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-// label_reachable.h
-
-// 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
-//
-// Unless required by applicable law or agreed to in writing, software
-// distributed under the License is distributed on an "AS IS" BASIS,
-// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
-// See the License for the specific language governing permissions and
-// limitations under the License.
-//
-// Copyright 2005-2010 Google, Inc.
-// Author: riley@google.com (Michael Riley)
-//
-// \file
-// Class to determine if a non-epsilon label can be read as the
-// first non-epsilon symbol along some path from a given state.
-
-
-#ifndef FST_LIB_LABEL_REACHABLE_H__
-#define FST_LIB_LABEL_REACHABLE_H__
-
-#include <tr1/unordered_map>
-using std::tr1::unordered_map;
-using std::tr1::unordered_multimap;
-#include <vector>
-using std::vector;
-
-#include <fst/accumulator.h>
-#include <fst/arcsort.h>
-#include <fst/interval-set.h>
-#include <fst/state-reachable.h>
-#include <fst/vector-fst.h>
-
-
-namespace fst {
-
-// Stores shareable data for label reachable class copies.
-template <typename L>
-class LabelReachableData {
- public:
- typedef L Label;
- typedef typename IntervalSet<L>::Interval Interval;
-
- explicit LabelReachableData(bool reach_input, bool keep_relabel_data = true)
- : reach_input_(reach_input),
- keep_relabel_data_(keep_relabel_data),
- have_relabel_data_(true),
- final_label_(kNoLabel) {}
-
- ~LabelReachableData() {}
-
- bool ReachInput() const { return reach_input_; }
-
- vector< IntervalSet<L> > *IntervalSets() { return &isets_; }
-
- unordered_map<L, L> *Label2Index() {
- if (!have_relabel_data_)
- FSTERROR() << "LabelReachableData: no relabeling data";
- return &label2index_;
- }
-
- Label FinalLabel() {
- if (final_label_ == kNoLabel)
- final_label_ = label2index_[kNoLabel];
- return final_label_;
- }
-
- static LabelReachableData<L> *Read(istream &istrm) {
- LabelReachableData<L> *data = new LabelReachableData<L>();
-
- ReadType(istrm, &data->reach_input_);
- ReadType(istrm, &data->keep_relabel_data_);
- data->have_relabel_data_ = data->keep_relabel_data_;
- if (data->keep_relabel_data_)
- ReadType(istrm, &data->label2index_);
- ReadType(istrm, &data->final_label_);
- ReadType(istrm, &data->isets_);
- return data;
- }
-
- bool Write(ostream &ostrm) {
- WriteType(ostrm, reach_input_);
- WriteType(ostrm, keep_relabel_data_);
- if (keep_relabel_data_)
- WriteType(ostrm, label2index_);
- WriteType(ostrm, FinalLabel());
- WriteType(ostrm, isets_);
- return true;
- }
-
- int RefCount() const { return ref_count_.count(); }
- int IncrRefCount() { return ref_count_.Incr(); }
- int DecrRefCount() { return ref_count_.Decr(); }
-
- private:
- LabelReachableData() {}
-
- bool reach_input_; // Input or output labels considered?
- bool keep_relabel_data_; // Save label2index_ to file?
- bool have_relabel_data_; // Using label2index_?
- Label final_label_; // Final label
- RefCounter ref_count_; // Reference count.
- unordered_map<L, L> label2index_; // Finds index for a label.
- vector<IntervalSet <L> > isets_; // Interval sets per state.
-
- DISALLOW_COPY_AND_ASSIGN(LabelReachableData);
-};
-
-
-// Tests reachability of labels from a given state. If reach_input =
-// true, then input labels are considered, o.w. output labels are
-// considered. To test for reachability from a state s, first do
-// SetState(s). Then a label l can be reached from state s of FST f
-// iff Reach(r) is true where r = Relabel(l). The relabeling is
-// required to ensure a compact representation of the reachable
-// labels.
-
-// The whole FST can be relabeled instead with Relabel(&f,
-// reach_input) so that the test Reach(r) applies directly to the
-// labels of the transformed FST f. The relabeled FST will also be
-// sorted appropriately for composition.
