[0] = 0.0;
+  for (StateId s = 0; s < num_states; s++) {
+    double this_alpha = (*alpha)[s];
+    for (ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -(arc.weight.Weight().Value1() +
+                          arc.weight.Weight().Value2());
+      (*alpha)[arc.nextstate] = LogAdd((*alpha)[arc.nextstate],
+                                       this_alpha + arc_like);
+    }
+  }
+
+  return true;
+}
+
+bool ComputeCompactLatticeBetas(const CompactLattice &clat,
+                                vector<double> *beta) {
+  using namespace fst;
+
+  // typedef the arc, weight types
+  typedef CompactLattice::Arc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  // Make sure the lattice is topologically sorted.
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    KALDI_WARN << "Input lattice must be topologically sorted.";
+    return false;
+  }
+  if (clat.Start() != 0) {
+    KALDI_WARN << "Input lattice must start from state 0.";
+    return false;
+  }
+
+  int32 num_states = clat.NumStates();
+  (*beta).resize(0);
+  (*beta).resize(num_states, kLogZeroDouble);
+
+  // Now propagate betas backward. Note that beta[final_state] contains the
+  // weight of the final state in the lattice -- compare that with alpha.
+  for (StateId s = num_states-1; s >= 0; s--) {
+    Weight f = clat.Final(s);
+    double this_beta = -(f.Weight().Value1()+f.Weight().Value2());
+    for (ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -(arc.weight.Weight().Value1() +
+                          arc.weight.Weight().Value2());
+      double arc_beta = (*beta)[arc.nextstate] + arc_like;
+      this_beta = LogAdd(this_beta, arc_beta);
+    }
+    (*beta)[s] = this_beta;
+  }
+
+  return true;
+}
+
+template<class LatType>  // could be Lattice or CompactLattice
+bool PruneLattice(BaseFloat beam, LatType *lat) {
+  typedef typename LatType::Arc Arc;
+  typedef typename Arc::Weight Weight;
+  typedef typename Arc::StateId StateId;
+
+  KALDI_ASSERT(beam > 0.0);
+  if (!lat->Properties(fst::kTopSorted, true)) {
+    if (fst::TopSort(lat) == false) {
+      KALDI_WARN << "Cycles detected in lattice";
+      return false;
+    }
+  }
+  // We assume states before "start" are not reachable, since
+  // the lattice is topologically sorted.
+  int32 start = lat->Start();
+  int32 num_states = lat->NumStates();
+  if (num_states == 0) return false;
+  std::vector<double> forward_cost(num_states,
+                                   std::numeric_limits<double>::infinity());  // viterbi forward.
+  forward_cost[start] = 0.0; // lattice can't have cycles so couldn't be
+  // less than this.
+  double best_final_cost = std::numeric_limits<double>::infinity();
+  // Update the forward probs.
+  // Thanks to Jing Zheng for finding a bug here.
+  for (int32 state = 0; state < num_states; state++) {
+    double this_forward_cost = forward_cost[state];
+    for (fst::ArcIterator<LatType> aiter(*lat, state);
+         !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc(aiter.Value());
+      StateId nextstate = arc.nextstate;
+      KALDI_ASSERT(nextstate > state && nextstate < num_states);
+      double next_forward_cost = this_forward_cost +
+          ConvertToCost(arc.weight);
+      if (forward_cost[nextstate] > next_forward_cost)
+        forward_cost[nextstate] = next_forward_cost;
+    }
+    Weight final_weight = lat->Final(state);
+    double this_final_cost = this_forward_cost +
+        ConvertToCost(final_weight);
+    if (this_final_cost < best_final_cost)
+      best_final_cost = this_final_cost;
+  }
+  int32 bad_state = lat->AddState(); // this state is not final.
+  double cutoff = best_final_cost + beam;
+
+  // Go backwards updating the backward probs (which share memory with the
+  // forward probs), and pruning arcs and deleting final-probs.  We prune arcs
+  // by making them point to the non-final state "bad_state".  We'll then use
+  // Trim() to remove unnecessary arcs and states.  [this is just easier than
+  // doing it ourselves.]
+  std::vector<double> &backward_cost(forward_cost);
+  for (int32 state = num_states - 1; state >= 0; state--) {
+    double this_forward_cost = forward_cost[state];
+    double this_backward_cost = ConvertToCost(lat->Final(state));
+    if (this_backward_cost + this_forward_cost > cutoff
+        && this_backward_cost != std::numeric_limits<double>::infinity())
+      lat->SetFinal(state, Weight::Zero());
+    for (fst::MutableArcIterator<LatType> aiter(lat, state);
+         !aiter.Done();
+         aiter.Next()) {
+      Arc arc(aiter.Value());
+      StateId nextstate = arc.nextstate;
+      KALDI_ASSERT(nextstate > state && nextstate < num_states);
+      double arc_cost = ConvertToCost(arc.weight),
+          arc_backward_cost = arc_cost + backward_cost[nextstate],
+          this_fb_cost = this_forward_cost + arc_backward_cost;
+      if (arc_backward_cost < this_backward_cost)
+        this_backward_cost = arc_backward_cost;
+      if (this_fb_cost > cutoff) { // Prune the arc.
+        arc.nextstate = bad_state;
+        aiter.SetValue(arc);
+      }
+    }
+    backward_cost[state] = this_backward_cost;
+  }
+  fst::Connect(lat);
+  return (lat->NumStates() > 0);
+}
+
+// instantiate the template for lattice and CompactLattice.
+template bool PruneLattice(BaseFloat beam, Lattice *lat);
+template bool PruneLattice(BaseFloat beam, CompactLattice *lat);
+
+
+BaseFloat LatticeForwardBackward(const Lattice &lat, Posterior *post,
+                                 double *acoustic_like_sum) {
+  // Note, Posterior is defined as follows:  Indexed [frame], then a list
+  // of (transition-id, posterior-probability) pairs.
+  // typedef std::vector<std::vector<std::pair<int32, BaseFloat> > > Posterior;
+  using namespace fst;
+  typedef Lattice::Arc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  if (acoustic_like_sum) *acoustic_like_sum = 0.0;
+
+  // Make sure the lattice is topologically sorted.
+  if (lat.Properties(fst::kTopSorted, true) == 0)
+    KALDI_ERR << "Input lattice must be topologically sorted.";
+  KALDI_ASSERT(lat.Start() == 0);
+
+  int32 num_states = lat.NumStates();
+  vector<int32> state_times;
+  int32 max_time = LatticeStateTimes(lat, &state_times);
+  std::vector<double> alpha(num_states, kLogZeroDouble);
+  std::vector<double> &beta(alpha); // we re-use the same memory for
+  // this, but it's semantically distinct so we name it differently.
+  double tot_forward_prob = kLogZeroDouble;
+
+  post->clear();
+  post->resize(max_time);
+
+  alpha[0] = 0.0;
+  // Propagate alphas forward.
+  for (StateId s = 0; s < num_states; s++) {
+    double this_alpha = alpha[s];
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight);
+      alpha[arc.nextstate] = LogAdd(alpha[arc.nextstate], this_alpha + arc_like);
+    }
+    Weight f = lat.Final(s);
+    if (f != Weight::Zero()) {
+      double final_like = this_alpha - (f.Value1() + f.Value2());
+      tot_forward_prob = LogAdd(tot_forward_prob, final_like);
+      KALDI_ASSERT(state_times[s] == max_time &&
+                   "Lattice is inconsistent (final-prob not at max_time)");
+    }
+  }
+  for (StateId s = num_states-1; s >= 0; s--) {
+    Weight f = lat.Final(s);
+    double this_beta = -(f.Value1() + f.Value2());
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight),
+          arc_beta = beta[arc.nextstate] + arc_like;
+      this_beta = LogAdd(this_beta, arc_beta);
+      int32 transition_id = arc.ilabel;
+
+      // The following "if" is an optimization to avoid un-needed exp().
+      if (transition_id != 0 || acoustic_like_sum != NULL) {
+        double posterior = Exp(alpha[s] + arc_beta - tot_forward_prob);
+
+        if (transition_id != 0) // Arc has a transition-id on it [not epsilon]
+          (*post)[state_times[s]].push_back(std::make_pair(transition_id,
+                                                           static_cast<kaldi::BaseFloat>(posterior)));
+        if (acoustic_like_sum != NULL)
+          *acoustic_like_sum -= posterior * arc.weight.Value2();
+      }
+    }
+    if (acoustic_like_sum != NULL && f != Weight::Zero()) {
+      double final_logprob = - ConvertToCost(f),
+          posterior = Exp(alpha[s] + final_logprob - tot_forward_prob);
+      *acoustic_like_sum -= posterior * f.Value2();
+    }
+    beta[s] = this_beta;
+  }
+  double tot_backward_prob = beta[0];
+  if (!ApproxEqual(tot_forward_prob, tot_backward_prob, 1e-8)) {
+    KALDI_WARN << "Total forward probability over lattice = " << tot_forward_prob
+              << ", while total backward probability = " << tot_backward_prob;
+  }
+  // Now combine any posteriors with the same transition-id.
+  for (int32 t = 0; t < max_time; t++)
+    MergePairVectorSumming(&((*post)[t]));
+  return tot_backward_prob;
+}
+
+
+void LatticeActivePhones(const Lattice &lat, const TransitionInformation &trans,
+                         const vector<int32> &silence_phones,
+                         vector< std::set<int32> > *active_phones) {
+  KALDI_ASSERT(IsSortedAndUniq(silence_phones));
+  vector<int32> state_times;
+  int32 num_states = lat.NumStates();
+  int32 max_time = LatticeStateTimes(lat, &state_times);
+  active_phones->clear();
+  active_phones->resize(max_time);
+  for (int32 state = 0; state < num_states; state++) {
+    int32 cur_time = state_times[state];
+    for (fst::ArcIterator<Lattice> aiter(lat, state); !aiter.Done();
+        aiter.Next()) {
+      const LatticeArc &arc = aiter.Value();
+      if (arc.ilabel != 0) {  // Non-epsilon arc
+        int32 phone = trans.TransitionIdToPhone(arc.ilabel);
+        if (!std::binary_search(silence_phones.begin(),
+                                silence_phones.end(), phone))
+          (*active_phones)[cur_time].insert(phone);
+      }
+    }  // end looping over arcs
+  }  // end looping over states
+}
+
+void ConvertLatticeToPhones(const TransitionInformation &trans,
+                            Lattice *lat) {
+  typedef LatticeArc Arc;
+  int32 num_states = lat->NumStates();
+  for (int32 state = 0; state < num_states; state++) {
+    for (fst::MutableArcIterator<Lattice> aiter(lat, state); !aiter.Done();
+        aiter.Next()) {
+      Arc arc(aiter.Value());
+      arc.olabel = 0; // remove any word.
+      if ((arc.ilabel != 0) // has a transition-id on input..
+          && (trans.TransitionIdIsStartOfPhone(arc.ilabel))
+          && (!trans.IsSelfLoop(arc.ilabel))) {
+         // && trans.IsFinal(arc.ilabel)) // there is one of these per phone...
+        arc.olabel = trans.TransitionIdToPhone(arc.ilabel);
+      }
+      aiter.SetValue(arc);
+    }  // end looping over arcs
+  }  // end looping over states
+}
+
+
+static inline double LogAddOrMax(bool viterbi, double a, double b) {
+  if (viterbi)
+    return std::max(a, b);
+  else
+    return LogAdd(a, b);
+}
+
+template<typename LatticeType>
+double ComputeLatticeAlphasAndBetas(const LatticeType &lat,
+                                    bool viterbi,
+                                    vector<double> *alpha,
+                                    vector<double> *beta) {
+  typedef typename LatticeType::Arc Arc;
+  typedef typename Arc::Weight Weight;
+  typedef typename Arc::StateId StateId;
+
+  StateId num_states = lat.NumStates();
+  KALDI_ASSERT(lat.Properties(fst::kTopSorted, true) == fst::kTopSorted);
+  KALDI_ASSERT(lat.Start() == 0);
+  alpha->clear();
+  beta->clear();
+  alpha->resize(num_states, kLogZeroDouble);
+  beta->resize(num_states, kLogZeroDouble);
+
+  double tot_forward_prob = kLogZeroDouble;
+  (*alpha)[0] = 0.0;
+  // Propagate alphas forward.
