// algo_test.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
// Regression test for various FST algorithms.
#ifndef FST_TEST_ALGO_TEST_H__
#define FST_TEST_ALGO_TEST_H__
#include <fst/fstlib.h>
#include <fst/random-weight.h>
DECLARE_int32(repeat); // defined in ./algo_test.cc
namespace fst {
// Mapper to change input and output label of every transition into
// epsilons.
template <class A>
class EpsMapper {
public:
EpsMapper() {}
A operator()(const A &arc) const {
return A(0, 0, arc.weight, arc.nextstate);
}
uint64 Properties(uint64 props) const {
props &= ~kNotAcceptor;
props |= kAcceptor;
props &= ~kNoIEpsilons & ~kNoOEpsilons & ~kNoEpsilons;
props |= kIEpsilons | kOEpsilons | kEpsilons;
props &= ~kNotILabelSorted & ~kNotOLabelSorted;
props |= kILabelSorted | kOLabelSorted;
return props;
}
MapFinalAction FinalAction() const { return MAP_NO_SUPERFINAL; }
MapSymbolsAction InputSymbolsAction() const { return MAP_COPY_SYMBOLS;}
MapSymbolsAction OutputSymbolsAction() const { return MAP_COPY_SYMBOLS;}
};
// This class tests a variety of identities and properties that must
// hold for various algorithms on weighted FSTs.
template <class Arc, class WeightGenerator>
class WeightedTester {
public:
typedef typename Arc::Label Label;
typedef typename Arc::StateId StateId;
typedef typename Arc::Weight Weight;
WeightedTester(int seed, const Fst<Arc> &zero_fst, const Fst<Arc> &one_fst,
const Fst<Arc> &univ_fst, WeightGenerator *weight_generator)
: seed_(seed), zero_fst_(zero_fst), one_fst_(one_fst),
univ_fst_(univ_fst), weight_generator_(weight_generator) {}
void Test(const Fst<Arc> &T1, const Fst<Arc> &T2, const Fst<Arc> &T3) {
TestRational(T1, T2, T3);
TestMap(T1);
TestCompose(T1, T2, T3);
TestSort(T1);
TestOptimize(T1);
TestSearch(T1);
}
private:
// Tests rational operations with identities
void TestRational(const Fst<Arc> &T1, const Fst<Arc> &T2,
const Fst<Arc> &T3) {
{
VLOG(1) << "Check destructive and delayed union are equivalent.";
VectorFst<Arc> U1(T1);
Union(&U1, T2);
UnionFst<Arc> U2(T1, T2);
CHECK(Equiv(U1, U2));
}
{
VLOG(1) << "Check destructive and delayed concatenation are equivalent.";
VectorFst<Arc> C1(T1);
Concat(&C1, T2);
ConcatFst<Arc> C2(T1, T2);
CHECK(Equiv(C1, C2));
VectorFst<Arc> C3(T2);
Concat(T1, &C3);
CHECK(Equiv(C3, C2));
}
{
VLOG(1) << "Check destructive and delayed closure* are equivalent.";
VectorFst<Arc> C1(T1);
Closure(&C1, CLOSURE_STAR);
ClosureFst<Arc> C2(T1, CLOSURE_STAR);
CHECK(Equiv(C1, C2));
}
{
VLOG(1) << "Check destructive and delayed closure+ are equivalent.";
VectorFst<Arc> C1(T1);
Closure(&C1, CLOSURE_PLUS);
ClosureFst<Arc> C2(T1, CLOSURE_PLUS);
CHECK(Equiv(C1, C2));
}
{
VLOG(1) << "Check union is associative (destructive).";
VectorFst<Arc> U1(T1);
Union(&U1, T2);
Union(&U1, T3);
VectorFst<Arc> U3(T2);
Union(&U3, T3);
VectorFst<Arc> U4(T1);
Union(&U4, U3);
CHECK(Equiv(U1, U4));
}
{
VLOG(1) << "Check union is associative (delayed).";
UnionFst<Arc> U1(T1, T2);
UnionFst<Arc> U2(U1, T3);
UnionFst<Arc> U3(T2, T3);
UnionFst<Arc> U4(T1, U3);
