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// finite-state transducer library.
//
// Expands a PDT to an FST.
#ifndef FST_EXTENSIONS_PDT_EXPAND_H_
#define FST_EXTENSIONS_PDT_EXPAND_H_
#include <forward_list>
#include <vector>
#include <fst/log.h>
#include <fst/extensions/pdt/paren.h>
#include <fst/extensions/pdt/pdt.h>
#include <fst/extensions/pdt/reverse.h>
#include <fst/extensions/pdt/shortest-path.h>
#include <fst/cache.h>
#include <fst/mutable-fst.h>
#include <fst/queue.h>
#include <fst/state-table.h>
#include <fst/test-properties.h>
namespace fst {
template <class Arc>
struct PdtExpandFstOptions : public CacheOptions {
bool keep_parentheses;
PdtStack<typename Arc::StateId, typename Arc::Label> *stack;
PdtStateTable<typename Arc::StateId, typename Arc::StateId> *state_table;
explicit PdtExpandFstOptions(
const CacheOptions &opts = CacheOptions(), bool keep_parentheses = false,
PdtStack<typename Arc::StateId, typename Arc::Label> *stack = nullptr,
PdtStateTable<typename Arc::StateId, typename Arc::StateId> *state_table =
nullptr)
: CacheOptions(opts),
keep_parentheses(keep_parentheses),
stack(stack),
state_table(state_table) {}
};
namespace internal {
// Implementation class for PdtExpandFst.
template <class Arc>
class PdtExpandFstImpl : public CacheImpl<Arc> {
public:
using Label = typename Arc::Label;
using StateId = typename Arc::StateId;
using Weight = typename Arc::Weight;
using StackId = StateId;
using StateTuple = PdtStateTuple<StateId, StackId>;
using FstImpl<Arc>::SetType;
using FstImpl<Arc>::SetProperties;
using FstImpl<Arc>::Properties;
using FstImpl<Arc>::SetInputSymbols;
using FstImpl<Arc>::SetOutputSymbols;
using CacheBaseImpl<CacheState<Arc>>::PushArc;
using CacheBaseImpl<CacheState<Arc>>::HasArcs;
using CacheBaseImpl<CacheState<Arc>>::HasFinal;
using CacheBaseImpl<CacheState<Arc>>::HasStart;
using CacheBaseImpl<CacheState<Arc>>::SetArcs;
using CacheBaseImpl<CacheState<Arc>>::SetFinal;
using CacheBaseImpl<CacheState<Arc>>::SetStart;
PdtExpandFstImpl(const Fst<Arc> &fst,
const std::vector<std::pair<Label, Label>> &parens,
const PdtExpandFstOptions<Arc> &opts)
: CacheImpl<Arc>(opts),
fst_(fst.Copy()),
stack_(opts.stack ? opts.stack : new PdtStack<StateId, Label>(parens)),
state_table_(opts.state_table ? opts.state_table
: new PdtStateTable<StateId, StackId>()),
own_stack_(opts.stack == 0),
own_state_table_(opts.state_table == 0),
keep_parentheses_(opts.keep_parentheses) {
SetType("expand");
const auto props = fst.Properties(kFstProperties, false);
SetProperties(PdtExpandProperties(props), kCopyProperties);
SetInputSymbols(fst.InputSymbols());
SetOutputSymbols(fst.OutputSymbols());
}
PdtExpandFstImpl(const PdtExpandFstImpl &impl)
: CacheImpl<Arc>(impl),
fst_(impl.fst_->Copy(true)),
stack_(new PdtStack<StateId, Label>(*impl.stack_)),
state_table_(new PdtStateTable<StateId, StackId>()),
own_stack_(true),
own_state_table_(true),
keep_parentheses_(impl.keep_parentheses_) {
SetType("expand");
SetProperties(impl.Properties(), kCopyProperties);
SetInputSymbols(impl.InputSymbols());
SetOutputSymbols(impl.OutputSymbols());
}
~PdtExpandFstImpl() override {
if (own_stack_) delete stack_;
if (own_state_table_) delete state_table_;
}
StateId Start() {
if (!HasStart()) {
const auto s = fst_->Start();
if (s == kNoStateId) return kNoStateId;
StateTuple tuple(s, 0);
const auto start = state_table_->FindState(tuple);
SetStart(start);
}
return CacheImpl<Arc>::Start();
}
Weight Final(StateId s) {
if (!HasFinal(s)) {
const auto &tuple = state_table_->Tuple(s);
const auto weight = fst_->Final(tuple.state_id);
if (weight != Weight::Zero() && tuple.stack_id == 0)
SetFinal(s, weight);
else
SetFinal(s, Weight::Zero());
}
return CacheImpl<Arc>::Final(s);
}
size_t NumArcs(StateId s) {
if (!HasArcs(s)) ExpandState(s);
return CacheImpl<Arc>::NumArcs(s);
}
size_t NumInputEpsilons(StateId s) {
if (!HasArcs(s)) ExpandState(s);
return CacheImpl<Arc>::NumInputEpsilons(s);
}
size_t NumOutputEpsilons(StateId s) {
if (!HasArcs(s)) ExpandState(s);
return CacheImpl<Arc>::NumOutputEpsilons(s);
}
void InitArcIterator(StateId s, ArcIteratorData<Arc> *data) {
if (!HasArcs(s)) ExpandState(s);
CacheImpl<Arc>::InitArcIterator(s, data);
}
// Computes the outgoing transitions from a state, creating new destination
// states as needed.
