// Copyright 2005-2024 Google LLC
|
|
//
|
|
// 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.
|
|
//
|
|
// See www.openfst.org for extensive documentation on this weighted
|
|
// finite-state transducer library.
|
|
//
|
|
// Classes to visit connected components of an FST.
|
|
|
|
#ifndef FST_CC_VISITORS_H_
|
|
#define FST_CC_VISITORS_H_
|
|
|
|
#include <cstdint>
|
|
#include <vector>
|
|
|
|
#include <fst/fst.h>
|
|
#include <fst/union-find.h>
|
|
|
|
namespace fst {
|
|
|
|
// Finds and returns connected components. Use with Visit().
|
|
template <class Arc>
|
|
class CcVisitor {
|
|
public:
|
|
using Weight = typename Arc::Weight;
|
|
using StateId = typename Arc::StateId;
|
|
|
|
// cc[i]: connected component number for state i.
|
|
explicit CcVisitor(std::vector<StateId> *cc)
|
|
: comps_(new UnionFind<StateId>(0, kNoStateId)), cc_(cc), nstates_(0) {}
|
|
|
|
// comps: connected components equiv classes.
|
|
explicit CcVisitor(UnionFind<StateId> *comps)
|
|
: comps_(comps), cc_(nullptr), nstates_(0) {}
|
|
|
|
~CcVisitor() {
|
|
if (cc_) delete comps_;
|
|
}
|
|
|
|
void InitVisit(const Fst<Arc> &fst) {}
|
|
|
|
bool InitState(StateId s, StateId root) {
|
|
++nstates_;
|
|
if (comps_->FindSet(s) == kNoStateId) comps_->MakeSet(s);
|
|
return true;
|
|
}
|
|
|
|
bool WhiteArc(StateId s, const Arc &arc) {
|
|
comps_->MakeSet(arc.nextstate);
|
|
comps_->Union(s, arc.nextstate);
|
|
return true;
|
|
}
|
|
|
|
bool GreyArc(StateId s, const Arc &arc) {
|
|
comps_->Union(s, arc.nextstate);
|
|
return true;
|
|
}
|
|
|
|
bool BlackArc(StateId s, const Arc &arc) {
|
|
comps_->Union(s, arc.nextstate);
|
|
return true;
|
|
}
|
|
|
|
void FinishState(StateId s) {}
|
|
|
|
void FinishVisit() {
|
|
if (cc_) GetCcVector(cc_);
|
|
}
|
|
|
|
// Returns number of components.
|
|
// cc[i]: connected component number for state i.
|
|
int GetCcVector(std::vector<StateId> *cc) {
|
|
cc->clear();
|
|
cc->resize(nstates_, kNoStateId);
|
|
StateId ncomp = 0;
|
|
for (StateId s = 0; s < nstates_; ++s) {
|
|
const auto rep = comps_->FindSet(s);
|
|
auto &comp = (*cc)[rep];
|
|
if (comp == kNoStateId) {
|
|
comp = ncomp;
|
|
++ncomp;
|
|
}
|
|
(*cc)[s] = comp;
|
|
}
|
|
return ncomp;
|
|
}
|
|
|
|
private:
|
|
UnionFind<StateId> *comps_; // Components.
|
|
std::vector<StateId> *cc_; // State's cc number.
|
|
StateId nstates_; // State count.
|
|
};
|
|
|
|
// Finds and returns strongly-connected components, accessible and
|
|
// coaccessible states and related properties. Uses Tarjan's single
|
|
// DFS SCC algorithm (see Aho, et al, "Design and Analysis of Computer
|
|
// Algorithms", 189pp). Use with DfsVisit();
|
|
template <class Arc>
|
|
class SccVisitor {
|
|
public:
|
|
using StateId = typename Arc::StateId;
|
|
using Weight = typename Arc::Weight;
|
|
|
|
// scc[i]: strongly-connected component number for state i.
|
|
// SCC numbers will be in topological order for acyclic input.
|
|
// access[i]: accessibility of state i.
|
|
// coaccess[i]: coaccessibility of state i.
|
|
// Any of above can be NULL.
|
|
// props: related property bits (cyclicity, initial cyclicity,
|
|
// accessibility, coaccessibility) set/cleared (o.w. unchanged).
|
|
SccVisitor(std::vector<StateId> *scc, std::vector<bool> *access,
|
|
std::vector<bool> *coaccess, uint64_t *props)
|
|
: scc_(scc), access_(access), coaccess_(coaccess), props_(props) {}
|
|
explicit SccVisitor(uint64_t *props)
|
|
: scc_(nullptr), access_(nullptr), coaccess_(nullptr), props_(props) {}
|
|
|
|
void InitVisit(const Fst<Arc> &fst);
|
|
|
|
bool InitState(StateId s, StateId root);
|
|
|
|
bool TreeArc(StateId s, const Arc &arc) { return true; }
|
|
|
|
bool BackArc(StateId s, const Arc &arc) {
|
|
const auto t = arc.nextstate;
|
|
if (dfnumber_[t] < lowlink_[s]) lowlink_[s] = dfnumber_[t];
|
|
if ((*coaccess_)[t]) (*coaccess_)[s] = true;
|
|
*props_ |= kCyclic;
|
|
*props_ &= ~kAcyclic;
|
|
if (t == start_) {
|
|
*props_ |= kInitialCyclic;
|
|
*props_ &= ~kInitialAcyclic;
|
|
}
|
|
return true;
|
|
}
|
|
|
|
bool ForwardOrCrossArc(StateId s, const Arc &arc) {
|
|
const auto t = arc.nextstate;
|
|
if (dfnumber_[t] < dfnumber_[s] /* cross edge */ && onstack_[t] &&
|
|
dfnumber_[t] < lowlink_[s]) {
|
|
lowlink_[s] = dfnumber_[t];
|
|
}
|
|
if ((*coaccess_)[t]) (*coaccess_)[s] = true;
|
|
return true;
|
|
}
|
|
|
|
// Last argument always ignored, but required by the interface.