+  for (StateId s = 0; s < num_states; s++) {
+    double this_alpha = (*alpha)[s];
+    for (fst::ArcIterator<LatticeType> aiter(lat, s); !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight);
+      (*alpha)[arc.nextstate] = LogAddOrMax(viterbi, (*alpha)[arc.nextstate],
+                                                this_alpha + arc_like);
+    }
+    Weight f = lat.Final(s);
+    if (f != Weight::Zero()) {
+      double final_like = this_alpha - ConvertToCost(f);
+      tot_forward_prob = LogAddOrMax(viterbi, tot_forward_prob, final_like);
+    }
+  }
+  for (StateId s = num_states-1; s >= 0; s--) { // it's guaranteed signed.
+    double this_beta = -ConvertToCost(lat.Final(s));
+    for (fst::ArcIterator<LatticeType> aiter(lat, s); !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight),
+          arc_beta = (*beta)[arc.nextstate] + arc_like;
+      this_beta = LogAddOrMax(viterbi, this_beta, arc_beta);
+    }
+    (*beta)[s] = this_beta;
+  }
+  double tot_backward_prob = (*beta)[lat.Start()];
+  if (!ApproxEqual(tot_forward_prob, tot_backward_prob, 1e-8)) {
+    KALDI_WARN << "Total forward probability over lattice = " << tot_forward_prob
+               << ", while total backward probability = " << tot_backward_prob;
+  }
+  // Split the difference when returning... they should be the same.
+  return 0.5 * (tot_backward_prob + tot_forward_prob);
+}
+
+// instantiate the template for Lattice and CompactLattice
+template
+double ComputeLatticeAlphasAndBetas(const Lattice &lat,
+                                    bool viterbi,
+                                    vector<double> *alpha,
+                                    vector<double> *beta);
+
+template
+double ComputeLatticeAlphasAndBetas(const CompactLattice &lat,
+                                    bool viterbi,
+                                    vector<double> *alpha,
+                                    vector<double> *beta);
+
+
+
+/// This is used in CompactLatticeLimitDepth.
+struct LatticeArcRecord {
+  BaseFloat logprob; // logprob <= 0 is the best Viterbi logprob of this arc,
+                     // minus the overall best-cost of the lattice.
+  CompactLatticeArc::StateId state; // state in the lattice.
+  size_t arc; // arc index within the state.
+  bool operator < (const LatticeArcRecord &other) const {
+    return logprob < other.logprob;
+  }
+};
+
+void CompactLatticeLimitDepth(int32 max_depth_per_frame,
+                              CompactLattice *clat) {
+  typedef CompactLatticeArc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  if (clat->Start() == fst::kNoStateId) {
+    KALDI_WARN << "Limiting depth of empty lattice.";
+    return;
+  }
+  if (clat->Properties(fst::kTopSorted, true) == 0) {
+    if (!TopSort(clat))
+      KALDI_ERR << "Topological sorting of lattice failed.";
+  }
+
+  vector<int32> state_times;
+  int32 T = CompactLatticeStateTimes(*clat, &state_times);
+
+  // The alpha and beta quantities here are "viterbi" alphas and beta.
+  std::vector<double> alpha;
+  std::vector<double> beta;
+  bool viterbi = true;
+  double best_prob = ComputeLatticeAlphasAndBetas(*clat, viterbi,
+                                                  &alpha, &beta);
+
+  std::vector<std::vector<LatticeArcRecord> > arc_records(T);
+
+  StateId num_states = clat->NumStates();
+  for (StateId s = 0; s < num_states; s++) {
+    for (fst::ArcIterator<CompactLattice> aiter(*clat, s); !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      LatticeArcRecord arc_record;
+      arc_record.state = s;
+      arc_record.arc = aiter.Position();
+      arc_record.logprob =
+          (alpha[s] + beta[arc.nextstate] - ConvertToCost(arc.weight))
+           - best_prob;
+      KALDI_ASSERT(arc_record.logprob < 0.1); // Should be zero or negative.
+      int32 num_frames = arc.weight.String().size(), start_t = state_times[s];
+      for (int32 t = start_t; t < start_t + num_frames; t++) {
+        KALDI_ASSERT(t < T);
+        arc_records[t].push_back(arc_record);
+      }
+    }
+  }
+  StateId dead_state = clat->AddState(); // A non-coaccesible state which we use
+                                         // to remove arcs (make them end
+                                         // there).
+  size_t max_depth = max_depth_per_frame;
+  for (int32 t = 0; t < T; t++) {
+    size_t size = arc_records[t].size();
+    if (size > max_depth) {
+      // we sort from worst to best, so we keep the later-numbered ones,
+      // and delete the lower-numbered ones.
+      size_t cutoff = size - max_depth;
+      std::nth_element(arc_records[t].begin(),
+                       arc_records[t].begin() + cutoff,
+                       arc_records[t].end());
+      for (size_t index = 0; index < cutoff; index++) {
+        LatticeArcRecord record(arc_records[t][index]);
+        fst::MutableArcIterator<CompactLattice> aiter(clat, record.state);
+        aiter.Seek(record.arc);
+        Arc arc = aiter.Value();
+        if (arc.nextstate != dead_state) { // not already killed.
+          arc.nextstate = dead_state;
+          aiter.SetValue(arc);
+        }
+      }
+    }
+  }
+  Connect(clat);
+  TopSortCompactLatticeIfNeeded(clat);
+}
+
+
+void TopSortCompactLatticeIfNeeded(CompactLattice *clat) {
+  if (clat->Properties(fst::kTopSorted, true) == 0) {
+    if (fst::TopSort(clat) == false) {
+      KALDI_ERR << "Topological sorting failed";
+    }
+  }
+}
+
+void TopSortLatticeIfNeeded(Lattice *lat) {
+  if (lat->Properties(fst::kTopSorted, true) == 0) {
+    if (fst::TopSort(lat) == false) {
+      KALDI_ERR << "Topological sorting failed";
+    }
+  }
+}
+
+
+/// Returns the depth of the lattice, defined as the average number of
+/// arcs crossing any given frame.  Returns 1 for empty lattices.
+/// Requires that input is topologically sorted.
+BaseFloat CompactLatticeDepth(const CompactLattice &clat,
+                              int32 *num_frames) {
+  typedef CompactLattice::Arc::StateId StateId;
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    KALDI_ERR << "Lattice input to CompactLatticeDepth was not topologically "
+              << "sorted.";
+  }
+  if (clat.Start() == fst::kNoStateId) {
+    *num_frames = 0;
+    return 1.0;
+  }
+  size_t num_arc_frames = 0;
+  int32 t;
+  {
+    vector<int32> state_times;
+    t = CompactLatticeStateTimes(clat, &state_times);
+  }
+  if (num_frames != NULL)
+    *num_frames = t;
+  for (StateId s = 0; s < clat.NumStates(); s++) {
+    for (fst::ArcIterator<CompactLattice> aiter(clat, s); !aiter.Done();
+         aiter.Next()) {
+      const CompactLatticeArc &arc = aiter.Value();
+      num_arc_frames += arc.weight.String().size();
+    }
+    num_arc_frames += clat.Final(s).String().size();
+  }
+  return num_arc_frames / static_cast<BaseFloat>(t);
+}
+
+
+void CompactLatticeDepthPerFrame(const CompactLattice &clat,
+                                 std::vector<int32> *depth_per_frame) {
+  typedef CompactLattice::Arc::StateId StateId;
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    KALDI_ERR << "Lattice input to CompactLatticeDepthPerFrame was not "
+              << "topologically sorted.";
+  }
+  if (clat.Start() == fst::kNoStateId) {
+    depth_per_frame->clear();
+    return;
+  }
+  vector<int32> state_times;
+  int32 T = CompactLatticeStateTimes(clat, &state_times);
+
+  depth_per_frame->clear();
+  if (T <= 0) {
+    return;
+  } else {
+    depth_per_frame->resize(T, 0);
+    for (StateId s = 0; s < clat.NumStates(); s++) {
+      int32 start_time = state_times[s];
+      for (fst::ArcIterator<CompactLattice> aiter(clat, s); !aiter.Done();
+           aiter.Next()) {
+        const CompactLatticeArc &arc = aiter.Value();
+        int32 len = arc.weight.String().size();
+        for (int32 t = start_time; t < start_time + len; t++) {
+          KALDI_ASSERT(t < T);
+          (*depth_per_frame)[t]++;
+        }
+      }
+      int32 final_len = clat.Final(s).String().size();
+      for (int32 t = start_time; t < start_time + final_len; t++) {
+        KALDI_ASSERT(t < T);
+        (*depth_per_frame)[t]++;
+      }
+    }
+  }
+}
+
+
+
+void ConvertCompactLatticeToPhones(const TransitionInformation &trans,
+                                   CompactLattice *clat) {
+  typedef CompactLatticeArc Arc;
+  typedef Arc::Weight Weight;
+  int32 num_states = clat->NumStates();
+  for (int32 state = 0; state < num_states; state++) {
+    for (fst::MutableArcIterator<CompactLattice> aiter(clat, state);
+         !aiter.Done();
+         aiter.Next()) {
+      Arc arc(aiter.Value());
+      std::vector<int32> phone_seq;
+      const std::vector<int32> &tid_seq = arc.weight.String();
+      for (std::vector<int32>::const_iterator iter = tid_seq.begin();
+           iter != tid_seq.end(); ++iter) {
+        if (trans.IsFinal(*iter))// note: there is one of these per phone...
+          phone_seq.push_back(trans.TransitionIdToPhone(*iter));
+      }
+      arc.weight.SetString(phone_seq);
+      aiter.SetValue(arc);
+    } // end looping over arcs
+    Weight f = clat->Final(state);
+    if (f != Weight::Zero()) {
+      std::vector<int32> phone_seq;
+      const std::vector<int32> &tid_seq = f.String();
+      for (std::vector<int32>::const_iterator iter = tid_seq.begin();
+           iter != tid_seq.end(); ++iter) {
+        if (trans.IsFinal(*iter))// note: there is one of these per phone...
+          phone_seq.push_back(trans.TransitionIdToPhone(*iter));
+      }
+      f.SetString(phone_seq);
+      clat->SetFinal(state, f);
+    }
+  }  // end looping over states
+}
+
+bool LatticeBoost(const TransitionInformation &trans,
+                  const std::vector<int32> &alignment,
+                  const std::vector<int32> &silence_phones,
+                  BaseFloat b,
+                  BaseFloat max_silence_error,
+                  Lattice *lat) {
+  TopSortLatticeIfNeeded(lat);
+
+  // get all stored properties (test==false means don't test if not known).
+  uint64 props = lat->Properties(fst::kFstProperties,
+                                 false);
+
+  KALDI_ASSERT(IsSortedAndUniq(silence_phones));
+  KALDI_ASSERT(max_silence_error >= 0.0 && max_silence_error <= 1.0);
+  vector<int32> state_times;
+  int32 num_states = lat->NumStates();
+  int32 num_frames = LatticeStateTimes(*lat, &state_times);
+  KALDI_ASSERT(num_frames == static_cast<int32>(alignment.size()));
+  for (int32 state = 0; state < num_states; state++) {
+    int32 cur_time = state_times[state];
+    for (fst::MutableArcIterator<Lattice> aiter(lat, state); !aiter.Done();
+         aiter.Next()) {
+      LatticeArc arc = aiter.Value();
+      if (arc.ilabel != 0) {  // Non-epsilon arc
+        if (arc.ilabel < 0 || arc.ilabel > trans.NumTransitionIds()) {
+          KALDI_WARN << "Lattice has out-of-range transition-ids: "
+                     << "lattice/model mismatch?";
+          return false;
+        }
+        int32 phone = trans.TransitionIdToPhone(arc.ilabel),
+            ref_phone = trans.TransitionIdToPhone(alignment[cur_time]);
+        BaseFloat frame_error;
+        if (phone == ref_phone) {
+          frame_error = 0.0;
+        } else { // an error...