void ExpandState(StateId s) {
StateTuple tuple = state_table_->Tuple(s);
for (ArcIterator<Fst<Arc>> aiter(*fst_, tuple.state_id); !aiter.Done();
aiter.Next()) {
auto arc = aiter.Value();
const auto stack_id = stack_->Find(tuple.stack_id, arc.ilabel);
if (stack_id == -1) { // Non-matching close parenthesis.
continue;
} else if ((stack_id != tuple.stack_id) && !keep_parentheses_) {
// Stack push/pop.
arc.ilabel = 0;
arc.olabel = 0;
}
StateTuple ntuple(arc.nextstate, stack_id);
arc.nextstate = state_table_->FindState(ntuple);
PushArc(s, arc);
}
SetArcs(s);
}
const PdtStack<StackId, Label> &GetStack() const { return *stack_; }
const PdtStateTable<StateId, StackId> &GetStateTable() const {
return *state_table_;
}
private:
// Properties for an expanded PDT.
inline uint64 PdtExpandProperties(uint64 inprops) {
return inprops & (kAcceptor | kAcyclic | kInitialAcyclic | kUnweighted);
}
std::unique_ptr<const Fst<Arc>> fst_;
PdtStack<StackId, Label> *stack_;
PdtStateTable<StateId, StackId> *state_table_;
bool own_stack_;
bool own_state_table_;
bool keep_parentheses_;
};
} // namespace internal
// Expands a pushdown transducer (PDT) encoded as an FST into an FST. This
// version is a delayed FST. In the PDT, some transitions are labeled with open
// or close parentheses. To be interpreted as a PDT, the parens must balance on
// a path. The open-close parenthesis label pairs are passed using the parens
// argument. The expansion enforces the parenthesis constraints. The PDT must be
// expandable as an FST.
//
// This class attaches interface to implementation and handles reference
// counting, delegating most methods to ImplToFst.
template <class A>
class PdtExpandFst : public ImplToFst<internal::PdtExpandFstImpl<A>> {
public:
using Arc = A;
using Label = typename Arc::Label;
using StateId = typename Arc::StateId;
using Weight = typename Arc::Weight;
using StackId = StateId;
using Store = DefaultCacheStore<Arc>;
using State = typename Store::State;
using Impl = internal::PdtExpandFstImpl<Arc>;
friend class ArcIterator<PdtExpandFst<Arc>>;
friend class StateIterator<PdtExpandFst<Arc>>;
PdtExpandFst(const Fst<Arc> &fst,
const std::vector<std::pair<Label, Label>> &parens)
: ImplToFst<Impl>(
std::make_shared<Impl>(fst, parens, PdtExpandFstOptions<A>())) {}
PdtExpandFst(const Fst<Arc> &fst,
const std::vector<std::pair<Label, Label>> &parens,
const PdtExpandFstOptions<Arc> &opts)
: ImplToFst<Impl>(std::make_shared<Impl>(fst, parens, opts)) {}
// See Fst<>::Copy() for doc.
PdtExpandFst(const PdtExpandFst<Arc> &fst, bool safe = false)
: ImplToFst<Impl>(fst, safe) {}
// Gets a copy of this ExpandFst. See Fst<>::Copy() for further doc.