CHECK(Equiv(U2, U4));
}
{
VLOG(1) << "Check union is associative (destructive delayed).";
UnionFst<Arc> U1(T1, T2);
Union(&U1, T3);
UnionFst<Arc> U3(T2, T3);
UnionFst<Arc> U4(T1, U3);
CHECK(Equiv(U1, U4));
}
{
VLOG(1) << "Check concatenation is associative (destructive).";
VectorFst<Arc> C1(T1);
Concat(&C1, T2);
Concat(&C1, T3);
VectorFst<Arc> C3(T2);
Concat(&C3, T3);
VectorFst<Arc> C4(T1);
Concat(&C4, C3);
CHECK(Equiv(C1, C4));
}
{
VLOG(1) << "Check concatenation is associative (delayed).";
ConcatFst<Arc> C1(T1, T2);
ConcatFst<Arc> C2(C1, T3);
ConcatFst<Arc> C3(T2, T3);
ConcatFst<Arc> C4(T1, C3);
CHECK(Equiv(C2, C4));
}
{
VLOG(1) << "Check concatenation is associative (destructive delayed).";
ConcatFst<Arc> C1(T1, T2);
Concat(&C1, T3);
ConcatFst<Arc> C3(T2, T3);
ConcatFst<Arc> C4(T1, C3);
CHECK(Equiv(C1, C4));
}
if (Weight::Properties() & kLeftSemiring) {
VLOG(1) << "Check concatenation left distributes"
<< " over union (destructive).";
VectorFst<Arc> U1(T1);
Union(&U1, T2);
VectorFst<Arc> C1(T3);
Concat(&C1, U1);
VectorFst<Arc> C2(T3);
Concat(&C2, T1);
VectorFst<Arc> C3(T3);
Concat(&C3, T2);
VectorFst<Arc> U2(C2);
Union(&U2, C3);
CHECK(Equiv(C1, U2));
}
if (Weight::Properties() & kRightSemiring) {
VLOG(1) << "Check concatenation right distributes"
<< " over union (destructive).";
VectorFst<Arc> U1(T1);
Union(&U1, T2);
VectorFst<Arc> C1(U1);
Concat(&C1, T3);
VectorFst<Arc> C2(T1);
Concat(&C2, T3);
VectorFst<Arc> C3(T2);
Concat(&C3, T3);
VectorFst<Arc> U2(C2);
Union(&U2, C3);
CHECK(Equiv(C1, U2));
}
if (Weight::Properties() & kLeftSemiring) {
VLOG(1) << "Check concatenation left distributes over union (delayed).";
UnionFst<Arc> U1(T1, T2);
ConcatFst<Arc> C1(T3, U1);
ConcatFst<Arc> C2(T3, T1);
ConcatFst<Arc> C3(T3, T2);
UnionFst<Arc> U2(C2, C3);
CHECK(Equiv(C1, U2));
}
if (Weight::Properties() & kRightSemiring) {
VLOG(1) << "Check concatenation right distributes over union (delayed).";
UnionFst<Arc> U1(T1, T2);
ConcatFst<Arc> C1(U1, T3);
ConcatFst<Arc> C2(T1, T3);
ConcatFst<Arc> C3(T2, T3);
UnionFst<Arc> U2(C2, C3);
CHECK(Equiv(C1, U2));
}
if (Weight::Properties() & kLeftSemiring) {
VLOG(1) << "Check T T* == T+ (destructive).";
VectorFst<Arc> S(T1);
Closure(&S, CLOSURE_STAR);
VectorFst<Arc> C(T1);
Concat(&C, S);
VectorFst<Arc> P(T1);
Closure(&P, CLOSURE_PLUS);
CHECK(Equiv(C, P));
}
if (Weight::Properties() & kRightSemiring) {
VLOG(1) << "Check T* T == T+ (destructive).";
VectorFst<Arc> S(T1);
Closure(&S, CLOSURE_STAR);
VectorFst<Arc> C(S);
Concat(&C, T1);
VectorFst<Arc> P(T1);
Closure(&P, CLOSURE_PLUS);
CHECK(Equiv(C, P));
}
if (Weight::Properties() & kLeftSemiring) {
VLOG(1) << "Check T T* == T+ (delayed).";
ClosureFst<Arc> S(T1, CLOSURE_STAR);
ConcatFst<Arc> C(T1, S);
ClosureFst<Arc> P(T1, CLOSURE_PLUS);
CHECK(Equiv(C, P));
}
if (Weight::Properties() & kRightSemiring) {
VLOG(1) << "Check T* T == T+ (delayed).";
ClosureFst<Arc> S(T1, CLOSURE_STAR);
ConcatFst<Arc> C(S, T1);
ClosureFst<Arc> P(T1, CLOSURE_PLUS);
CHECK(Equiv(C, P));
}
}
// Tests map-based operations.