+          if (std::binary_search(silence_phones.begin(), silence_phones.end(), phone))
+            frame_error = max_silence_error;
+          else
+            frame_error = 1.0;
+        }
+        BaseFloat delta_cost = -b * frame_error; // negative cost if
+        // frame is wrong, to boost likelihood of arcs with errors on them.
+        // Add this cost to the graph part.
+        arc.weight.SetValue1(arc.weight.Value1() + delta_cost);
+        aiter.SetValue(arc);
+      }
+    }
+  }
+  // All we changed is the weights, so any properties that were
+  // known before, are still known, except for whether or not the
+  // lattice was weighted.
+  lat->SetProperties(props,
+                     ~(fst::kWeighted|fst::kUnweighted));
+
+  return true;
+}
+
+
+
+BaseFloat LatticeForwardBackwardMpeVariants(
+    const TransitionInformation &trans,
+    const std::vector<int32> &silence_phones,
+    const Lattice &lat,
+    const std::vector<int32> &num_ali,
+    std::string criterion,
+    bool one_silence_class,
+    Posterior *post) {
+  using namespace fst;
+  typedef Lattice::Arc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  KALDI_ASSERT(criterion == "mpfe" || criterion == "smbr");
+  bool is_mpfe = (criterion == "mpfe");
+
+  if (lat.Properties(fst::kTopSorted, true) == 0)
+    KALDI_ERR << "Input lattice must be topologically sorted.";
+  KALDI_ASSERT(lat.Start() == 0);
+
+  int32 num_states = lat.NumStates();
+  vector<int32> state_times;
+  int32 max_time = LatticeStateTimes(lat, &state_times);
+  KALDI_ASSERT(max_time == static_cast<int32>(num_ali.size()));
+  std::vector<double> alpha(num_states, kLogZeroDouble),
+      alpha_smbr(num_states, 0), //forward variable for sMBR
+      beta(num_states, kLogZeroDouble),
+      beta_smbr(num_states, 0); //backward variable for sMBR
+
+  double tot_forward_prob = kLogZeroDouble;
+  double tot_forward_score = 0;
+
+  post->clear();
+  post->resize(max_time);
+
+  alpha[0] = 0.0;
+  // First Pass Forward,
+  for (StateId s = 0; s < num_states; s++) {
+    double this_alpha = alpha[s];
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight);
+      alpha[arc.nextstate] = LogAdd(alpha[arc.nextstate], this_alpha + arc_like);
+    }
+    Weight f = lat.Final(s);
+    if (f != Weight::Zero()) {
+      double final_like = this_alpha - (f.Value1() + f.Value2());
+      tot_forward_prob = LogAdd(tot_forward_prob, final_like);
+      KALDI_ASSERT(state_times[s] == max_time &&
+                   "Lattice is inconsistent (final-prob not at max_time)");
+    }
+  }
+  // First Pass Backward,
+  for (StateId s = num_states-1; s >= 0; s--) {
+    Weight f = lat.Final(s);
+    double this_beta = -(f.Value1() + f.Value2());
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight),
+          arc_beta = beta[arc.nextstate] + arc_like;
+      this_beta = LogAdd(this_beta, arc_beta);
+    }
+    beta[s] = this_beta;
+  }
+  // First Pass Forward-Backward Check
+  double tot_backward_prob = beta[0];
+  // may loose the condition somehow here 1e-6 (was 1e-8)
+  if (!ApproxEqual(tot_forward_prob, tot_backward_prob, 1e-6)) {
+    KALDI_ERR << "Total forward probability over lattice = " << tot_forward_prob
+              << ", while total backward probability = " << tot_backward_prob;
+  }
+
+  alpha_smbr[0] = 0.0;
+  // Second Pass Forward, calculate forward for MPFE/SMBR
+  for (StateId s = 0; s < num_states; s++) {
+    double this_alpha = alpha[s];
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight);
+      double frame_acc = 0.0;
+      if (arc.ilabel != 0) {
+        int32 cur_time = state_times[s];
+        int32 phone = trans.TransitionIdToPhone(arc.ilabel),
+            ref_phone = trans.TransitionIdToPhone(num_ali[cur_time]);
+        bool phone_is_sil = std::binary_search(silence_phones.begin(),
+                                               silence_phones.end(),
+                                               phone),
+            ref_phone_is_sil = std::binary_search(silence_phones.begin(),
+                                                  silence_phones.end(),
+                                                  ref_phone),
+            both_sil = phone_is_sil && ref_phone_is_sil;
+        if (!is_mpfe) { // smbr.
+          int32 pdf = trans.TransitionIdToPdf(arc.ilabel),
+              ref_pdf = trans.TransitionIdToPdf(num_ali[cur_time]);
+          if (!one_silence_class)  // old behavior
+            frame_acc = (pdf == ref_pdf && !phone_is_sil) ? 1.0 : 0.0;
+          else
+            frame_acc = (pdf == ref_pdf || both_sil) ? 1.0 : 0.0;
+        } else {
+          if (!one_silence_class)  // old behavior
+            frame_acc = (phone == ref_phone && !phone_is_sil) ? 1.0 : 0.0;
+          else
+            frame_acc = (phone == ref_phone || both_sil) ? 1.0 : 0.0;
+        }
+      }
+      double arc_scale = Exp(alpha[s] + arc_like - alpha[arc.nextstate]);
+      alpha_smbr[arc.nextstate] += arc_scale * (alpha_smbr[s] + frame_acc);
+    }
+    Weight f = lat.Final(s);
+    if (f != Weight::Zero()) {
+      double final_like = this_alpha - (f.Value1() + f.Value2());
+      double arc_scale = Exp(final_like - tot_forward_prob);
+      tot_forward_score += arc_scale * alpha_smbr[s];
+      KALDI_ASSERT(state_times[s] == max_time &&
+                   "Lattice is inconsistent (final-prob not at max_time)");
+    }
+  }
+  // Second Pass Backward, collect Mpe style posteriors
+  for (StateId s = num_states-1; s >= 0; s--) {
+    for (ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_like = -ConvertToCost(arc.weight),
+          arc_beta = beta[arc.nextstate] + arc_like;
+      double frame_acc = 0.0;
+      int32 transition_id = arc.ilabel;
+      if (arc.ilabel != 0) {
+        int32 cur_time = state_times[s];
+        int32 phone = trans.TransitionIdToPhone(arc.ilabel),
+            ref_phone = trans.TransitionIdToPhone(num_ali[cur_time]);
+        bool phone_is_sil = std::binary_search(silence_phones.begin(),
+                                               silence_phones.end(), phone),
+            ref_phone_is_sil = std::binary_search(silence_phones.begin(),
+                                                  silence_phones.end(),
+                                                  ref_phone),
+            both_sil = phone_is_sil && ref_phone_is_sil;
+        if (!is_mpfe) { // smbr.
+          int32 pdf = trans.TransitionIdToPdf(arc.ilabel),
+              ref_pdf = trans.TransitionIdToPdf(num_ali[cur_time]);
+          if (!one_silence_class)  // old behavior
+            frame_acc = (pdf == ref_pdf && !phone_is_sil) ? 1.0 : 0.0;
+          else
+            frame_acc = (pdf == ref_pdf || both_sil) ? 1.0 : 0.0;
+        } else {
+          if (!one_silence_class)  // old behavior
+            frame_acc = (phone == ref_phone && !phone_is_sil) ? 1.0 : 0.0;
+          else
+            frame_acc = (phone == ref_phone || both_sil) ? 1.0 : 0.0;
+        }
+      }
+      double arc_scale = Exp(beta[arc.nextstate] + arc_like - beta[s]);
+      // check arc_scale NAN,
+      // this is to prevent partial paths in Lattices
+      // i.e., paths don't survive to the final state
+      if (KALDI_ISNAN(arc_scale)) arc_scale = 0;
+      beta_smbr[s] += arc_scale * (beta_smbr[arc.nextstate] + frame_acc);
+
+      if (transition_id != 0) { // Arc has a transition-id on it [not epsilon]
+        double posterior = Exp(alpha[s] + arc_beta - tot_forward_prob);
+        double acc_diff = alpha_smbr[s] + frame_acc + beta_smbr[arc.nextstate]
+                               - tot_forward_score;
+        double posterior_smbr = posterior * acc_diff;
+        (*post)[state_times[s]].push_back(std::make_pair(transition_id,
+                                                         static_cast<BaseFloat>(posterior_smbr)));
+      }
+    }
+  }
+
+  //Second Pass Forward Backward check
+  double tot_backward_score = beta_smbr[0];  // Initial state id == 0
+  // may loose the condition somehow here 1e-5/1e-4
+  if (!ApproxEqual(tot_forward_score, tot_backward_score, 1e-4)) {
+    KALDI_ERR << "Total forward score over lattice = " << tot_forward_score
+              << ", while total backward score = " << tot_backward_score;
+  }
+
+  // Output the computed posteriors
+  for (int32 t = 0; t < max_time; t++)
+    MergePairVectorSumming(&((*post)[t]));
+  return tot_forward_score;
+}
+
+bool CompactLatticeToWordAlignment(const CompactLattice &clat,
+                                   std::vector<int32> *words,
+                                   std::vector<int32> *begin_times,
+                                   std::vector<int32> *lengths) {
+  words->clear();
+  begin_times->clear();
+  lengths->clear();
+  typedef CompactLattice::Arc Arc;
+  typedef Arc::Label Label;
+  typedef CompactLattice::StateId StateId;
+  typedef CompactLattice::Weight Weight;
+  using namespace fst;
+  StateId state = clat.Start();
+  int32 cur_time = 0;
+  if (state == kNoStateId) {
+    KALDI_WARN << "Empty lattice.";
+    return false;
+  }
+  while (1) {
+    Weight final = clat.Final(state);
+    size_t num_arcs = clat.NumArcs(state);
+    if (final != Weight::Zero()) {
+      if (num_arcs != 0) {
+        KALDI_WARN << "Lattice is not linear.";
+        return false;
+      }
+      if (! final.String().empty()) {
+        KALDI_WARN << "Lattice has alignments on final-weight: probably "
+            "was not word-aligned (alignments will be approximate)";
+      }
+      return true;
+    } else {
+      if (num_arcs != 1) {
+        KALDI_WARN << "Lattice is not linear: num-arcs = " << num_arcs;
+        return false;
+      }
+      fst::ArcIterator<CompactLattice> aiter(clat, state);
+      const Arc &arc = aiter.Value();
+      Label word_id = arc.ilabel; // Note: ilabel==olabel, since acceptor.
+      // Also note: word_id may be zero; we output it anyway.
+      int32 length = arc.weight.String().size();
+      words->push_back(word_id);
+      begin_times->push_back(cur_time);
+      lengths->push_back(length);
+      cur_time += length;
+      state = arc.nextstate;
+    }
+  }
+}
+
+
+void CompactLatticeShortestPath(const CompactLattice &clat,
+                                CompactLattice *shortest_path) {
+  using namespace fst;
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    CompactLattice clat_copy(clat);
+    if (!TopSort(&clat_copy))
+      KALDI_ERR << "Was not able to topologically sort lattice (cycles found?)";
+    CompactLatticeShortestPath(clat_copy, shortest_path);
+    return;
+  }
+  // Now we can assume it's topologically sorted.