PdtExpandFst<Arc> *Copy(bool safe = false) const override {
return new PdtExpandFst<Arc>(*this, safe);
}
inline void InitStateIterator(StateIteratorData<Arc> *data) const override;
void InitArcIterator(StateId s, ArcIteratorData<Arc> *data) const override {
GetMutableImpl()->InitArcIterator(s, data);
}
const PdtStack<StackId, Label> &GetStack() const {
return GetImpl()->GetStack();
}
const PdtStateTable<StateId, StackId> &GetStateTable() const {
return GetImpl()->GetStateTable();
}
private:
using ImplToFst<Impl>::GetImpl;
using ImplToFst<Impl>::GetMutableImpl;
void operator=(const PdtExpandFst &) = delete;
};
// Specialization for PdtExpandFst.
template <class Arc>
class StateIterator<PdtExpandFst<Arc>>
: public CacheStateIterator<PdtExpandFst<Arc>> {
public:
explicit StateIterator(const PdtExpandFst<Arc> &fst)
: CacheStateIterator<PdtExpandFst<Arc>>(fst, fst.GetMutableImpl()) {}
};
// Specialization for PdtExpandFst.
template <class Arc>
class ArcIterator<PdtExpandFst<Arc>>
: public CacheArcIterator<PdtExpandFst<Arc>> {
public:
using StateId = typename Arc::StateId;
ArcIterator(const PdtExpandFst<Arc> &fst, StateId s)
: CacheArcIterator<PdtExpandFst<Arc>>(fst.GetMutableImpl(), s) {
if (!fst.GetImpl()->HasArcs(s)) fst.GetMutableImpl()->ExpandState(s);
}
};
template <class Arc>
inline void PdtExpandFst<Arc>::InitStateIterator(
StateIteratorData<Arc> *data) const {
data->base = new StateIterator<PdtExpandFst<Arc>>(*this);
}
// PrunedExpand prunes the delayed expansion of a pushdown transducer (PDT)
// encoded as an FST into an FST. In the PDT, some transitions are labeled with
// open or close parentheses. To be interpreted as a PDT, the parens must
// balance on a path. The open-close parenthesis label pairs are passed
// using the parens argument. The expansion enforces the parenthesis
// constraints.
//
// The algorithm works by visiting the delayed ExpandFst using a shortest-stack
// first queue discipline and relies on the shortest-distance information
// computed using a reverse shortest-path call to perform the pruning.
//
// The algorithm maintains the same state ordering between the ExpandFst being
// visited (efst_) and the result of pruning written into the MutableFst (ofst_)
// to improve readability.
template <class Arc>
class PdtPrunedExpand {
public:
using Label = typename Arc::Label;
using StateId = typename Arc::StateId;
using Weight = typename Arc::Weight;
using StackId = StateId;
using Stack = PdtStack<StackId, Label>;
using StateTable = PdtStateTable<StateId, StackId>;
using SetIterator = typename internal::PdtBalanceData<Arc>::SetIterator;
// Constructor taking as input a PDT specified by by an input FST and a vector
// of parentheses. The keep_parentheses argument specifies whether parentheses
// are replaced by epsilons or not during the expansion. The cache options are
// passed to the underlying ExpandFst.
PdtPrunedExpand(const Fst<Arc> &ifst,
const std::vector<std::pair<Label, Label>> &parens,
bool keep_parentheses = false,
const CacheOptions &opts = CacheOptions())
: ifst_(ifst.Copy()),
keep_parentheses_(keep_parentheses),
stack_(parens),
efst_(ifst, parens,
PdtExpandFstOptions<Arc>(opts, true, &stack_, &state_table_)),
queue_(state_table_, stack_, stack_length_, distance_, fdistance_),
error_(false) {
Reverse(*ifst_, parens, &rfst_);
VectorFst<Arc> path;
reverse_shortest_path_.reset(new PdtShortestPath<Arc, FifoQueue<StateId>>(
rfst_, parens,
PdtShortestPathOptions<Arc, FifoQueue<StateId>>(true, false)));
reverse_shortest_path_->ShortestPath(&path);
error_ = (path.Properties(kError, true) == kError);
balance_data_.reset(reverse_shortest_path_->GetBalanceData()->Reverse(
rfst_.NumStates(), 10, -1));
InitCloseParenMultimap(parens);
}
bool Error() const { return error_; }
// Expands and prunes the input PDT according to the provided weight
// threshold, wirting the result into an output mutable FST.
void Expand(MutableFst<Arc> *ofst, const Weight &threshold);
private:
static constexpr uint8 kEnqueued = 0x01;
static constexpr uint8 kExpanded = 0x02;
static constexpr uint8 kSourceState = 0x04;
// Comparison functor used by the queue:
//
// 1. States corresponding to shortest stack first, and
// 2. for stacks of matching length, reverse lexicographic order is used, and
// 3. for states with the same stack, shortest-first order is used.
class StackCompare {
public:
StackCompare(const StateTable &state_table, const Stack &stack,
const std::vector<StackId> &stack_length,
const std::vector<Weight> &distance,
const std::vector<Weight> &fdistance)
: state_table_(state_table),
stack_(stack),
stack_length_(stack_length),
distance_(distance),
fdistance_(fdistance) {}
bool operator()(StateId s1, StateId s2) const {
auto si1 = state_table_.Tuple(s1).stack_id;
auto si2 = state_table_.Tuple(s2).stack_id;
if (stack_length_[si1] < stack_length_[si2]) return true;
if (stack_length_[si1] > stack_length_[si2]) return false;
// If stack IDs are equal, use A*.