-//
-// Reachablity of a final state from state s (via an epsilon path)
-// can be tested with ReachFinal();
-//
-// Reachability can also be tested on the set of labels specified by
-// an arc iterator, useful for FST composition. In particular,
-// Reach(aiter, ...) is true if labels on the input (output) side of
-// the transitions of the arc iterator, when iter_input is true
-// (false), can be reached from the state s. The iterator labels must
-// have already been relabeled.
-//
-// With the arc iterator test of reachability, the begin position, end
-// position and accumulated arc weight of the matches can be
-// returned. The optional template argument controls how reachable arc
-// weights are accumulated. The default uses the semiring
-// Plus(). Alternative ones can be used to distribute the weights in
-// composition in various ways.
-template <class A, class S = DefaultAccumulator<A> >
-class LabelReachable {
- public:
- typedef A Arc;
- typedef typename A::StateId StateId;
- typedef typename A::Label Label;
- typedef typename A::Weight Weight;
- typedef typename IntervalSet<Label>::Interval Interval;
-
- LabelReachable(const Fst<A> &fst, bool reach_input, S *s = 0,
- bool keep_relabel_data = true)
- : fst_(new VectorFst<Arc>(fst)),
- s_(kNoStateId),
- data_(new LabelReachableData<Label>(reach_input, keep_relabel_data)),
- accumulator_(s ? s : new S()),
- ncalls_(0),
- nintervals_(0),
- error_(false) {
- StateId ins = fst_->NumStates();
- TransformFst();
- FindIntervals(ins);
- delete fst_;
- }
-
- explicit LabelReachable(LabelReachableData<Label> *data, S *s = 0)
- : fst_(0),
- s_(kNoStateId),
- data_(data),
- accumulator_(s ? s : new S()),
- ncalls_(0),
- nintervals_(0),
- error_(false) {
- data_->IncrRefCount();
- }
-
- LabelReachable(const LabelReachable<A, S> &reachable) :
- fst_(0),
- s_(kNoStateId),
- data_(reachable.data_),
- accumulator_(new S(*reachable.accumulator_)),
- ncalls_(0),
- nintervals_(0),
- error_(reachable.error_) {
- data_->IncrRefCount();
- }
-
- ~LabelReachable() {
- if (!data_->DecrRefCount())
- delete data_;
- delete accumulator_;
- if (ncalls_ > 0) {
- VLOG(2) << "# of calls: " << ncalls_;
- VLOG(2) << "# of intervals/call: " << (nintervals_ / ncalls_);
- }
- }
-
- // Relabels w.r.t labels that give compact label sets.
- Label Relabel(Label label) {
- if (label == 0 || error_)
- return label;
- unordered_map<Label, Label> &label2index = *data_->Label2Index();
- Label &relabel = label2index[label];
- if (!relabel) // Add new label
- relabel = label2index.size() + 1;
- return relabel;
- }
-
- // Relabels Fst w.r.t to labels that give compact label sets.
- void Relabel(MutableFst<Arc> *fst, bool relabel_input) {
- for (StateIterator< MutableFst<Arc> > siter(*fst);
- !siter.Done(); siter.Next()) {
- StateId s = siter.Value();
- for (MutableArcIterator< MutableFst<Arc> > aiter(fst, s);
- !aiter.Done();
- aiter.Next()) {
- Arc arc = aiter.Value();
- if (relabel_input)
- arc.ilabel = Relabel(arc.ilabel);
- else
- arc.olabel = Relabel(arc.olabel);
- aiter.SetValue(arc);
- }
- }
- if (relabel_input) {
- ArcSort(fst, ILabelCompare<Arc>());
- fst->SetInputSymbols(0);
- } else {
- ArcSort(fst, OLabelCompare<Arc>());
- fst->SetOutputSymbols(0);
- }
- }
-
- // Returns relabeling pairs (cf. relabel.h::Relabel()).
- // If 'avoid_collisions' is true, extra pairs are added to
- // ensure no collisions when relabeling automata that have
- // labels unseen here.