+  shortest_path->DeleteStates();
+  if (clat.Start() == kNoStateId) return;
+  typedef CompactLatticeArc Arc;
+  typedef Arc::StateId StateId;
+  typedef CompactLatticeWeight Weight;
+  vector<std::pair<double, StateId> > best_cost_and_pred(clat.NumStates() + 1);
+  StateId superfinal = clat.NumStates();
+  for (StateId s = 0; s <= clat.NumStates(); s++) {
+    best_cost_and_pred[s].first = std::numeric_limits<double>::infinity();
+    best_cost_and_pred[s].second = fst::kNoStateId;
+  }
+  best_cost_and_pred[clat.Start()].first = 0;
+  for (StateId s = 0; s < clat.NumStates(); s++) {
+    double my_cost = best_cost_and_pred[s].first;
+    for (ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done();
+         aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double arc_cost = ConvertToCost(arc.weight),
+          next_cost = my_cost + arc_cost;
+      if (next_cost < best_cost_and_pred[arc.nextstate].first) {
+        best_cost_and_pred[arc.nextstate].first = next_cost;
+        best_cost_and_pred[arc.nextstate].second = s;
+      }
+    }
+    double final_cost = ConvertToCost(clat.Final(s)),
+        tot_final = my_cost + final_cost;
+    if (tot_final < best_cost_and_pred[superfinal].first) {
+      best_cost_and_pred[superfinal].first = tot_final;
+      best_cost_and_pred[superfinal].second = s;
+    }
+  }
+  std::vector<StateId> states; // states on best path.
+  StateId cur_state = superfinal, start_state = clat.Start();
+  while (cur_state != start_state) {
+    StateId prev_state = best_cost_and_pred[cur_state].second;
+    if (prev_state == kNoStateId) {
+      KALDI_WARN << "Failure in best-path algorithm for lattice (infinite costs?)";
+      return; // return empty best-path.
+    }
+    states.push_back(prev_state);
+    KALDI_ASSERT(cur_state != prev_state && "Lattice with cycles");
+    cur_state = prev_state;
+  }
+  std::reverse(states.begin(), states.end());
+  for (size_t i = 0; i < states.size(); i++)
+    shortest_path->AddState();
+  for (StateId s = 0; static_cast<size_t>(s) < states.size(); s++) {
+    if (s == 0) shortest_path->SetStart(s);
+    if (static_cast<size_t>(s + 1) < states.size()) { // transition to next state.
+      bool have_arc = false;
+      Arc cur_arc;
+      for (ArcIterator<CompactLattice> aiter(clat, states[s]);
+           !aiter.Done();
+           aiter.Next()) {
+        const Arc &arc = aiter.Value();
+        if (arc.nextstate == states[s+1]) {
+          if (!have_arc ||
+              ConvertToCost(arc.weight) < ConvertToCost(cur_arc.weight)) {
+            cur_arc = arc;
+            have_arc = true;
+          }
+        }
+      }
+      KALDI_ASSERT(have_arc && "Code error.");
+      shortest_path->AddArc(s, Arc(cur_arc.ilabel, cur_arc.olabel,
+                                   cur_arc.weight, s+1));
+    } else { // final-prob.
+      shortest_path->SetFinal(s, clat.Final(states[s]));
+    }
+  }
+}
+
+
+void ExpandCompactLattice(const CompactLattice &clat,
+                          double epsilon,
+                          CompactLattice *expand_clat) {
+  using namespace fst;
+  typedef CompactLattice::Arc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+  typedef std::pair<StateId, StateId> StatePair;
+  typedef unordered_map<StatePair, StateId, PairHasher<StateId> > MapType;
+  typedef MapType::iterator IterType;
+
+  if (clat.Start() == kNoStateId) return;
+  // Make sure the input lattice is topologically sorted.
+  if (clat.Properties(kTopSorted, true) == 0) {
+    CompactLattice clat_copy(clat);
+    KALDI_LOG << "Topsort this lattice.";
+    if (!TopSort(&clat_copy))
+      KALDI_ERR << "Was not able to topologically sort lattice (cycles found?)";
+    ExpandCompactLattice(clat_copy, epsilon, expand_clat);
+    return;
+  }
+
+  // Compute backward logprobs betas for the expanded lattice.
+  // Note: the backward logprobs in the original lattice <clat> and the
+  // expanded lattice <expand_clat> are the same.
+  int32 num_states = clat.NumStates();
+  std::vector<double> beta(num_states, kLogZeroDouble);
+  ComputeCompactLatticeBetas(clat, &beta);
+  double tot_backward_logprob = beta[0];
+  std::vector<double> alpha;
+  alpha.push_back(0.0);
+  expand_clat->DeleteStates();
+  MapType state_map; // Map from state pair (orig_state, copy_state) to
+  // copy_state, where orig_state is a state in the original lattice, and
+  // copy_state is its corresponding one in the expanded lattice.
+  unordered_map<StateId, StateId> states; // Map from orig_state to its
+  // copy_state for states with incoming arcs' posteriors <= epsilon.
+  std::queue<StatePair> state_queue;
+
+  // Set start state in the expanded lattice.
+  StateId start_state = expand_clat->AddState();
+  expand_clat->SetStart(start_state);
+  StatePair start_pair(clat.Start(), start_state);
+  state_queue.push(start_pair);
+  std::pair<IterType, bool> result =
+    state_map.insert(std::make_pair(start_pair, start_state));
+  KALDI_ASSERT(result.second == true);
+
+  // Expand <clat> and update forward logprobs alphas in <expand_clat>.
+  while (!state_queue.empty()) {
+    StatePair s = state_queue.front();
+    StateId s1 = s.first,
+            s2 = s.second;
+    state_queue.pop();
+
+    Weight f = clat.Final(s1);
+    if (f != Weight::Zero()) {
+      KALDI_ASSERT(state_map.find(s) != state_map.end());
+      expand_clat->SetFinal(state_map[s], f);
+    }
+
+    for (ArcIterator<CompactLattice> aiter(clat, s1);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      StateId orig_state = arc.nextstate;
+      double arc_like = -ConvertToCost(arc.weight),
+             this_alpha = alpha[s2] + arc_like,
+             arc_post = Exp(this_alpha + beta[orig_state] -
+                            tot_backward_logprob);
+      // Generate the expanded lattice.
+      StateId copy_state;
+      if (arc_post > epsilon) {
+        copy_state = expand_clat->AddState();
+        StatePair next_pair(orig_state, copy_state);
+        std::pair<IterType, bool> result =
+          state_map.insert(std::make_pair(next_pair, copy_state));
+        KALDI_ASSERT(result.second == true);
+        state_queue.push(next_pair);
+      } else {
+        unordered_map<StateId, StateId>::iterator iter = states.find(orig_state);
+        if (iter == states.end() ) { // The counterpart state of orig_state
+                                   // has not been created in <expand_clat> yet.
+          copy_state = expand_clat->AddState();
+          StatePair next_pair(orig_state, copy_state);
+          std::pair<IterType, bool> result =
+            state_map.insert(std::make_pair(next_pair, copy_state));
+          KALDI_ASSERT(result.second == true);
+          state_queue.push(next_pair);
+          states[orig_state] = copy_state;
+        } else {
+          copy_state = iter->second;
+        }
+      }
+      // Create an arc from state_map[s] to copy_state in the expanded lattice.
+      expand_clat->AddArc(state_map[s], Arc(arc.ilabel, arc.olabel, arc.weight,
+                                            copy_state));
+      // Compute forward logprobs alpha for the expanded lattice.
+      if ((alpha.size() - 1) < copy_state) { // The first time to compute alpha
+                                             // for copy_state in <expand_clat>.
+        alpha.push_back(this_alpha);
+      } else { // Accumulate alpha.
+        alpha[copy_state] = LogAdd(alpha[copy_state], this_alpha);
+      }
+    }
+  } // end while
+}
+
+
+void CompactLatticeBestCostsAndTracebacks(
+    const CompactLattice &clat,
+    CostTraceType *forward_best_cost_and_pred,
+    CostTraceType *backward_best_cost_and_pred) {
+
+  // typedef the arc, weight types
+  typedef CompactLatticeArc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+
+  forward_best_cost_and_pred->clear();
+  backward_best_cost_and_pred->clear();
+  forward_best_cost_and_pred->resize(clat.NumStates());
+  backward_best_cost_and_pred->resize(clat.NumStates());
+  // Initialize the cost and predecessor state for each state.
+  for (StateId s = 0; s < clat.NumStates(); s++) {
+    (*forward_best_cost_and_pred)[s].first =
+                                        std::numeric_limits<double>::infinity();
+    (*backward_best_cost_and_pred)[s].first =
+                                        std::numeric_limits<double>::infinity();
+    (*forward_best_cost_and_pred)[s].second = fst::kNoStateId;
+    (*backward_best_cost_and_pred)[s].second = fst::kNoStateId;
+  }
+
+  StateId start_state = clat.Start();
+  (*forward_best_cost_and_pred)[start_state].first = 0;
+  // Transverse the lattice forwardly to compute the best cost from the start
+  // state to each state and the best predecessor state of each state.
+  for (StateId s = 0; s < clat.NumStates(); s++) {
+    double cur_cost = (*forward_best_cost_and_pred)[s].first;
+    for (fst::ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double next_cost = cur_cost + ConvertToCost(arc.weight);
+      if (next_cost < (*forward_best_cost_and_pred)[arc.nextstate].first) {
+        (*forward_best_cost_and_pred)[arc.nextstate].first = next_cost;
+        (*forward_best_cost_and_pred)[arc.nextstate].second = s;
+      }
+    }
+  }
+  // Transverse the lattice backwardly to compute the best cost from a final
+  // state to each state and the best predecessor state of each state.
+  for (StateId s = clat.NumStates() - 1; s >= 0; s--) {
+    double this_cost = ConvertToCost(clat.Final(s));
+    for (fst::ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      double next_cost = (*backward_best_cost_and_pred)[arc.nextstate].first +
+        ConvertToCost(arc.weight);
+      if (next_cost < this_cost) {
+        this_cost = next_cost;
+        (*backward_best_cost_and_pred)[s].second = arc.nextstate;
+      }
+    }
+    (*backward_best_cost_and_pred)[s].first = this_cost;
+  }
+}
+
+
+void AddNnlmScoreToCompactLattice(const MapT &nnlm_scores,
+                                  CompactLattice *clat) {
+  if (clat->Start() == fst::kNoStateId) return;
+  // Make sure the input lattice is topologically sorted.
+  if (clat->Properties(fst::kTopSorted, true) == 0) {
+    KALDI_LOG << "Topsort this lattice.";
+    if (!TopSort(clat))
+      KALDI_ERR << "Was not able to topologically sort lattice (cycles found?)";
+    AddNnlmScoreToCompactLattice(nnlm_scores, clat);
+    return;
+  }
+
+  // typedef the arc, weight types
+  typedef CompactLatticeArc Arc;
+  typedef Arc::Weight Weight;
+  typedef Arc::StateId StateId;
+  typedef std::pair<int32, int32> StatePair;
+
+  int32 num_states = clat->NumStates();
+  unordered_map<StatePair, bool, PairHasher<int32> > final_state_check;
+  for (StateId s = 0; s < num_states; s++) {
+    for (fst::MutableArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      Arc arc(aiter.Value());
+      StatePair arc_index = std::make_pair(static_cast<int32>(s),
+                                           static_cast<int32>(arc.nextstate));
+      MapT::const_iterator it = nnlm_scores.find(arc_index);
+      double nnlm_score;
+      if (it != nnlm_scores.end())
+        nnlm_score = it->second;
+      else
+        KALDI_ERR << "Some arc does not have neural language model score.";
+      if (arc.ilabel != 0) { // if there is a word on this arc
+        LatticeWeight weight = arc.weight.Weight();
+        // Add associated neural LM score to each arc.
+        weight.SetValue1(weight.Value1() + nnlm_score);
+        arc.weight.SetWeight(weight);
+        aiter.SetValue(arc);
+      }
+      Weight clat_final = clat->Final(arc.nextstate);
+      StatePair final_pair = std::make_pair(arc.nextstate, arc.nextstate);
+      // Add neural LM scores to each final state only once.