if (si1 == si2) {
return less_(Distance(s1), Distance(s2));
}
// If lengths are equal, uses reverse lexicographic order.
for (; si1 != si2; si1 = stack_.Pop(si1), si2 = stack_.Pop(si2)) {
if (stack_.Top(si1) < stack_.Top(si2)) return true;
if (stack_.Top(si1) > stack_.Top(si2)) return false;
}
return false;
}
private:
Weight Distance(StateId s) const {
return (s < distance_.size()) && (s < fdistance_.size())
? Times(distance_[s], fdistance_[s])
: Weight::Zero();
}
const StateTable &state_table_;
const Stack &stack_;
const std::vector<StackId> &stack_length_;
const std::vector<Weight> &distance_;
const std::vector<Weight> &fdistance_;
const NaturalLess<Weight> less_;
};
class ShortestStackFirstQueue
: public ShortestFirstQueue<StateId, StackCompare> {
public:
ShortestStackFirstQueue(const PdtStateTable<StateId, StackId> &state_table,
const Stack &stack,
const std::vector<StackId> &stack_length,
const std::vector<Weight> &distance,
const std::vector<Weight> &fdistance)
: ShortestFirstQueue<StateId, StackCompare>(StackCompare(
state_table, stack, stack_length, distance, fdistance)) {}
};
void InitCloseParenMultimap(
const std::vector<std::pair<Label, Label>> &parens);
Weight DistanceToDest(StateId source, StateId dest) const;
uint8 Flags(StateId s) const;
void SetFlags(StateId s, uint8 flags, uint8 mask);
Weight Distance(StateId s) const;
void SetDistance(StateId s, Weight weight);
Weight FinalDistance(StateId s) const;
void SetFinalDistance(StateId s, Weight weight);
StateId SourceState(StateId s) const;
void SetSourceState(StateId s, StateId p);
void AddStateAndEnqueue(StateId s);
void Relax(StateId s, const Arc &arc, Weight weight);
bool PruneArc(StateId s, const Arc &arc);
void ProcStart();
void ProcFinal(StateId s);
bool ProcNonParen(StateId s, const Arc &arc, bool add_arc);
bool ProcOpenParen(StateId s, const Arc &arc, StackId si, StackId nsi);
bool ProcCloseParen(StateId s, const Arc &arc);
void ProcDestStates(StateId s, StackId si);
// Input PDT.
std::unique_ptr<Fst<Arc>> ifst_;
// Reversed PDT.
VectorFst<Arc> rfst_;
// Keep parentheses in ofst?
const bool keep_parentheses_;
// State table for efst_.
StateTable state_table_;
// Stack trie.
Stack stack_;
// Expanded PDT.
PdtExpandFst<Arc> efst_;
// Length of stack for given stack ID.
std::vector<StackId> stack_length_;
// Distance from initial state in efst_/ofst.
std::vector<Weight> distance_;
// Distance to final states in efst_/ofst.
std::vector<Weight> fdistance_;
// Queue used to visit efst_.
ShortestStackFirstQueue queue_;
// Construction time failure?
bool error_;
// Status flags for states in efst_/ofst.
std::vector<uint8> flags_;
// PDT source state for each expanded state.
std::vector<StateId> sources_;
// Shortest path for rfst_.
std::unique_ptr<PdtShortestPath<Arc, FifoQueue<StateId>>>
reverse_shortest_path_;
std::unique_ptr<internal::PdtBalanceData<Arc>> balance_data_;
// Maps open paren arcs to balancing close paren arcs.
typename PdtShortestPath<Arc, FifoQueue<StateId>>::CloseParenMultimap
close_paren_multimap_;
MutableFst<Arc> *ofst_; // Output FST.
Weight limit_; // Weight limit.
// Maps a state s in ifst (i.e., the source of a closed paranthesis matching
// the top of current_stack_id_ to final states in efst_.
std::unordered_map<StateId, Weight> dest_map_;
// Stack ID of the states currently at the top of the queue, i.e., the states
// currently being popped and processed.