- void RelabelPairs(vector<pair<Label, Label> > *pairs,
- bool avoid_collisions = false) {
- pairs->clear();
- unordered_map<Label, Label> &label2index = *data_->Label2Index();
- // Maps labels to their new values in [1, label2index().size()]
- for (typename unordered_map<Label, Label>::const_iterator
- it = label2index.begin(); it != label2index.end(); ++it)
- if (it->second != data_->FinalLabel())
- pairs->push_back(pair<Label, Label>(it->first, it->second));
- if (avoid_collisions) {
- // Ensures any label in [1, label2index().size()] is mapped either
- // by the above step or to label2index() + 1 (to avoid collisions).
- for (int i = 1; i <= label2index.size(); ++i) {
- typename unordered_map<Label, Label>::const_iterator
- it = label2index.find(i);
- if (it == label2index.end() || it->second == data_->FinalLabel())
- pairs->push_back(pair<Label, Label>(i, label2index.size() + 1));
- }
- }
- }
-
- // Set current state. Optionally set state associated
- // with arc iterator to be passed to Reach.
- void SetState(StateId s, StateId aiter_s = kNoStateId) {
- s_ = s;
- if (aiter_s != kNoStateId) {
- accumulator_->SetState(aiter_s);
- if (accumulator_->Error()) error_ = true;
- }
- }
-
- // Can reach this label from current state?
- // Original labels must be transformed by the Relabel methods above.
- bool Reach(Label label) {
- if (label == 0 || error_)
- return false;
- vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
- return isets[s_].Member(label);
-
- }
-
- // Can reach final state (via epsilon transitions) from this state?
- bool ReachFinal() {
- if (error_) return false;
- vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
- return isets[s_].Member(data_->FinalLabel());
- }
-
- // Initialize with secondary FST to be used with Reach(Iterator,...).
- // If copy is true, then 'fst' is a copy of the FST used in the
- // previous call to this method (useful to avoid unnecessary updates).
- template <class F>
- void ReachInit(const F &fst, bool copy = false) {
- accumulator_->Init(fst, copy);
- if (accumulator_->Error()) error_ = true;
- }
-
- // Can reach any arc iterator label between iterator positions
- // aiter_begin and aiter_end? If aiter_input = true, then iterator
- // input labels are considered, o.w. output labels are considered.
- // Arc iterator labels must be transformed by the Relabel methods
- // above. If compute_weight is true, user may call ReachWeight().
- template <class Iterator>
- bool Reach(Iterator *aiter, ssize_t aiter_begin,
- ssize_t aiter_end, bool aiter_input, bool compute_weight) {
- if (error_) return false;
- vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
- const vector<Interval> *intervals = isets[s_].Intervals();
- ++ncalls_;
- nintervals_ += intervals->size();
-
- reach_begin_ = -1;
- reach_end_ = -1;
- reach_weight_ = Weight::Zero();
-
- uint32 flags = aiter->Flags(); // save flags to restore them on exit
- aiter->SetFlags(kArcNoCache, kArcNoCache); // make caching optional
- aiter->Seek(aiter_begin);
-
- if (2 * (aiter_end - aiter_begin) < intervals->size()) {
- // Check each arc against intervals.
- // Set arc iterator flags to only compute the ilabel or olabel values,
- // since they are the only values required for most of the arcs processed.
- aiter->SetFlags(aiter_input ? kArcILabelValue : kArcOLabelValue,
- kArcValueFlags);
- Label reach_label = kNoLabel;
- for (ssize_t aiter_pos = aiter_begin;
- aiter_pos < aiter_end; aiter->Next(), ++aiter_pos) {
- const A &arc = aiter->Value();
- Label label = aiter_input ? arc.ilabel : arc.olabel;
- if (label == reach_label || Reach(label)) {
- reach_label = label;
- if (reach_begin_ < 0)
- reach_begin_ = aiter_pos;
- reach_end_ = aiter_pos + 1;
- if (compute_weight) {
- if (!(aiter->Flags() & kArcWeightValue)) {
- // If the 'arc.weight' wasn't computed by the call
- // to 'aiter->Value()' above, we need to call
- // 'aiter->Value()' again after having set the arc iterator
- // flags to compute the arc weight value.