+      if (clat_final != CompactLatticeWeight::Zero() &&
+          final_state_check.find(final_pair) == final_state_check.end()) {
+        MapT::const_iterator final_it = nnlm_scores.find(final_pair);
+        double final_nnlm_score = 0.0;
+        if (final_it != nnlm_scores.end())
+          final_nnlm_score = final_it->second;
+        // Add neural LM scores to the final weight.
+        Weight final_weight(LatticeWeight(clat_final.Weight().Value1() +
+                                          final_nnlm_score,
+                                          clat_final.Weight().Value2()),
+                                          clat_final.String());
+        clat->SetFinal(arc.nextstate, final_weight);
+        final_state_check[final_pair] = true;
+      }
+    } // end looping over arcs
+  } // end looping over states
+}
+
+void AddWordInsPenToCompactLattice(BaseFloat word_ins_penalty,
+                                   CompactLattice *clat) {
+  typedef CompactLatticeArc Arc;
+  int32 num_states = clat->NumStates();
+
+  //scan the lattice
+  for (int32 state = 0; state < num_states; state++) {
+    for (fst::MutableArcIterator<CompactLattice> aiter(clat, state);
+         !aiter.Done(); aiter.Next()) {
+
+      Arc arc(aiter.Value());
+
+      if (arc.ilabel != 0) { // if there is a word on this arc
+        LatticeWeight weight = arc.weight.Weight();
+        // add word insertion penalty to lattice
+        weight.SetValue1( weight.Value1() + word_ins_penalty);
+        arc.weight.SetWeight(weight);
+        aiter.SetValue(arc);
+      }
+    } // end looping over arcs
+  }  // end looping over states
+}
+
+struct ClatRescoreTuple {
+  ClatRescoreTuple(int32 state, int32 arc, int32 tid):
+      state_id(state), arc_id(arc), tid(tid) { }
+  int32 state_id;
+  int32 arc_id;
+  int32 tid;
+};
+
+/** RescoreCompactLatticeInternal is the internal code for both
+    RescoreCompactLattice and RescoreCompatLatticeSpeedup.  For
+    RescoreCompactLattice, "tmodel" will be NULL and speedup_factor will be 1.0.
+ */
+bool RescoreCompactLatticeInternal(
+    const TransitionInformation *tmodel,
+    BaseFloat speedup_factor,
+    DecodableInterface *decodable,
+    CompactLattice *clat) {
+  KALDI_ASSERT(speedup_factor >= 1.0);
+  if (clat->NumStates() == 0) {
+    KALDI_WARN << "Rescoring empty lattice";
+    return false;
+  }
+  if (!clat->Properties(fst::kTopSorted, true)) {
+    if (fst::TopSort(clat) == false) {
+      KALDI_WARN << "Cycles detected in lattice.";
+      return false;
+    }
+  }
+  std::vector<int32> state_times;
+  int32 utt_len = kaldi::CompactLatticeStateTimes(*clat, &state_times);
+
+  std::vector<std::vector<ClatRescoreTuple> > time_to_state(utt_len);
+
+  int32 num_states = clat->NumStates();
+  KALDI_ASSERT(num_states == state_times.size());
+  for (size_t state = 0; state < num_states; state++) {
+    KALDI_ASSERT(state_times[state] >= 0);
+    int32 t = state_times[state];
+    int32 arc_id = 0;
+    for (fst::MutableArcIterator<CompactLattice> aiter(clat, state);
+         !aiter.Done(); aiter.Next(), arc_id++) {
+      CompactLatticeArc arc = aiter.Value();
+      std::vector<int32> arc_string = arc.weight.String();
+
+      for (size_t offset = 0; offset < arc_string.size(); offset++) {
+        if (t < utt_len) { // end state may be past this..
+          int32 tid = arc_string[offset];
+          time_to_state[t+offset].push_back(ClatRescoreTuple(state, arc_id, tid));
+        } else {
+          if (t != utt_len) {
+            KALDI_WARN << "There appears to be lattice/feature mismatch, "
+                       << "aborting.";
+            return false;
+          }
+        }
+      }
+    }
+    if (clat->Final(state) != CompactLatticeWeight::Zero()) {
+      arc_id = -1;
+      std::vector<int32> arc_string = clat->Final(state).String();
+      for (size_t offset = 0; offset < arc_string.size(); offset++) {
+        KALDI_ASSERT(t + offset < utt_len); // already checked in
+        // CompactLatticeStateTimes, so would be code error.
+        time_to_state[t+offset].push_back(
+            ClatRescoreTuple(state, arc_id, arc_string[offset]));
+      }
+    }
+  }
+
+  for (int32 t = 0; t < utt_len; t++) {
+    if ((t < utt_len - 1) && decodable->IsLastFrame(t)) {
+      KALDI_WARN << "Features are too short for lattice: utt-len is "
+                 << utt_len << ", " << t << " is last frame";
+      return false;
+    }
+    // frame_scale is the scale we put on the computed acoustic probs for this
+    // frame.  It will always be 1.0 if tmodel == NULL (i.e. if we are not doing
+    // the "speedup" code).  For frames with multiple pdf-ids it will be one.
+    // For frames with only one pdf-id, it will equal speedup_factor (>=1.0)
+    // with probability 1.0 / speedup_factor, and zero otherwise.  If it is zero,
+    // we can avoid computing the probabilities.
+    BaseFloat frame_scale = 1.0;
+    KALDI_ASSERT(!time_to_state[t].empty());
+    if (tmodel != NULL) {
+      int32 pdf_id = tmodel->TransitionIdToPdf(time_to_state[t][0].tid);
+      bool frame_has_multiple_pdfs = false;
+      for (size_t i = 1; i < time_to_state[t].size(); i++) {
+        if (tmodel->TransitionIdToPdf(time_to_state[t][i].tid) != pdf_id) {
+          frame_has_multiple_pdfs = true;
+          break;
+        }
+      }
+      if (frame_has_multiple_pdfs) {
+        frame_scale = 1.0;
+      } else {
+        if (WithProb(1.0 / speedup_factor)) {
+          frame_scale = speedup_factor;
+        } else {
+          frame_scale = 0.0;
+        }
+      }
+      if (frame_scale == 0.0)
+        continue; // the code below would be pointless.
+    }
+
+    for (size_t i = 0; i < time_to_state[t].size(); i++) {
+      int32 state = time_to_state[t][i].state_id;
+      int32 arc_id = time_to_state[t][i].arc_id;
+      int32 tid = time_to_state[t][i].tid;
+
+      if (arc_id == -1) { // Final state
+        // Access the trans_id
+        CompactLatticeWeight curr_clat_weight = clat->Final(state);
+
+        // Calculate likelihood
+        BaseFloat log_like = decodable->LogLikelihood(t, tid) * frame_scale;
+        // update weight
+        CompactLatticeWeight new_clat_weight = curr_clat_weight;
+        LatticeWeight new_lat_weight = new_clat_weight.Weight();
+        new_lat_weight.SetValue2(-log_like + curr_clat_weight.Weight().Value2());
+        new_clat_weight.SetWeight(new_lat_weight);
+        clat->SetFinal(state, new_clat_weight);
+      } else {
+        fst::MutableArcIterator<CompactLattice> aiter(clat, state);
+
+        aiter.Seek(arc_id);
+        CompactLatticeArc arc = aiter.Value();
+
+        // Calculate likelihood
+        BaseFloat log_like = decodable->LogLikelihood(t, tid) * frame_scale;
+        // update weight
+        LatticeWeight new_weight = arc.weight.Weight();
+        new_weight.SetValue2(-log_like + arc.weight.Weight().Value2());
+        arc.weight.SetWeight(new_weight);
+        aiter.SetValue(arc);
+      }
+    }
+  }
+  return true;
+}
+
+
+bool RescoreCompactLatticeSpeedup(
+    const TransitionInformation &tmodel,
+    BaseFloat speedup_factor,
+    DecodableInterface *decodable,
+    CompactLattice *clat) {
+  return RescoreCompactLatticeInternal(&tmodel, speedup_factor, decodable, clat);
+}
+
+bool RescoreCompactLattice(DecodableInterface *decodable,
+                           CompactLattice *clat) {
+  return RescoreCompactLatticeInternal(NULL, 1.0, decodable, clat);
+}
+
+
+bool RescoreLattice(DecodableInterface *decodable,
+                    Lattice *lat) {
+  if (lat->NumStates() == 0) {
+    KALDI_WARN << "Rescoring empty lattice";
+    return false;
+  }
+  if (!lat->Properties(fst::kTopSorted, true)) {
+    if (fst::TopSort(lat) == false) {
+      KALDI_WARN << "Cycles detected in lattice.";
+      return false;
+    }
+  }
+  std::vector<int32> state_times;
+  int32 utt_len = kaldi::LatticeStateTimes(*lat, &state_times);
+
+  std::vector<std::vector<int32> > time_to_state(utt_len );
+
+  int32 num_states = lat->NumStates();
+  KALDI_ASSERT(num_states == state_times.size());
+  for (size_t state = 0; state < num_states; state++) {
+    int32 t = state_times[state];
+    // Don't check t >= 0 because non-accessible states could have t = -1.
+    KALDI_ASSERT(t <= utt_len);
+    if (t >= 0 && t < utt_len)
+      time_to_state[t].push_back(state);
+  }
+
+  for (int32 t = 0; t < utt_len; t++) {
+    if ((t < utt_len - 1) && decodable->IsLastFrame(t)) {
+      KALDI_WARN << "Features are too short for lattice: utt-len is "
+                 << utt_len << ", " << t << " is last frame";
+      return false;
+    }
+    for (size_t i = 0; i < time_to_state[t].size(); i++) {
+      int32 state = time_to_state[t][i];
+      for (fst::MutableArcIterator<Lattice> aiter(lat, state);
+           !aiter.Done(); aiter.Next()) {
+        LatticeArc arc = aiter.Value();
+        if (arc.ilabel != 0) {
+          int32 trans_id = arc.ilabel; // Note: it doesn't necessarily
+          // have to be a transition-id, just whatever the Decodable
+          // object is expecting, but it's normally a transition-id.
+
+          BaseFloat log_like = decodable->LogLikelihood(t, trans_id);
+          arc.weight.SetValue2(-log_like + arc.weight.Value2());
+          aiter.SetValue(arc);
+        }
+      }
+    }
+  }
+  return true;
+}
+
+
+int32 LongestSentenceLength(const Lattice &lat) {
+  typedef Lattice::Arc Arc;
+  typedef Arc::Label Label;
+  typedef Arc::StateId StateId;
+
+  if (lat.Properties(fst::kTopSorted, true) == 0) {
+    Lattice lat_copy(lat);
+    if (!TopSort(&lat_copy))
+      KALDI_ERR << "Was not able to topologically sort lattice (cycles found?)";
+    return LongestSentenceLength(lat_copy);
+  }
+  std::vector<int32> max_length(lat.NumStates(), 0);
+  int32 lattice_max_length = 0;
+  for (StateId s = 0; s < lat.NumStates(); s++) {
+    int32 this_max_length = max_length[s];
+    for (fst::ArcIterator<Lattice> aiter(lat, s); !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      bool arc_has_word = (arc.olabel != 0);
+      StateId nextstate = arc.nextstate;
+      KALDI_ASSERT(static_cast<size_t>(nextstate) < max_length.size());
+      if (arc_has_word) {
+        // A lattice should ideally not have cycles anyway; a cycle with a word
+        // on is something very bad.