StackId current_stack_id_;
ssize_t current_paren_id_; // Paren ID at top of current stack.
ssize_t cached_stack_id_;
StateId cached_source_;
// The set of pairs of destination states and weights to final states for the
// source state cached_source_ and the paren ID cached_paren_id_; i.e., the
// set of source states of a closed parenthesis with paren ID cached_paren_id
// balancing an incoming open parenthesis with paren ID cached_paren_id_ in
// state cached_source_.
std::forward_list<std::pair<StateId, Weight>> cached_dest_list_;
NaturalLess<Weight> less_;
};
// Initializes close paren multimap, mapping pairs (s, paren_id) to all the arcs
// out of s labeled with close parenthese for paren_id.
template <class Arc>
void PdtPrunedExpand<Arc>::InitCloseParenMultimap(
const std::vector<std::pair<Label, Label>> &parens) {
std::unordered_map<Label, Label> paren_map;
for (size_t i = 0; i < parens.size(); ++i) {
const auto &pair = parens[i];
paren_map[pair.first] = i;
paren_map[pair.second] = i;
}
for (StateIterator<Fst<Arc>> siter(*ifst_); !siter.Done(); siter.Next()) {
const auto s = siter.Value();
for (ArcIterator<Fst<Arc>> aiter(*ifst_, s); !aiter.Done(); aiter.Next()) {
const auto &arc = aiter.Value();
const auto it = paren_map.find(arc.ilabel);
if (it == paren_map.end()) continue;
if (arc.ilabel == parens[it->second].second) { // Close paren.
const internal::ParenState<Arc> key(it->second, s);
close_paren_multimap_.emplace(key, arc);
}
}
}
}
// Returns the weight of the shortest balanced path from source to dest
// in ifst_; dest must be the source state of a close paren arc.
template <class Arc>
typename Arc::Weight PdtPrunedExpand<Arc>::DistanceToDest(StateId source,
StateId dest) const {
using SearchState =
typename PdtShortestPath<Arc, FifoQueue<StateId>>::SearchState;
const SearchState ss(source + 1, dest + 1);
const auto distance =
reverse_shortest_path_->GetShortestPathData().Distance(ss);
VLOG(2) << "D(" << source << ", " << dest << ") =" << distance;
return distance;
}
// Returns the flags for state s in ofst_.
template <class Arc>
uint8 PdtPrunedExpand<Arc>::Flags(StateId s) const {
return s < flags_.size() ? flags_[s] : 0;
}
// Modifies the flags for state s in ofst_.
template <class Arc>
void PdtPrunedExpand<Arc>::SetFlags(StateId s, uint8 flags, uint8 mask) {
while (flags_.size() <= s) flags_.push_back(0);
flags_[s] &= ~mask;
flags_[s] |= flags & mask;
}
// Returns the shortest distance from the initial state to s in ofst_.
template <class Arc>
typename Arc::Weight PdtPrunedExpand<Arc>::Distance(StateId s) const {
return s < distance_.size() ? distance_[s] : Weight::Zero();
}
// Sets the shortest distance from the initial state to s in ofst_.
template <class Arc>
void PdtPrunedExpand<Arc>::SetDistance(StateId s, Weight weight) {
while (distance_.size() <= s) distance_.push_back(Weight::Zero());
distance_[s] = std::move(weight);
}
// Returns the shortest distance from s to the final states in ofst_.
template <class Arc>
typename Arc::Weight PdtPrunedExpand<Arc>::FinalDistance(StateId s) const {
return s < fdistance_.size() ? fdistance_[s] : Weight::Zero();
}
// Sets the shortest distance from s to the final states in ofst_.
template <class Arc>
void PdtPrunedExpand<Arc>::SetFinalDistance(StateId s, Weight weight) {
while (fdistance_.size() <= s) fdistance_.push_back(Weight::Zero());
fdistance_[s] = std::move(weight);
}
// Returns the PDT source state of state s in ofst_.
template <class Arc>
typename Arc::StateId PdtPrunedExpand<Arc>::SourceState(StateId s) const {
return s < sources_.size() ? sources_[s] : kNoStateId;
}
// Sets the PDT source state of state s in ofst_ to state p'in ifst_.
template <class Arc>
void PdtPrunedExpand<Arc>::SetSourceState(StateId s, StateId p) {
while (sources_.size() <= s) sources_.push_back(kNoStateId);
sources_[s] = p;
}
// Adds state s of efst_ to ofst_ and inserts it in the queue, modifying the
// flags for s accordingly.
template <class Arc>
void PdtPrunedExpand<Arc>::AddStateAndEnqueue(StateId s) {
if (!(Flags(s) & (kEnqueued | kExpanded))) {
while (ofst_->NumStates() <= s) ofst_->AddState();
queue_.Enqueue(s);
SetFlags(s, kEnqueued, kEnqueued);
} else if (Flags(s) & kEnqueued) {
queue_.Update(s);
}
// TODO(allauzen): Check everything is fine when kExpanded?