- aiter->SetFlags(kArcWeightValue, kArcValueFlags);
- const A &arcb = aiter->Value();
- // Call the accumulator.
- reach_weight_ = accumulator_->Sum(reach_weight_, arcb.weight);
- // Only ilabel or olabel required to process the following
- // arcs.
- aiter->SetFlags(aiter_input ? kArcILabelValue : kArcOLabelValue,
- kArcValueFlags);
- } else {
- // Call the accumulator.
- reach_weight_ = accumulator_->Sum(reach_weight_, arc.weight);
- }
- }
- }
- }
- } else {
- // Check each interval against arcs
- ssize_t begin_low, end_low = aiter_begin;
- for (typename vector<Interval>::const_iterator
- iiter = intervals->begin();
- iiter != intervals->end(); ++iiter) {
- begin_low = LowerBound(aiter, end_low, aiter_end,
- aiter_input, iiter->begin);
- end_low = LowerBound(aiter, begin_low, aiter_end,
- aiter_input, iiter->end);
- if (end_low - begin_low > 0) {
- if (reach_begin_ < 0)
- reach_begin_ = begin_low;
- reach_end_ = end_low;
- if (compute_weight) {
- aiter->SetFlags(kArcWeightValue, kArcValueFlags);
- reach_weight_ = accumulator_->Sum(reach_weight_, aiter,
- begin_low, end_low);
- }
- }
- }
- }
-
- aiter->SetFlags(flags, kArcFlags); // restore original flag values
- return reach_begin_ >= 0;
- }
-
- // Returns iterator position of first matching arc.
- ssize_t ReachBegin() const { return reach_begin_; }
-
- // Returns iterator position one past last matching arc.
- ssize_t ReachEnd() const { return reach_end_; }
-
- // Return the sum of the weights for matching arcs.
- // Valid only if compute_weight was true in Reach() call.
- Weight ReachWeight() const { return reach_weight_; }
-
- // Access to the relabeling map. Excludes epsilon (0) label but
- // includes kNoLabel that is used internally for super-final
- // transitons.
- const unordered_map<Label, Label>& Label2Index() const {
- return *data_->Label2Index();
- }
-
- LabelReachableData<Label> *GetData() const { return data_; }
-
- bool Error() const { return error_ || accumulator_->Error(); }
-
- private:
- // Redirects labeled arcs (input or output labels determined by
- // ReachInput()) to new label-specific final states. Each original
- // final state is redirected via a transition labeled with kNoLabel
- // to a new kNoLabel-specific final state. Creates super-initial
- // state for all states with zero in-degree.
- void TransformFst() {
- StateId ins = fst_->NumStates();
- StateId ons = ins;
-
- vector<ssize_t> indeg(ins, 0);
-
- // Redirects labeled arcs to new final states.
- for (StateId s = 0; s < ins; ++s) {
- for (MutableArcIterator< VectorFst<Arc> > aiter(fst_, s);
- !aiter.Done();
- aiter.Next()) {
- Arc arc = aiter.Value();
- Label label = data_->ReachInput() ? arc.ilabel : arc.olabel;
- if (label) {
- if (label2state_.find(label) == label2state_.end()) {
- label2state_[label] = ons;
- indeg.push_back(0);
- ++ons;
- }
- arc.nextstate = label2state_[label];
- aiter.SetValue(arc);
- }
- ++indeg[arc.nextstate]; // Finds in-degrees for next step.
- }
-
- // Redirects final weights to new final state.
- Weight final = fst_->Final(s);
- if (final != Weight::Zero()) {
- if (label2state_.find(kNoLabel) == label2state_.end()) {
- label2state_[kNoLabel] = ons;
- indeg.push_back(0);
- ++ons;
- }
- Arc arc(kNoLabel, kNoLabel, final, label2state_[kNoLabel]);
- fst_->AddArc(s, arc);
- ++indeg[arc.nextstate]; // Finds in-degrees for next step.