|
|
void FinishState(StateId state, StateId p, const Arc *);
|
|
|
|
void FinishVisit() {
|
|
// Numbers SCCs in topological order when acyclic.
|
|
if (scc_) {
|
|
for (size_t s = 0; s < scc_->size(); ++s) {
|
|
(*scc_)[s] = nscc_ - 1 - (*scc_)[s];
|
|
}
|
|
}
|
|
if (coaccess_internal_) delete coaccess_;
|
|
}
|
|
|
|
private:
|
|
std::vector<StateId> *scc_; // State's scc number.
|
|
std::vector<bool> *access_; // State's accessibility.
|
|
std::vector<bool> *coaccess_; // State's coaccessibility.
|
|
uint64_t *props_;
|
|
const Fst<Arc> *fst_;
|
|
StateId start_;
|
|
StateId nstates_; // State count.
|
|
StateId nscc_; // SCC count.
|
|
bool coaccess_internal_;
|
|
std::vector<StateId> dfnumber_; // State discovery times.
|
|
std::vector<StateId>
|
|
lowlink_; // lowlink[state] == dfnumber[state] => SCC root
|
|
std::vector<bool> onstack_; // Is a state on the SCC stack?
|
|
std::vector<StateId> scc_stack_; // SCC stack, with random access.
|
|
};
|
|
|
|
template <class Arc>
|
|
inline void SccVisitor<Arc>::InitVisit(const Fst<Arc> &fst) {
|
|
if (scc_) scc_->clear();
|
|
if (access_) access_->clear();
|
|
if (coaccess_) {
|
|
coaccess_->clear();
|
|
coaccess_internal_ = false;
|
|
} else {
|
|
coaccess_ = new std::vector<bool>;
|
|
coaccess_internal_ = true;
|
|
}
|
|
*props_ |= kAcyclic | kInitialAcyclic | kAccessible | kCoAccessible;
|
|
*props_ &= ~(kCyclic | kInitialCyclic | kNotAccessible | kNotCoAccessible);
|
|
fst_ = &fst;
|
|
start_ = fst.Start();
|
|
nstates_ = 0;
|
|
nscc_ = 0;
|
|
dfnumber_.clear();
|
|
lowlink_.clear();
|
|
onstack_.clear();
|
|
scc_stack_.clear();
|
|
}
|
|
|
|
template <class Arc>
|
|
inline bool SccVisitor<Arc>::InitState(StateId s, StateId root) {
|
|
scc_stack_.push_back(s);
|
|
if (static_cast<StateId>(dfnumber_.size()) <= s) {
|
|
if (scc_) scc_->resize(s + 1, -1);
|
|
if (access_) access_->resize(s + 1, false);
|
|
coaccess_->resize(s + 1, false);
|
|
dfnumber_.resize(s + 1, -1);
|
|
lowlink_.resize(s + 1, -1);
|
|
onstack_.resize(s + 1, false);
|
|
}
|
|
dfnumber_[s] = nstates_;
|
|
lowlink_[s] = nstates_;
|
|
onstack_[s] = true;
|
|
if (root == start_) {
|
|
if (access_) (*access_)[s] = true;
|
|
} else {
|
|
if (access_) (*access_)[s] = false;
|
|
*props_ |= kNotAccessible;
|
|
*props_ &= ~kAccessible;
|
|
}
|
|
++nstates_;
|
|
return true;
|
|
}
|
|
|
|
template <class Arc>
|
|
inline void SccVisitor<Arc>::FinishState(StateId s, StateId p, const Arc *) {
|
|
if (fst_->Final(s) != Weight::Zero()) (*coaccess_)[s] = true;
|
|
if (dfnumber_[s] == lowlink_[s]) { // Root of new SCC.
|
|
bool scc_coaccess = false;
|
|
auto i = scc_stack_.size();
|
|
StateId t;
|
|
do {
|
|
t = scc_stack_[--i];
|
|
if ((*coaccess_)[t]) scc_coaccess = true;
|
|
} while (s != t);
|
|
do {
|
|
t = scc_stack_.back();
|
|
if (scc_) (*scc_)[t] = nscc_;
|
|
if (scc_coaccess) (*coaccess_)[t] = true;
|
|
onstack_[t] = false;
|
|
scc_stack_.pop_back();
|
|
} while (s != t);
|
|
if (!scc_coaccess) {
|
|
*props_ |= kNotCoAccessible;
|
|
*props_ &= ~kCoAccessible;
|
|
}
|
|
++nscc_;
|
|
}
|
|
if (p != kNoStateId) {
|
|
if ((*coaccess_)[s]) (*coaccess_)[p] = true;
|
|
if (lowlink_[s] < lowlink_[p]) lowlink_[p] = lowlink_[s];
|
|
}
|
|
}
|
|
|
|
} // namespace fst
|
|
|
|
#endif // FST_CC_VISITORS_H_
|