}
// Relaxes arc out of state s in ofst_ as follows:
//
// 1. If the distance to s times the weight of arc is smaller than
// the currently stored distance for arc.nextstate, updates
// Distance(arc.nextstate) with a new estimate
// 2. If fd is less than the currently stored distance from arc.nextstate to the
// final state, updates with new estimate.
template <class Arc>
void PdtPrunedExpand<Arc>::Relax(StateId s, const Arc &arc, Weight fd) {
const auto nd = Times(Distance(s), arc.weight);
if (less_(nd, Distance(arc.nextstate))) {
SetDistance(arc.nextstate, nd);
SetSourceState(arc.nextstate, SourceState(s));
}
if (less_(fd, FinalDistance(arc.nextstate))) {
SetFinalDistance(arc.nextstate, fd);
}
VLOG(2) << "Relax: " << s << ", d[s] = " << Distance(s) << ", to "
<< arc.nextstate << ", d[ns] = " << Distance(arc.nextstate)
<< ", nd = " << nd;
}
// Returns whether the arc out of state s in efst needs pruned.
template <class Arc>
bool PdtPrunedExpand<Arc>::PruneArc(StateId s, const Arc &arc) {
VLOG(2) << "Prune ?";
auto fd = Weight::Zero();
if ((cached_source_ != SourceState(s)) ||
(cached_stack_id_ != current_stack_id_)) {
cached_source_ = SourceState(s);
cached_stack_id_ = current_stack_id_;
cached_dest_list_.clear();
if (cached_source_ != ifst_->Start()) {
for (auto set_iter =
balance_data_->Find(current_paren_id_, cached_source_);
!set_iter.Done(); set_iter.Next()) {
auto dest = set_iter.Element();
const auto it = dest_map_.find(dest);
cached_dest_list_.push_front(*it);
}
} else {
// TODO(allauzen): queue discipline should prevent this from ever
// happening.
// Replace by a check.
cached_dest_list_.push_front(
std::make_pair(rfst_.Start() - 1, Weight::One()));
}
}
for (auto it = cached_dest_list_.begin(); it != cached_dest_list_.end();
++it) {
const auto d =
DistanceToDest(state_table_.Tuple(arc.nextstate).state_id, it->first);
fd = Plus(fd, Times(d, it->second));
}
Relax(s, arc, fd);
return less_(limit_, Times(Distance(s), Times(arc.weight, fd)));
}
// Adds start state of efst_ to ofst_, enqueues it, and initializes the distance
// data structures.
template <class Arc>
void PdtPrunedExpand<Arc>::ProcStart() {
const auto s = efst_.Start();
AddStateAndEnqueue(s);
ofst_->SetStart(s);
SetSourceState(s, ifst_->Start());
current_stack_id_ = 0;
current_paren_id_ = -1;
stack_length_.push_back(0);
const auto r = rfst_.Start() - 1;
cached_source_ = ifst_->Start();
cached_stack_id_ = 0;
cached_dest_list_.push_front(std::make_pair(r, Weight::One()));
const PdtStateTuple<StateId, StackId> tuple(r, 0);
SetFinalDistance(state_table_.FindState(tuple), Weight::One());
SetDistance(s, Weight::One());
const auto d = DistanceToDest(ifst_->Start(), r);
SetFinalDistance(s, d);
VLOG(2) << d;
}
// Makes s final in ofst_ if shortest accepting path ending in s is below
// threshold.
template <class Arc>
void PdtPrunedExpand<Arc>::ProcFinal(StateId s) {
const auto weight = efst_.Final(s);
if (weight == Weight::Zero()) return;
if (less_(limit_, Times(Distance(s), weight))) return;
ofst_->SetFinal(s, weight);
}
// Returns true when an arc (or meta-arc) leaving state s in efst_ is below the
// threshold. When add_arc is true, arc is added to ofst_.
template <class Arc>
bool PdtPrunedExpand<Arc>::ProcNonParen(StateId s, const Arc &arc,
bool add_arc) {
VLOG(2) << "ProcNonParen: " << s << " to " << arc.nextstate << ", "
<< arc.ilabel << ":" << arc.olabel << " / " << arc.weight
<< ", add_arc = " << (add_arc ? "true" : "false");
if (PruneArc(s, arc)) return false;
if (add_arc) ofst_->AddArc(s, arc);
AddStateAndEnqueue(arc.nextstate);
return true;
}
// Processes an open paren arc leaving state s in ofst_. When the arc is labeled
// with an open paren,
//
// 1. Considers each (shortest) balanced path starting in s by taking the arc
// and ending by a close paren balancing the open paren of as a meta-arc,
// processing and pruning each meta-arc as a non-paren arc, inserting its
// destination to the queue;
// 2. if at least one of these meta-arcs has not been pruned, adds the
// destination of arc to ofst_ as a new source state for the stack ID nsi, and
// inserts it in the queue.