+        KALDI_ASSERT(nextstate > s && "Lattice has cycles with words on.");
+        max_length[nextstate] = std::max(max_length[nextstate],
+                                         this_max_length + 1);
+      } else {
+        max_length[nextstate] = std::max(max_length[nextstate],
+                                         this_max_length);
+      }
+    }
+    if (lat.Final(s) != LatticeWeight::Zero())
+      lattice_max_length = std::max(lattice_max_length, max_length[s]);
+  }
+  return lattice_max_length;
+}
+
+int32 LongestSentenceLength(const CompactLattice &clat) {
+  typedef CompactLattice::Arc Arc;
+  typedef Arc::Label Label;
+  typedef Arc::StateId StateId;
+
+  if (clat.Properties(fst::kTopSorted, true) == 0) {
+    CompactLattice clat_copy(clat);
+    if (!TopSort(&clat_copy))
+      KALDI_ERR << "Was not able to topologically sort lattice (cycles found?)";
+    return LongestSentenceLength(clat_copy);
+  }
+  std::vector<int32> max_length(clat.NumStates(), 0);
+  int32 lattice_max_length = 0;
+  for (StateId s = 0; s < clat.NumStates(); s++) {
+    int32 this_max_length = max_length[s];
+    for (fst::ArcIterator<CompactLattice> aiter(clat, s);
+         !aiter.Done(); aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      bool arc_has_word = (arc.ilabel != 0); // note: olabel == ilabel.
+      // also note: for normal CompactLattice, e.g. as produced by
+      // determinization, all arcs will have nonzero labels, but the user might
+      // decide to remplace some of the labels with zero for some reason, and we
+      // want to support this.
+      StateId nextstate = arc.nextstate;
+      KALDI_ASSERT(static_cast<size_t>(nextstate) < max_length.size());
+      KALDI_ASSERT(nextstate > s && "CompactLattice has cycles");
+      if (arc_has_word)
+        max_length[nextstate] = std::max(max_length[nextstate],
+                                         this_max_length + 1);
+      else
+        max_length[nextstate] = std::max(max_length[nextstate],
+                                         this_max_length);
+    }
+    if (clat.Final(s) != CompactLatticeWeight::Zero())
+      lattice_max_length = std::max(lattice_max_length, max_length[s]);
+  }
+  return lattice_max_length;
+}
+
+void ComposeCompactLatticeDeterministic(
+    const CompactLattice& clat,
+    fst::DeterministicOnDemandFst<fst::StdArc>* det_fst,
+    CompactLattice* composed_clat) {
+  // StdFst::Arc and CompactLatticeArc has the same StateId type.
+  typedef fst::StdArc::StateId StateId;
+  typedef fst::StdArc::Weight Weight1;
+  typedef CompactLatticeArc::Weight Weight2;
+  typedef std::pair<StateId, StateId> StatePair;
+  typedef unordered_map<StatePair, StateId, PairHasher<StateId> > MapType;
+  typedef MapType::iterator IterType;
+
+  // Empties the output FST.
+  KALDI_ASSERT(composed_clat != NULL);
+  composed_clat->DeleteStates();
+
+  MapType state_map;
+  std::queue<StatePair> state_queue;
+
+  // Sets start state in <composed_clat>.
+  StateId start_state = composed_clat->AddState();
+  StatePair start_pair(clat.Start(), det_fst->Start());
+  composed_clat->SetStart(start_state);
+  state_queue.push(start_pair);
+  std::pair<IterType, bool> result =
+      state_map.insert(std::make_pair(start_pair, start_state));
+  KALDI_ASSERT(result.second == true);
+
+  // Starts composition here.
+  while (!state_queue.empty()) {
+    // Gets the first state in the queue.
+    StatePair s = state_queue.front();
+    StateId s1 = s.first;
+    StateId s2 = s.second;
+    state_queue.pop();
+
+
+    Weight2 clat_final = clat.Final(s1);
+    if (clat_final.Weight().Value1() !=
+        std::numeric_limits<BaseFloat>::infinity()) {
+      // Test for whether the final-prob of state s1 was zero.
+      Weight1 det_fst_final = det_fst->Final(s2);
+      if (det_fst_final.Value() !=
+          std::numeric_limits<BaseFloat>::infinity()) {
+        // Test for whether the final-prob of state s2 was zero.  If neither
+        // source-state final prob was zero, then we should create final state
+        // in fst_composed. We compute the product manually since this is more
+        // efficient.
+        Weight2 final_weight(LatticeWeight(clat_final.Weight().Value1() +
+                                           det_fst_final.Value(),
+                                           clat_final.Weight().Value2()),
+                             clat_final.String());
+        // we can assume final_weight is not Zero(), since neither of
+        // the sources was zero.
+        KALDI_ASSERT(state_map.find(s) != state_map.end());
+        composed_clat->SetFinal(state_map[s], final_weight);
+      }
+    }
+
+    // Loops over pair of edges at s1 and s2.
+    for (fst::ArcIterator<CompactLattice> aiter(clat, s1);
+         !aiter.Done(); aiter.Next()) {
+      const CompactLatticeArc& arc1 = aiter.Value();
+      fst::StdArc arc2;
+      StateId next_state1 = arc1.nextstate, next_state2;
+      bool matched = false;
+
+      if (arc1.olabel == 0) {
+        // If the symbol on <arc1> is <epsilon>, we transit to the next state
+        // for <clat>, but keep <det_fst> at the current state.
+        matched = true;
+        next_state2 = s2;
+      } else {
+        // Otherwise try to find the matched arc in <det_fst>.
+        matched = det_fst->GetArc(s2, arc1.olabel, &arc2);
+        if (matched) {
+          next_state2 = arc2.nextstate;
+        }
+      }
+
+      // If matched arc is found in <det_fst>, then we have to add new arcs to
+      // <composed_clat>.
+      if (matched) {
+        StatePair next_state_pair(next_state1, next_state2);
+        IterType siter = state_map.find(next_state_pair);
+        StateId next_state;
+
+        // Adds composed state to <state_map>.
+        if (siter == state_map.end()) {
+          // If the composed state has not been created yet, create it.
+          next_state = composed_clat->AddState();
+          std::pair<const StatePair, StateId> next_state_map(next_state_pair,
+                                                             next_state);
+          std::pair<IterType, bool> result = state_map.insert(next_state_map);
+          KALDI_ASSERT(result.second);
+          state_queue.push(next_state_pair);
+        } else {
+          // If the composed state is already in <state_map>, we can directly
+          // use that.
+          next_state = siter->second;
+        }
+
+        // Adds arc to <composed_clat>.
+        if (arc1.olabel == 0) {
+          composed_clat->AddArc(state_map[s],
+                                CompactLatticeArc(arc1.ilabel, 0,
+                                                  arc1.weight, next_state));
+        } else {
+          Weight2 composed_weight(
+              LatticeWeight(arc1.weight.Weight().Value1() +
+                            arc2.weight.Value(),
+                            arc1.weight.Weight().Value2()),
+              arc1.weight.String());
+          composed_clat->AddArc(state_map[s],
+                                CompactLatticeArc(arc1.ilabel, arc2.olabel,
+                                                  composed_weight, next_state));
+        }
+      }
+    }
+  }
+  fst::Connect(composed_clat);
+}
+
+
+void ComputeAcousticScoresMap(
+    const Lattice &lat,
+    unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+                                        PairHasher<int32> > *acoustic_scores) {
+  // typedef the arc, weight types
+  typedef Lattice::Arc Arc;
+  typedef Arc::Weight LatticeWeight;
+  typedef Arc::StateId StateId;
+
+  acoustic_scores->clear();
+
+  std::vector<int32> state_times;
+  LatticeStateTimes(lat, &state_times);   // Assumes the input is top sorted
+
+  KALDI_ASSERT(lat.Start() == 0);
+
+  for (StateId s = 0; s < lat.NumStates(); s++) {
+    int32 t = state_times[s];
+    for (fst::ArcIterator<Lattice> aiter(lat, s); !aiter.Done();
+          aiter.Next()) {
+      const Arc &arc = aiter.Value();
+      const LatticeWeight &weight = arc.weight;
+
+      int32 tid = arc.ilabel;
+
+      if (tid != 0) {
+        unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+          PairHasher<int32> >::iterator it = acoustic_scores->find(std::make_pair(t, tid));
+        if (it == acoustic_scores->end()) {
+          acoustic_scores->insert(std::make_pair(std::make_pair(t, tid),
+                                          std::make_pair(weight.Value2(), 1)));
+        } else {
+          if (it->second.second == 2
+                && it->second.first / it->second.second != weight.Value2()) {
+            KALDI_VLOG(2) << "Transitions on the same frame have different "
+                          << "acoustic costs for tid " << tid << "; "
+                          << it->second.first / it->second.second
+                          << " vs " << weight.Value2();
+          }
+          it->second.first += weight.Value2();
+          it->second.second++;
+        }
+      } else {
+        // Arcs with epsilon input label (tid) must have 0 acoustic cost
+        KALDI_ASSERT(weight.Value2() == 0);
+      }
+    }
+
+    LatticeWeight f = lat.Final(s);
+    if (f != LatticeWeight::Zero()) {
+      // Final acoustic cost must be 0 as we are reading from
+      // non-determinized, non-compact lattice
+      KALDI_ASSERT(f.Value2() == 0.0);
+    }
+  }
+}
+
+void ReplaceAcousticScoresFromMap(
+    const unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+                                        PairHasher<int32> > &acoustic_scores,
+    Lattice *lat) {
+  // typedef the arc, weight types
+  typedef Lattice::Arc Arc;
+  typedef Arc::Weight LatticeWeight;
+  typedef Arc::StateId StateId;
+
+  TopSortLatticeIfNeeded(lat);
+
+  std::vector<int32> state_times;
+  LatticeStateTimes(*lat, &state_times);
+
+  KALDI_ASSERT(lat->Start() == 0);
+
+  for (StateId s = 0; s < lat->NumStates(); s++) {
+    int32 t = state_times[s];
+    for (fst::MutableArcIterator<Lattice> aiter(lat, s);
+         !aiter.Done(); aiter.Next()) {
+      Arc arc(aiter.Value());
+
+      int32 tid = arc.ilabel;
+      if (tid != 0) {
+        unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+          PairHasher<int32> >::const_iterator it = acoustic_scores.find(std::make_pair(t, tid));
+        if (it == acoustic_scores.end()) {
+          KALDI_ERR << "Could not find tid " << tid << " at time " << t
+                    << " in the acoustic scores map.";
+        } else {
+          arc.weight.SetValue2(it->second.first / it->second.second);
+        }
+      } else {
+        // For epsilon arcs, set acoustic cost to 0.0
+        arc.weight.SetValue2(0.0);
+      }
+      aiter.SetValue(arc);
+    }
+
+    LatticeWeight f = lat->Final(s);
+    if (f != LatticeWeight::Zero()) {
+      // Set final acoustic cost to 0.0
+      f.SetValue2(0.0);
+      lat->SetFinal(s, f);
+    }
+  }
+}
+
+}  // namespace kaldi

speechx/speechx/kaldi/lat/lattice-functions.h

+// lat/lattice-functions.h
+
+// Copyright 2009-2012   Saarland University (author: Arnab Ghoshal)
+//           2012-2013   Johns Hopkins University (Author: Daniel Povey);
+//                       Bagher BabaAli
+//                2014   Guoguo Chen
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+
+#ifndef KALDI_LAT_LATTICE_FUNCTIONS_H_
+#define KALDI_LAT_LATTICE_FUNCTIONS_H_
+
+#include <vector>
+#include <map>
+
+#include "base/kaldi-common.h"
+#include "fstext/fstext-lib.h"
+#include "itf/decodable-itf.h"
+#include "itf/transition-information.h"
+#include "lat/kaldi-lattice.h"
+
+namespace kaldi {
+
+// Redundant with the typedef in hmm/posterior.h. We want functions
+// using the Posterior type to be usable without a dependency on the
+// hmm library.
+typedef std::vector<std::vector<std::pair<int32, BaseFloat> > > Posterior;
+
+/**
+   This function extracts the per-frame log likelihoods from a linear
+   lattice (which we refer to as an 'nbest' lattice elsewhere in Kaldi code).
+   The dimension of *per_frame_loglikes will be set to the
+   number of input symbols in 'nbest'.  The elements of
+   '*per_frame_loglikes' will be set to the .Value2() elements of the lattice
+   weights, which represent the acoustic costs; you may want to scale this
+   vector afterward by -1/acoustic_scale to get the original loglikes.