void TestMap(const Fst<Arc> &T) {
{
VLOG(1) << "Check destructive and delayed projection are equivalent.";
VectorFst<Arc> P1(T);
Project(&P1, PROJECT_INPUT);
ProjectFst<Arc> P2(T, PROJECT_INPUT);
CHECK(Equiv(P1, P2));
}
{
VLOG(1) << "Check destructive and delayed inversion are equivalent.";
VectorFst<Arc> I1(T);
Invert(&I1);
InvertFst<Arc> I2(T);
CHECK(Equiv(I1, I2));
}
{
VLOG(1) << "Check Pi_1(T) = Pi_2(T^-1) (destructive).";
VectorFst<Arc> P1(T);
VectorFst<Arc> I1(T);
Project(&P1, PROJECT_INPUT);
Invert(&I1);
Project(&I1, PROJECT_OUTPUT);
CHECK(Equiv(P1, I1));
}
{
VLOG(1) << "Check Pi_2(T) = Pi_1(T^-1) (destructive).";
VectorFst<Arc> P1(T);
VectorFst<Arc> I1(T);
Project(&P1, PROJECT_OUTPUT);
Invert(&I1);
Project(&I1, PROJECT_INPUT);
CHECK(Equiv(P1, I1));
}
{
VLOG(1) << "Check Pi_1(T) = Pi_2(T^-1) (delayed).";
ProjectFst<Arc> P1(T, PROJECT_INPUT);
InvertFst<Arc> I1(T);
ProjectFst<Arc> P2(I1, PROJECT_OUTPUT);
CHECK(Equiv(P1, P2));
}
{
VLOG(1) << "Check Pi_2(T) = Pi_1(T^-1) (delayed).";
ProjectFst<Arc> P1(T, PROJECT_OUTPUT);
InvertFst<Arc> I1(T);
ProjectFst<Arc> P2(I1, PROJECT_INPUT);
CHECK(Equiv(P1, P2));
}
{
VLOG(1) << "Check destructive relabeling";
static const int kNumLabels = 10;
// set up relabeling pairs
vector<Label> labelset(kNumLabels);
for (size_t i = 0; i < kNumLabels; ++i) labelset[i] = i;
for (size_t i = 0; i < kNumLabels; ++i) {
swap(labelset[i], labelset[rand() % kNumLabels]);
}
vector<pair<Label, Label> > ipairs1(kNumLabels);
vector<pair<Label, Label> > opairs1(kNumLabels);
for (size_t i = 0; i < kNumLabels; ++i) {
ipairs1[i] = make_pair(i, labelset[i]);
opairs1[i] = make_pair(labelset[i], i);
}
VectorFst<Arc> R(T);
Relabel(&R, ipairs1, opairs1);
vector<pair<Label, Label> > ipairs2(kNumLabels);
vector<pair<Label, Label> > opairs2(kNumLabels);
for (size_t i = 0; i < kNumLabels; ++i) {
ipairs2[i] = make_pair(labelset[i], i);
opairs2[i] = make_pair(i, labelset[i]);
}
Relabel(&R, ipairs2, opairs2);
CHECK(Equiv(R, T));
VLOG(1) << "Check on-the-fly relabeling";
RelabelFst<Arc> Rdelay(T, ipairs1, opairs1);
RelabelFst<Arc> RRdelay(Rdelay, ipairs2, opairs2);
CHECK(Equiv(RRdelay, T));
}
{
VLOG(1) << "Check encoding/decoding (destructive).";
VectorFst<Arc> D(T);
uint32 encode_props = 0;
if (rand() % 2)
encode_props |= kEncodeLabels;
if (rand() % 2)
encode_props |= kEncodeWeights;