template <class Arc>
bool PdtPrunedExpand<Arc>::ProcOpenParen(StateId s, const Arc &arc, StackId si,
StackId nsi) {
// Updates the stack length when needed.
while (stack_length_.size() <= nsi) stack_length_.push_back(-1);
if (stack_length_[nsi] == -1) stack_length_[nsi] = stack_length_[si] + 1;
const auto ns = arc.nextstate;
VLOG(2) << "Open paren: " << s << "(" << state_table_.Tuple(s).state_id
<< ") to " << ns << "(" << state_table_.Tuple(ns).state_id << ")";
bool proc_arc = false;
auto fd = Weight::Zero();
const auto paren_id = stack_.ParenId(arc.ilabel);
std::forward_list<StateId> sources;
for (auto set_iter =
balance_data_->Find(paren_id, state_table_.Tuple(ns).state_id);
!set_iter.Done(); set_iter.Next()) {
sources.push_front(set_iter.Element());
}
for (const auto source : sources) {
VLOG(2) << "Close paren source: " << source;
const internal::ParenState<Arc> paren_state(paren_id, source);
for (auto it = close_paren_multimap_.find(paren_state);
it != close_paren_multimap_.end() && paren_state == it->first; ++it) {
auto meta_arc = it->second;
const PdtStateTuple<StateId, StackId> tuple(meta_arc.nextstate, si);
meta_arc.nextstate = state_table_.FindState(tuple);
const auto state_id = state_table_.Tuple(ns).state_id;
const auto d = DistanceToDest(state_id, source);
VLOG(2) << state_id << ", " << source;
VLOG(2) << "Meta arc weight = " << arc.weight << " Times " << d
<< " Times " << meta_arc.weight;
meta_arc.weight = Times(arc.weight, Times(d, meta_arc.weight));
proc_arc |= ProcNonParen(s, meta_arc, false);
fd = Plus(
fd,
Times(Times(DistanceToDest(state_table_.Tuple(ns).state_id, source),
it->second.weight),
FinalDistance(meta_arc.nextstate)));
}
}
if (proc_arc) {
VLOG(2) << "Proc open paren " << s << " to " << arc.nextstate;
ofst_->AddArc(
s, keep_parentheses_ ? arc : Arc(0, 0, arc.weight, arc.nextstate));
AddStateAndEnqueue(arc.nextstate);
const auto nd = Times(Distance(s), arc.weight);
if (less_(nd, Distance(arc.nextstate))) SetDistance(arc.nextstate, nd);
// FinalDistance not necessary for source state since pruning decided using
// meta-arcs above. But this is a problem with A*, hence the following.
if (less_(fd, FinalDistance(arc.nextstate)))
SetFinalDistance(arc.nextstate, fd);
SetFlags(arc.nextstate, kSourceState, kSourceState);
}
return proc_arc;
}
// Checks that shortest path through close paren arc in efst_ is below
// threshold, and if so, adds it to ofst_.
template <class Arc>
bool PdtPrunedExpand<Arc>::ProcCloseParen(StateId s, const Arc &arc) {
const auto weight =
Times(Distance(s), Times(arc.weight, FinalDistance(arc.nextstate)));
if (less_(limit_, weight)) return false;
ofst_->AddArc(s,
keep_parentheses_ ? arc : Arc(0, 0, arc.weight, arc.nextstate));
return true;
}
// When state s in ofst_ is a source state for stack ID si, identifies all the
// corresponding possible destination states, that is, all the states in ifst_
// that have an outgoing close paren arc balancing the incoming open paren taken
// to get to s. For each such state t, computes the shortest distance from (t,
// si) to the final states in ofst_. Stores this information in dest_map_.
template <class Arc>
void PdtPrunedExpand<Arc>::ProcDestStates(StateId s, StackId si) {
if (!(Flags(s) & kSourceState)) return;
if (si != current_stack_id_) {
dest_map_.clear();
current_stack_id_ = si;
current_paren_id_ = stack_.Top(current_stack_id_);
VLOG(2) << "StackID " << si << " dequeued for first time";
}
// TODO(allauzen): clean up source state business; rename current function to
// ProcSourceState.