+   If there are acoustic costs on input-epsilon arcs or the final-prob in 'nbest'
+   (and this should not normally be the case in situations where it makes
+   sense to call this function), they will be included to the cost of the
+   preceding input symbol, or the following input symbol for input-epsilons
+   encountered prior to any input symbol.  If 'nbest' has no input symbols,
+   'per_frame_loglikes' will be set to the empty vector.
+**/
+void GetPerFrameAcousticCosts(const Lattice &nbest,
+                              Vector<BaseFloat> *per_frame_loglikes);
+
+/// This function iterates over the states of a topologically sorted lattice and
+/// counts the time instance corresponding to each state. The times are returned
+/// in a vector of integers 'times' which is resized to have a size equal to the
+/// number of states in the lattice. The function also returns the maximum time
+/// in the lattice (this will equal the number of frames in the file).
+int32 LatticeStateTimes(const Lattice &lat, std::vector<int32> *times);
+
+/// As LatticeStateTimes, but in the CompactLattice format.  Note: must
+/// be topologically sorted.  Returns length of the utterance in frames, which
+/// might not be the same as the maximum time in the lattice, due to frames
+/// in the final-prob.
+int32 CompactLatticeStateTimes(const CompactLattice &clat,
+                               std::vector<int32> *times);
+
+/// This function does the forward-backward over lattices and computes the
+/// posterior probabilities of the arcs. It returns the total log-probability
+/// of the lattice.  The Posterior quantities contain pairs of (transition-id, weight)
+/// on each frame.
+/// If the pointer "acoustic_like_sum" is provided, this value is set to
+/// the sum over the arcs, of the posterior of the arc times the
+/// acoustic likelihood [i.e. negated acoustic score] on that link.
+/// This is used in combination with other quantities to work out
+/// the objective function in MMI discriminative training.
+BaseFloat LatticeForwardBackward(const Lattice &lat,
+                                 Posterior *arc_post,
+                                 double *acoustic_like_sum = NULL);
+
+// This function is something similar to LatticeForwardBackward(), but it is on
+// the CompactLattice lattice format. Also we only need the alpha in the forward
+// path, not the posteriors.
+bool ComputeCompactLatticeAlphas(const CompactLattice &lat,
+                                 std::vector<double> *alpha);
+
+// A sibling of the function CompactLatticeAlphas()... We compute the beta from
+// the backward path here.
+bool ComputeCompactLatticeBetas(const CompactLattice &lat,
+                                std::vector<double> *beta);
+
+
+// Computes (normal or Viterbi) alphas and betas; returns (total-prob, or
+// best-path negated cost) Note: in either case, the alphas and betas are
+// negated costs.  Requires that lat be topologically sorted.  This code
+// will work for either CompactLattice or Lattice.
+template<typename LatticeType>
+double ComputeLatticeAlphasAndBetas(const LatticeType &lat,
+                                    bool viterbi,
+                                    std::vector<double> *alpha,
+                                    std::vector<double> *beta);
+
+
+/// Topologically sort the compact lattice if not already topologically sorted.
+/// Will crash if the lattice cannot be topologically sorted.
+void TopSortCompactLatticeIfNeeded(CompactLattice *clat);
+
+
+/// Topologically sort the lattice if not already topologically sorted.
+/// Will crash if lattice cannot be topologically sorted.
+void TopSortLatticeIfNeeded(Lattice *clat);
+
+/// Returns the depth of the lattice, defined as the average number of arcs (or
+/// final-prob strings) crossing any given frame.  Returns 1 for empty lattices.
+/// Requires that clat is topologically sorted!
+BaseFloat CompactLatticeDepth(const CompactLattice &clat,
+                              int32 *num_frames = NULL);
+
+/// This function returns, for each frame, the number of arcs crossing that
+/// frame.
+void CompactLatticeDepthPerFrame(const CompactLattice &clat,
+                                 std::vector<int32> *depth_per_frame);
+
+
+/// This function limits the depth of the lattice, per frame: that means, it
+/// does not allow more than a specified number of arcs active on any given
+/// frame.  This can be used to reduce the size of the "very deep" portions of
+/// the lattice.
+void CompactLatticeLimitDepth(int32 max_arcs_per_frame,
+                              CompactLattice *clat);
+
+
+/// Given a lattice, and a transition model to map pdf-ids to phones,
+/// outputs for each frame the set of phones active on that frame.  If
+/// sil_phones (which must be sorted and uniq) is nonempty, it excludes
+/// phones in this list.
+void LatticeActivePhones(const Lattice &lat, const TransitionInformation &trans,
+                         const std::vector<int32> &sil_phones,
+                         std::vector<std::set<int32> > *active_phones);
+
+/// Given a lattice, and a transition model to map pdf-ids to phones,
+/// replace the output symbols (presumably words), with phones; we
+/// use the TransitionModel to work out the phone sequence.  Note
+/// that the phone labels are not exactly aligned with the phone
+/// boundaries.  We put a phone label to coincide with any transition
+/// to the final, nonemitting state of a phone (this state always exists,
+/// we ensure this in HmmTopology::Check()).  This would be the last
+/// transition-id in the phone if reordering is not done (but typically
+/// we do reorder).
+/// Also see PhoneAlignLattice, in phone-align-lattice.h.
+void ConvertLatticeToPhones(const TransitionInformation &trans_model,
+                            Lattice *lat);
+
+/// Prunes a lattice or compact lattice.  Returns true on success, false if
+/// there was some kind of failure.
+template<class LatticeType>
+bool PruneLattice(BaseFloat beam, LatticeType *lat);
+
+
+/// Given a lattice, and a transition model to map pdf-ids to phones,
+/// replace the sequences of transition-ids with sequences of phones.
+/// Note that this is different from ConvertLatticeToPhones, in that
+/// we replace the transition-ids not the words.
+void ConvertCompactLatticeToPhones(const TransitionInformation &trans_model,
+                                   CompactLattice *clat);
+
+/// Boosts LM probabilities by b * [number of frame errors]; equivalently, adds
+/// -b*[number of frame errors] to the graph-component of the cost of each arc/path.
+/// There is a frame error if a particular transition-id on a particular frame
+/// corresponds to a phone not matching transcription's alignment for that frame.
+/// This is used in "margin-inspired" discriminative training, esp. Boosted MMI.
+/// The TransitionInformation is used to map transition-ids in the lattice
+/// input-side to phones; the phones appearing in
+/// "silence_phones" are treated specially in that we replace the frame error f
+/// (either zero or 1) for a frame, with the minimum of f or max_silence_error.
+/// For the normal recipe, max_silence_error would be zero.
+/// Returns true on success, false if there was some kind of mismatch.
+/// At input, silence_phones must be sorted and unique.
+bool LatticeBoost(const TransitionInformation &trans,
+                  const std::vector<int32> &alignment,
+                  const std::vector<int32> &silence_phones,
+                  BaseFloat b,
+                  BaseFloat max_silence_error,
+                  Lattice *lat);
+
+
+/**
+   This function implements either the MPFE (minimum phone frame error) or SMBR
+   (state-level minimum bayes risk) forward-backward, depending on whether
+   "criterion" is "mpfe" or "smbr".  It returns the MPFE
+   criterion of SMBR criterion for this utterance, and outputs the posteriors (which
+   may be positive or negative) into "post".
+
+   @param [in] trans    The transition model. Used to map the
+                        transition-ids to phones or pdfs.
+   @param [in] silence_phones   A list of integer ids of silence phones. The
+                        silence frames i.e. the frames where num_ali
+                        corresponds to a silence phones are treated specially.
+                        The behavior is determined by 'one_silence_class'
+                        being false (traditional behavior) or true.
+                        Usually in our setup, several phones including
+                        the silence, vocalized noise, non-spoken noise
+                        and unk are treated as "silence phones"
+   @param [in] lat      The denominator lattice
+   @param [in] num_ali  The numerator alignment
+   @param [in] criterion    The objective function. Must be "mpfe" or "smbr"
+                        for MPFE (minimum phone frame error) or sMBR
+                        (state minimum bayes risk) training.
+   @param [in] one_silence_class   Determines how the silence frames are treated.
+                        Setting this to false gives the old traditional behavior,
+                        where the silence frames (according to num_ali) are
+                        treated as incorrect. However, this means that the
+                        insertions are not penalized by the objective.
+                        Setting this to true gives the new behaviour, where we
+                        treat silence as any other phone, except that all pdfs
+                        of silence phones are collapsed into a single class for
+                        the frame-error computation. This can possible reduce
+                        the insertions in the trained model. This is closer to
+                        the WER metric that we actually care about, since WER is
+                        generally computed after filtering out noises, but
+                        does penalize insertions.
+    @param [out] post   The "MBR posteriors" i.e. derivatives w.r.t to the
+                        pseudo log-likelihoods of states at each frame.
+*/
+BaseFloat LatticeForwardBackwardMpeVariants(
+    const TransitionInformation &trans,
+    const std::vector<int32> &silence_phones,
+    const Lattice &lat,
+    const std::vector<int32> &num_ali,
+    std::string criterion,
+    bool one_silence_class,
+    Posterior *post);
+
+/// This function takes a CompactLattice that should only contain a single
+/// linear sequence (e.g. derived from lattice-1best), and that should have been
+/// processed so that the arcs in the CompactLattice align correctly with the
+/// word boundaries (e.g. by lattice-align-words).  It outputs 3 vectors of the
+/// same size, which give, for each word in the lattice (in sequence), the word
+/// label and the begin time and length in frames.  This is done even for zero
+/// (epsilon) words, generally corresponding to optional silence-- if you don't
+/// want them, just ignore them in the output.
+/// This function will print a warning and return false, if the lattice
+/// did not have the correct format (e.g. if it is empty or it is not
+/// linear).
+bool CompactLatticeToWordAlignment(const CompactLattice &clat,
+                                   std::vector<int32> *words,
+                                   std::vector<int32> *begin_times,
+                                   std::vector<int32> *lengths);
+
+/// A form of the shortest-path/best-path algorithm that's specially coded for
+/// CompactLattice.  Requires that clat be acyclic.
+void CompactLatticeShortestPath(const CompactLattice &clat,
+                                CompactLattice *shortest_path);
+
+/// This function expands a CompactLattice to ensure high-probability paths
+/// have unique histories. Arcs with posteriors larger than epsilon get splitted.
+void ExpandCompactLattice(const CompactLattice &clat,
+                          double epsilon,
+                          CompactLattice *expand_clat);
+
+/// For each state, compute forward and backward best (viterbi) costs and its
+/// traceback states (for generating best paths later). The forward best cost
+/// for a state is the cost of the best path from the start state to the state.
+/// The traceback state of this state is its predecessor state in the best path.
+/// The backward best cost for a state is the cost of the best path from the
+/// state to a final one. Its traceback state is the successor state in the best
+/// path in the forward direction.
+/// Note: final weights of states are in backward_best_cost_and_pred.
+/// Requires the input CompactLattice clat be acyclic.
+typedef std::vector<std::pair<double,
+        CompactLatticeArc::StateId> > CostTraceType;
+void CompactLatticeBestCostsAndTracebacks(
+    const CompactLattice &clat,
+    CostTraceType *forward_best_cost_and_pred,
+    CostTraceType *backward_best_cost_and_pred);
+
+/// This function adds estimated neural language model scores of words in a
+/// minimal list of hypotheses that covers a lattice, to the graph scores on the
+/// arcs. The list of hypotheses are generated by latbin/lattice-path-cover.
+typedef unordered_map<std::pair<int32, int32>, double, PairHasher<int32> > MapT;
+void AddNnlmScoreToCompactLattice(const MapT &nnlm_scores,
+                                  CompactLattice *clat);
+
+/// This function add the word insertion penalty to graph score of each word
+/// in the compact lattice
+void AddWordInsPenToCompactLattice(BaseFloat word_ins_penalty,
+                                   CompactLattice *clat);
+
+/// This function *adds* the negated scores obtained from the Decodable object,
+/// to the acoustic scores on the arcs.  If you want to replace them, you should
+/// use ScaleCompactLattice to first set the acoustic scores to zero.  Returns
+/// true on success, false on error (typically some kind of mismatched inputs).