EncodeMapper<Arc> encoder(encode_props, ENCODE);
Encode(&D, &encoder);
Decode(&D, encoder);
CHECK(Equiv(D, T));
}
{
VLOG(1) << "Check encoding/decoding (delayed).";
uint32 encode_props = 0;
if (rand() % 2)
encode_props |= kEncodeLabels;
if (rand() % 2)
encode_props |= kEncodeWeights;
EncodeMapper<Arc> encoder(encode_props, ENCODE);
EncodeFst<Arc> E(T, &encoder);
VectorFst<Arc> Encoded(E);
DecodeFst<Arc> D(Encoded, encoder);
CHECK(Equiv(D, T));
}
{
VLOG(1) << "Check gallic mappers (constructive).";
ToGallicMapper<Arc> to_mapper;
FromGallicMapper<Arc> from_mapper;
VectorFst< GallicArc<Arc> > G;
VectorFst<Arc> F;
ArcMap(T, &G, to_mapper);
ArcMap(G, &F, from_mapper);
CHECK(Equiv(T, F));
}
{
VLOG(1) << "Check gallic mappers (delayed).";
ToGallicMapper<Arc> to_mapper;
FromGallicMapper<Arc> from_mapper;
ArcMapFst<Arc, GallicArc<Arc>, ToGallicMapper<Arc> >
G(T, to_mapper);
ArcMapFst<GallicArc<Arc>, Arc, FromGallicMapper<Arc> >
F(G, from_mapper);
CHECK(Equiv(T, F));
}
}
// Tests compose-based operations.
void TestCompose(const Fst<Arc> &T1, const Fst<Arc> &T2,
const Fst<Arc> &T3) {
if (!(Weight::Properties() & kCommutative))
return;
VectorFst<Arc> S1(T1);
VectorFst<Arc> S2(T2);
VectorFst<Arc> S3(T3);
ILabelCompare<Arc> icomp;
OLabelCompare<Arc> ocomp;
ArcSort(&S1, ocomp);
ArcSort(&S2, ocomp);
ArcSort(&S3, icomp);
{
VLOG(1) << "Check composition is associative.";
ComposeFst<Arc> C1(S1, S2);
ComposeFst<Arc> C2(C1, S3);
ComposeFst<Arc> C3(S2, S3);
ComposeFst<Arc> C4(S1, C3);
CHECK(Equiv(C2, C4));
}
{
VLOG(1) << "Check composition left distributes over union.";
UnionFst<Arc> U1(S2, S3);
ComposeFst<Arc> C1(S1, U1);
ComposeFst<Arc> C2(S1, S2);
ComposeFst<Arc> C3(S1, S3);
UnionFst<Arc> U2(C2, C3);
CHECK(Equiv(C1, U2));
}
{
VLOG(1) << "Check composition right distributes over union.";
UnionFst<Arc> U1(S1, S2);
ComposeFst<Arc> C1(U1, S3);
ComposeFst<Arc> C2(S1, S3);
ComposeFst<Arc> C3(S2, S3);
UnionFst<Arc> U2(C2, C3);
CHECK(Equiv(C1, U2));
}
VectorFst<Arc> A1(S1);
VectorFst<Arc> A2(S2);
VectorFst<Arc> A3(S3);
Project(&A1, PROJECT_OUTPUT);
Project(&A2, PROJECT_INPUT);
Project(&A3, PROJECT_INPUT);
{
VLOG(1) << "Check intersection is commutative.";
IntersectFst<Arc> I1(A1, A2);
IntersectFst<Arc> I2(A2, A1);
CHECK(Equiv(I1, I2));
}
{
VLOG(1) << "Check all epsilon filters leads to equivalent results.";
typedef Matcher< Fst<Arc> > M;
ComposeFst<Arc> C1(S1, S2);