SetSourceState(s, state_table_.Tuple(s).state_id);
const auto paren_id = stack_.Top(si);
for (auto set_iter =
balance_data_->Find(paren_id, state_table_.Tuple(s).state_id);
!set_iter.Done(); set_iter.Next()) {
const auto dest_state = set_iter.Element();
if (dest_map_.find(dest_state) != dest_map_.end()) continue;
auto dest_weight = Weight::Zero();
internal::ParenState<Arc> paren_state(paren_id, dest_state);
for (auto it = close_paren_multimap_.find(paren_state);
it != close_paren_multimap_.end() && paren_state == it->first; ++it) {
const auto &arc = it->second;
const PdtStateTuple<StateId, StackId> tuple(arc.nextstate,
stack_.Pop(si));
dest_weight =
Plus(dest_weight,
Times(arc.weight, FinalDistance(state_table_.FindState(tuple))));
}
dest_map_[dest_state] = dest_weight;
VLOG(2) << "State " << dest_state << " is a dest state for stack ID " << si
<< " with weight " << dest_weight;
}
}
// Expands and prunes the input PDT, writing the result in ofst.
template <class Arc>
void PdtPrunedExpand<Arc>::Expand(MutableFst<Arc> *ofst,
const typename Arc::Weight &threshold) {
ofst_ = ofst;
if (error_) {
ofst_->SetProperties(kError, kError);
return;
}
ofst_->DeleteStates();
ofst_->SetInputSymbols(ifst_->InputSymbols());
ofst_->SetOutputSymbols(ifst_->OutputSymbols());
limit_ = Times(DistanceToDest(ifst_->Start(), rfst_.Start() - 1), threshold);
flags_.clear();
ProcStart();
while (!queue_.Empty()) {
const auto s = queue_.Head();
queue_.Dequeue();
SetFlags(s, kExpanded, kExpanded | kEnqueued);
VLOG(2) << s << " dequeued!";
ProcFinal(s);
StackId stack_id = state_table_.Tuple(s).stack_id;
ProcDestStates(s, stack_id);
for (ArcIterator<PdtExpandFst<Arc>> aiter(efst_, s); !aiter.Done();
aiter.Next()) {
const auto &arc = aiter.Value();
const auto nextstack_id = state_table_.Tuple(arc.nextstate).stack_id;
if (stack_id == nextstack_id) {
ProcNonParen(s, arc, true);
} else if (stack_id == stack_.Pop(nextstack_id)) {
ProcOpenParen(s, arc, stack_id, nextstack_id);
} else {
ProcCloseParen(s, arc);
}
}
VLOG(2) << "d[" << s << "] = " << Distance(s) << ", fd[" << s
<< "] = " << FinalDistance(s);
}
}
// Expand functions.
template <class Arc>
struct PdtExpandOptions {
using Weight = typename Arc::Weight;
bool connect;
bool keep_parentheses;
Weight weight_threshold;
PdtExpandOptions(bool connect = true, bool keep_parentheses = false,
Weight weight_threshold = Weight::Zero())
: connect(connect),
keep_parentheses(keep_parentheses),
weight_threshold(std::move(weight_threshold)) {}
};
// Expands a pushdown transducer (PDT) encoded as an FST into an FST. This
// version writes the expanded PDT to a mutable FST. In the PDT, some
// transitions are labeled with open or close parentheses. To be interpreted as
// a PDT, the parens must balance on a path. The open-close parenthesis label
// pairs are passed using the parens argument. Expansion enforces the
// parenthesis constraints. The PDT must be expandable as an FST.
template <class Arc>
void Expand(
const Fst<Arc> &ifst,
const std::vector<std::pair<typename Arc::Label, typename Arc::Label>>
&parens,
MutableFst<Arc> *ofst, const PdtExpandOptions<Arc> &opts) {
PdtExpandFstOptions<Arc> eopts;
eopts.gc_limit = 0;
if (opts.weight_threshold == Arc::Weight::Zero()) {
eopts.keep_parentheses = opts.keep_parentheses;
*ofst = PdtExpandFst<Arc>(ifst, parens, eopts);
} else {
PdtPrunedExpand<Arc> pruned_expand(ifst, parens, opts.keep_parentheses);
pruned_expand.Expand(ofst, opts.weight_threshold);
}
if (opts.connect) Connect(ofst);
}
// Expands a pushdown transducer (PDT) encoded as an FST into an FST. This
// version writes the expanded PDT result to a mutable FST. In the PDT, some
// transitions are labeled with open or close parentheses. To be interpreted as
// a PDT, the parens must balance on a path. The open-close parenthesis label
// pairs are passed using the parents argument. Expansion enforces the
// parenthesis constraints. The PDT must be expandable as an FST.
template <class Arc>
void Expand(const Fst<Arc> &ifst,
const std::vector<std::pair<typename Arc::Label, typename Arc::Label>>
&parens, MutableFst<Arc> *ofst, bool connect = true,
bool keep_parentheses = false) {
const PdtExpandOptions<Arc> opts(connect, keep_parentheses);
Expand(ifst, parens, ofst, opts);
}
} // namespace fst
#endif // FST_EXTENSIONS_PDT_EXPAND_H_
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