+bool RescoreCompactLattice(DecodableInterface *decodable,
+                           CompactLattice *clat);
+
+
+/// This function returns the number of words in the longest sentence in a
+/// CompactLattice (i.e. the the maximum of any path, of the count of
+/// olabels on that path).
+int32 LongestSentenceLength(const Lattice &lat);
+
+/// This function returns the number of words in the longest sentence in a
+/// CompactLattice, i.e. the the maximum of any path, of the count of
+/// labels on that path... note, in CompactLattice, the ilabels and olabels
+/// are identical because it is an acceptor.
+int32 LongestSentenceLength(const CompactLattice &lat);
+
+
+/// This function is like RescoreCompactLattice, but it is modified to avoid
+/// computing probabilities on most frames where all the pdf-ids are the same.
+/// (it needs the transition-model to work out whether two transition-ids map to
+/// the same pdf-id, and it assumes that the lattice has transition-ids on it).
+/// The naive thing would be to just set all probabilities to zero on frames
+/// where all the pdf-ids are the same (because this value won't affect the
+/// lattice posterior).  But this would become confusing when we compute
+/// corpus-level diagnostics such as the MMI objective function.  Instead,
+/// imagine speedup_factor = 100 (it must be >= 1.0)... with probability (1.0 /
+/// speedup_factor) we compute those likelihoods and multiply them by
+/// speedup_factor; otherwise we set them to zero.  This gives the right
+/// expected probability so our corpus-level diagnostics will be about right.
+bool RescoreCompactLatticeSpeedup(
+    const TransitionInformation &tmodel,
+    BaseFloat speedup_factor,
+    DecodableInterface *decodable,
+    CompactLattice *clat);
+
+
+/// This function *adds* the negated scores obtained from the Decodable object,
+/// to the acoustic scores on the arcs.  If you want to replace them, you should
+/// use ScaleCompactLattice to first set the acoustic scores to zero.  Returns
+/// true on success, false on error (e.g. some kind of mismatched inputs).
+/// The input labels, if nonzero, are interpreted as transition-ids or whatever
+/// other index the Decodable object expects.
+bool RescoreLattice(DecodableInterface *decodable,
+                    Lattice *lat);
+
+/// This function Composes a CompactLattice format lattice with a
+/// DeterministicOnDemandFst<fst::StdFst> format fst, and outputs another
+/// CompactLattice format lattice. The first element (the one that corresponds
+/// to LM weight) in CompactLatticeWeight is used for composition.
+///
+/// Note that the DeterministicOnDemandFst interface is not "const", therefore
+/// we cannot use "const" for <det_fst>.
+void ComposeCompactLatticeDeterministic(
+    const CompactLattice& clat,
+    fst::DeterministicOnDemandFst<fst::StdArc>* det_fst,
+    CompactLattice* composed_clat);
+
+/// This function computes the mapping from the pair 
+/// (frame-index, transition-id) to the pair 
+/// (sum-of-acoustic-scores, num-of-occurences) over all occurences of the 
+/// transition-id in that frame.
+/// frame-index in the lattice. 
+/// This function is useful for retaining the acoustic scores in a 
+/// non-compact lattice after a process like determinization where the 
+/// frame-level acoustic scores are typically lost.
+/// The function ReplaceAcousticScoresFromMap is used to restore the 
+/// acoustic scores computed by this function.
+///
+///   @param [in] lat   Input lattice. Expected to be top-sorted. Otherwise the 
+///                     function will crash. 
+///   @param [out] acoustic_scores  
+///                     Pointer to a map from the pair (frame-index,
+///                     transition-id) to a pair (sum-of-acoustic-scores,
+///                     num-of-occurences).
+///                     Usually the acoustic scores for a pdf-id (and hence
+///                     transition-id) on a frame will be the same for all the
+///                     occurences of the pdf-id in that frame. 
+///                     But if not, we will take the average of the acoustic
+///                     scores. Hence, we store both the sum-of-acoustic-scores
+///                     and the num-of-occurences of the transition-id in that
+///                     frame.
+void ComputeAcousticScoresMap(
+    const Lattice &lat,
+    unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+                                        PairHasher<int32> > *acoustic_scores);
+
+/// This function restores acoustic scores computed using the function
+/// ComputeAcousticScoresMap into the lattice.
+///
+///   @param [in] acoustic_scores  
+///                      A map from the pair (frame-index, transition-id) to a
+///                      pair (sum-of-acoustic-scores, num-of-occurences) of 
+///                      the occurences of the transition-id in that frame.
+///                      See the comments for ComputeAcousticScoresMap for 
+///                      details.
+///   @param [out] lat   Pointer to the output lattice.
+void ReplaceAcousticScoresFromMap(
+    const unordered_map<std::pair<int32, int32>, std::pair<BaseFloat, int32>,
+                                        PairHasher<int32> > &acoustic_scores,
+    Lattice *lat);
+
+}  // namespace kaldi
+
+#endif  // KALDI_LAT_LATTICE_FUNCTIONS_H_

speechx/speechx/nnet/decodable-itf.h

+// itf/decodable-itf.h
+
+// Copyright 2009-2011  Microsoft Corporation;  Saarland University;
+//                      Mirko Hannemann;  Go Vivace Inc.;
+//                2013  Johns Hopkins University (author: Daniel Povey)
+
+// See ../../COPYING for clarification regarding multiple authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//  http://www.apache.org/licenses/LICENSE-2.0
+//
+// THIS CODE IS PROVIDED *AS IS* BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+// KIND, EITHER EXPRESS OR IMPLIED, INCLUDING WITHOUT LIMITATION ANY IMPLIED
+// WARRANTIES OR CONDITIONS OF TITLE, FITNESS FOR A PARTICULAR PURPOSE,
+// MERCHANTABLITY OR NON-INFRINGEMENT.
+// See the Apache 2 License for the specific language governing permissions and
+// limitations under the License.
+
+#ifndef KALDI_ITF_DECODABLE_ITF_H_
+#define KALDI_ITF_DECODABLE_ITF_H_ 1
+#include "base/kaldi-common.h"
+
+namespace kaldi {
+/// @ingroup Interfaces
+/// @{
+
+
+/**
+    DecodableInterface provides a link between the (acoustic-modeling and
+    feature-processing) code and the decoder.  The idea is to make this
+    interface as small as possible, and to make it as agnostic as possible about
+    the form of the acoustic model (e.g. don't assume the probabilities are a
+    function of just a vector of floats), and about the decoder (e.g. don't
+    assume it accesses frames in strict left-to-right order).  For normal
+    models, without on-line operation, the "decodable" sub-class will just be a
+    wrapper around a matrix of features and an acoustic model, and it will
+    answer the question 'what is the acoustic likelihood for this index and this
+    frame?'.
+
+    For online decoding, where the features are coming in in real time, it is
+    important to understand the IsLastFrame() and NumFramesReady() functions.
+    There are two ways these are used: the old online-decoding code, in ../online/,
+    and the new online-decoding code, in ../online2/.  In the old online-decoding
+    code, the decoder would do:
+    \code{.cc}
+    for (int frame = 0; !decodable.IsLastFrame(frame); frame++) {
+      // Process this frame
+    }
+    \endcode
+   and the call to IsLastFrame would block if the features had not arrived yet.
+   The decodable object would have to know when to terminate the decoding.  This
+   online-decoding mode is still supported, it is what happens when you call, for
+   example, LatticeFasterDecoder::Decode().
+
+   We realized that this "blocking" mode of decoding is not very convenient
+   because it forces the program to be multi-threaded and makes it complex to
+   control endpointing.  In the "new" decoding code, you don't call (for example)
+   LatticeFasterDecoder::Decode(), you call LatticeFasterDecoder::InitDecoding(),
+   and then each time you get more features, you provide them to the decodable
+   object, and you call LatticeFasterDecoder::AdvanceDecoding(), which does
+   something like this:
+   \code{.cc}
+   while (num_frames_decoded_ < decodable.NumFramesReady()) {
+     // Decode one more frame [increments num_frames_decoded_]
+   }
+   \endcode
+   So the decodable object never has IsLastFrame() called.  For decoding where
+   you are starting with a matrix of features, the NumFramesReady() function will
+   always just return the number of frames in the file, and IsLastFrame() will
+   return true for the last frame.
+
+   For truly online decoding, the "old" online decodable objects in ../online/
+   have a "blocking" IsLastFrame() and will crash if you call NumFramesReady().
+   The "new" online decodable objects in ../online2/ return the number of frames
+   currently accessible if you call NumFramesReady().  You will likely not need
+   to call IsLastFrame(), but we implement it to only return true for the last
+   frame of the file once we've decided to terminate decoding.
+*/
+class DecodableInterface {
+ public:
+  /// Returns the log likelihood, which will be negated in the decoder.
+  /// The "frame" starts from zero.  You should verify that NumFramesReady() > frame
+  /// before calling this.
+  virtual BaseFloat LogLikelihood(int32 frame, int32 index) = 0;
+
+  /// Returns true if this is the last frame.  Frames are zero-based, so the
+  /// first frame is zero.  IsLastFrame(-1) will return false, unless the file
+  /// is empty (which is a case that I'm not sure all the code will handle, so
+  /// be careful).  Caution: the behavior of this function in an online setting
+  /// is being changed somewhat.  In future it may return false in cases where
+  /// we haven't yet decided to terminate decoding, but later true if we decide
+  /// to terminate decoding.  The plan in future is to rely more on
+  /// NumFramesReady(), and in future, IsLastFrame() would always return false
+  /// in an online-decoding setting, and would only return true in a
+  /// decoding-from-matrix setting where we want to allow the last delta or LDA
+  /// features to be flushed out for compatibility with the baseline setup.
+  virtual bool IsLastFrame(int32 frame) const = 0;
+
+  /// The call NumFramesReady() will return the number of frames currently available
+  /// for this decodable object.  This is for use in setups where you don't want the
+  /// decoder to block while waiting for input.  This is newly added as of Jan 2014,
+  /// and I hope, going forward, to rely on this mechanism more than IsLastFrame to
+  /// know when to stop decoding.
+  virtual int32 NumFramesReady() const {
+    KALDI_ERR << "NumFramesReady() not implemented for this decodable type.";
+    return -1;
+  }
+
+  /// Returns the number of states in the acoustic model
+  /// (they will be indexed one-based, i.e. from 1 to NumIndices();
+  /// this is for compatibility with OpenFst).
+  virtual int32 NumIndices() const = 0;
+
+  virtual ~DecodableInterface() {}
+};
+/// @}
+}  // namespace Kaldi
+
+#endif  // KALDI_ITF_DECODABLE_ITF_H_

speechx/speechx/nnet/decodable.h

+#include "nnet/decodable-itf.h"
+
+#include "base/common.h"
+
+namespace ppsepeech {
+  struct DecodeableConfig;
+
+  class Decodeable : public kaldi::DecodableInterface {
+    public: 
+      virtual Init(Decodeable config) = 0;
+      virtual Acceptlikeihood() = 0;
+    private:
+      std::share_ptr<FeatureExtractorInterface> frontend_;
+      std::share_ptr<NnetInterface> nnet_;
+      //Cache nnet_cache_;
+  }
+
+}  // namespace ppspeech
\ No newline at end of file

speechx/speechx/nnet/nnet_interface.h

@@ -8,7 +8,7 @@ namespace ppspeech {
 
 class NnetInterface {
   public:
-    virtual ~NnetForwardInterface() {}
+    virtual ~NnetInterface() {}
     virtual void FeedForward(const kaldi::Matrix<BaseFloat>& features, 
                              kaldi::Matrix<kaldi::BaseFloat>* inferences) const = 0;