ComposeFst<Arc> C2(
S1, S2,
ComposeFstOptions<Arc, M, AltSequenceComposeFilter<M> >());
ComposeFst<Arc> C3(
S1, S2,
ComposeFstOptions<Arc, M, MatchComposeFilter<M> >());
CHECK(Equiv(C1, C2));
CHECK(Equiv(C1, C3));
}
}
// Tests sorting operations
void TestSort(const Fst<Arc> &T) {
ILabelCompare<Arc> icomp;
OLabelCompare<Arc> ocomp;
{
VLOG(1) << "Check arc sorted Fst is equivalent to its input.";
VectorFst<Arc> S1(T);
ArcSort(&S1, icomp);
CHECK(Equiv(T, S1));
}
{
VLOG(1) << "Check destructive and delayed arcsort are equivalent.";
VectorFst<Arc> S1(T);
ArcSort(&S1, icomp);
ArcSortFst< Arc, ILabelCompare<Arc> > S2(T, icomp);
CHECK(Equiv(S1, S2));
}
{
VLOG(1) << "Check ilabel sorting vs. olabel sorting with inversions.";
VectorFst<Arc> S1(T);
VectorFst<Arc> S2(T);
ArcSort(&S1, icomp);
Invert(&S2);
ArcSort(&S2, ocomp);
Invert(&S2);
CHECK(Equiv(S1, S2));
}
{
VLOG(1) << "Check topologically sorted Fst is equivalent to its input.";
VectorFst<Arc> S1(T);
TopSort(&S1);
CHECK(Equiv(T, S1));
}
{
VLOG(1) << "Check reverse(reverse(T)) = T";
VectorFst< ReverseArc<Arc> > R1;
VectorFst<Arc> R2;
Reverse(T, &R1);
Reverse(R1, &R2);
CHECK(Equiv(T, R2));
}
}
// Tests optimization operations
void TestOptimize(const Fst<Arc> &T) {
uint64 tprops = T.Properties(kFstProperties, true);
uint64 wprops = Weight::Properties();
VectorFst<Arc> A(T);
Project(&A, PROJECT_INPUT);
{
VLOG(1) << "Check connected FST is equivalent to its input.";
VectorFst<Arc> C1(T);
Connect(&C1);
CHECK(Equiv(T, C1));
}
if ((wprops & kSemiring) == kSemiring &&
(tprops & kAcyclic || wprops & kIdempotent)) {
VLOG(1) << "Check epsilon-removed FST is equivalent to its input.";
VectorFst<Arc> R1(T);
RmEpsilon(&R1);
CHECK(Equiv(T, R1));
VLOG(1) << "Check destructive and delayed epsilon removal"
<< "are equivalent.";
RmEpsilonFst<Arc> R2(T);
CHECK(Equiv(R1, R2));
VLOG(1) << "Check an FST with a large proportion"
<< " of epsilon transitions:";
// Maps all transitions of T to epsilon-transitions and append
// a non-epsilon transition.
VectorFst<Arc> U;
ArcMap(T, &U, EpsMapper<Arc>());
VectorFst<Arc> V;
V.SetStart(V.AddState());
Arc arc(1, 1, Weight::One(), V.AddState());
V.AddArc(V.Start(), arc);
V.SetFinal(arc.nextstate, Weight::One());
Concat(&U, V);
// Check that epsilon-removal preserves the shortest-distance
// from the initial state to the final states.