-
- fst_->SetFinal(s, Weight::Zero());
- }
- }
-
- // Add new final states to Fst.
- while (fst_->NumStates() < ons) {
- StateId s = fst_->AddState();
- fst_->SetFinal(s, Weight::One());
- }
-
- // Creates a super-initial state for all states with zero in-degree.
- StateId start = fst_->AddState();
- fst_->SetStart(start);
- for (StateId s = 0; s < start; ++s) {
- if (indeg[s] == 0) {
- Arc arc(0, 0, Weight::One(), s);
- fst_->AddArc(start, arc);
- }
- }
- }
-
- void FindIntervals(StateId ins) {
- StateReachable<A, Label> state_reachable(*fst_);
- if (state_reachable.Error()) {
- error_ = true;
- return;
- }
-
- vector<Label> &state2index = state_reachable.State2Index();
- vector< IntervalSet<Label> > &isets = *data_->IntervalSets();
- isets = state_reachable.IntervalSets();
- isets.resize(ins);
-
- unordered_map<Label, Label> &label2index = *data_->Label2Index();
- for (typename unordered_map<Label, StateId>::const_iterator
- it = label2state_.begin();
- it != label2state_.end();
- ++it) {
- Label l = it->first;
- StateId s = it->second;
- Label i = state2index[s];
- label2index[l] = i;
- }
- label2state_.clear();
-
- double nintervals = 0;
- ssize_t non_intervals = 0;
- for (ssize_t s = 0; s < ins; ++s) {
- nintervals += isets[s].Size();
- if (isets[s].Size() > 1) {
- ++non_intervals;
- VLOG(3) << "state: " << s << " # of intervals: " << isets[s].Size();
- }
- }
- VLOG(2) << "# of states: " << ins;
- VLOG(2) << "# of intervals: " << nintervals;
- VLOG(2) << "# of intervals/state: " << nintervals/ins;
- VLOG(2) << "# of non-interval states: " << non_intervals;
- }
-
- template <class Iterator>
- ssize_t LowerBound(Iterator *aiter, ssize_t aiter_begin,
- ssize_t aiter_end, bool aiter_input,
- Label match_label) const {
- // Only need to compute the ilabel or olabel of arcs when
- // performing the binary search.
- aiter->SetFlags(aiter_input ? kArcILabelValue : kArcOLabelValue,
- kArcValueFlags);
- ssize_t low = aiter_begin;
- ssize_t high = aiter_end;
- while (low < high) {
- ssize_t mid = (low + high) / 2;
- aiter->Seek(mid);
- Label label = aiter_input ?
- aiter->Value().ilabel : aiter->Value().olabel;
- if (label > match_label) {
- high = mid;
- } else if (label < match_label) {
- low = mid + 1;
- } else {
- // Find first matching label (when non-deterministic)
- for (ssize_t i = mid; i > low; --i) {
- aiter->Seek(i - 1);
- label = aiter_input ? aiter->Value().ilabel : aiter->Value().olabel;
- if (label != match_label) {
- aiter->Seek(i);
- aiter->SetFlags(kArcValueFlags, kArcValueFlags);
- return i;
- }
- }
- aiter->SetFlags(kArcValueFlags, kArcValueFlags);
- return low;
- }
- }
- aiter->Seek(low);
- aiter->SetFlags(kArcValueFlags, kArcValueFlags);
- return low;
- }
-
- VectorFst<Arc> *fst_;
- StateId s_; // Current state
- unordered_map<Label, StateId> label2state_; // Finds final state for a label
-
- ssize_t reach_begin_; // Iterator pos of first match
- ssize_t reach_end_; // Iterator pos after last match
- Weight reach_weight_; // Gives weight sum of arc iterator
- // arcs with reachable labels.
- LabelReachableData<Label> *data_; // Shareable data between copies
- S *accumulator_; // Sums arc weights
-
- double ncalls_;
- double nintervals_;
- bool error_;
-
- void operator=(const LabelReachable<A, S> &); // Disallow
-};
-
-} // namespace fst
-
-#endif // FST_LIB_LABEL_REACHABLE_H__