vector<Weight> d;
ShortestDistance(U, &d, true);
Weight w = U.Start() < d.size() ? d[U.Start()] : Weight::Zero();
VectorFst<Arc> U1(U);
RmEpsilon(&U1);
ShortestDistance(U1, &d, true);
Weight w1 = U1.Start() < d.size() ? d[U1.Start()] : Weight::Zero();
CHECK(ApproxEqual(w, w1, kTestDelta));
RmEpsilonFst<Arc> U2(U);
ShortestDistance(U2, &d, true);
Weight w2 = U2.Start() < d.size() ? d[U2.Start()] : Weight::Zero();
CHECK(ApproxEqual(w, w2, kTestDelta));
}
if ((wprops & kSemiring) == kSemiring && tprops & kAcyclic) {
VLOG(1) << "Check determinized FSA is equivalent to its input.";
DeterminizeFst<Arc> D(A);
CHECK(Equiv(A, D));
int n;
{
VLOG(1) << "Check size(min(det(A))) <= size(det(A))"
<< " and min(det(A)) equiv det(A)";
VectorFst<Arc> M(D);
n = M.NumStates();
Minimize(&M);
CHECK(Equiv(D, M));
CHECK(M.NumStates() <= n);
n = M.NumStates();
}
if (n && (wprops & kIdempotent) == kIdempotent &&
A.Properties(kNoEpsilons, true)) {
VLOG(1) << "Check that Revuz's algorithm leads to the"
<< " same number of states as Brozozowski's algorithm";
// Skip test if A is the empty machine or contains epsilons or
// if the semiring is not idempotent (to avoid floating point
// errors)
VectorFst<Arc> R;
Reverse(A, &R);
RmEpsilon(&R);
DeterminizeFst<Arc> DR(R);
VectorFst<Arc> RD;
Reverse(DR, &RD);
DeterminizeFst<Arc> DRD(RD);
VectorFst<Arc> M(DRD);
CHECK_EQ(n + 1, M.NumStates()); // Accounts for the epsilon transition
// to the initial state
}
}
if (Arc::Type() == LogArc::Type() || Arc::Type() == StdArc::Type()) {
VLOG(1) << "Check reweight(T) equiv T";
vector<Weight> potential;
VectorFst<Arc> RI(T);
VectorFst<Arc> RF(T);
while (potential.size() < RI.NumStates())
potential.push_back((*weight_generator_)());
Reweight(&RI, potential, REWEIGHT_TO_INITIAL);
CHECK(Equiv(T, RI));
Reweight(&RF, potential, REWEIGHT_TO_FINAL);
CHECK(Equiv(T, RF));
}
if ((wprops & kIdempotent) || (tprops & kAcyclic)) {
VLOG(1) << "Check pushed FST is equivalent to input FST.";
// Pushing towards the final state.
if (wprops & kRightSemiring) {
VectorFst<Arc> P1;
Push<Arc, REWEIGHT_TO_FINAL>(T, &P1, kPushLabels);
CHECK(Equiv(T, P1));
VectorFst<Arc> P2;
Push<Arc, REWEIGHT_TO_FINAL>(T, &P2, kPushWeights);
CHECK(Equiv(T, P2));
VectorFst<Arc> P3;
Push<Arc, REWEIGHT_TO_FINAL>(T, &P3, kPushLabels | kPushWeights);
CHECK(Equiv(T, P3));
}
// Pushing towards the initial state.
if (wprops & kLeftSemiring) {
VectorFst<Arc> P1;
Push<Arc, REWEIGHT_TO_INITIAL>(T, &P1, kPushLabels);
CHECK(Equiv(T, P1));
VectorFst<Arc> P2;
Push<Arc, REWEIGHT_TO_INITIAL>(T, &P2, kPushWeights);
CHECK(Equiv(T, P2));
VectorFst<Arc> P3;
Push<Arc, REWEIGHT_TO_INITIAL>(T, &P3, kPushLabels | kPushWeights);
CHECK(Equiv(T, P3));
}
}
if ((wprops & (kPath | kCommutative)) == (kPath | kCommutative)) {
VLOG(1) << "Check pruning algorithm";
{
VLOG(1) << "Check equiv. of constructive and destructive algorithms";
Weight thresold = (*weight_generator_)();
VectorFst<Arc> P1(T);
Prune(&P1, thresold);
VectorFst<Arc> P2;
Prune(T, &P2, thresold);
CHECK(Equiv(P1,P2));
}
{
VLOG(1) << "Check prune(reverse) equiv reverse(prune)";
Weight thresold = (*weight_generator_)();
VectorFst< ReverseArc<Arc> > R;
VectorFst<Arc> P1(T);
VectorFst<Arc> P2;
Prune(&P1, thresold);
Reverse(T, &R);
Prune(&R, thresold.Reverse());
Reverse(R, &P2);
CHECK(Equiv(P1, P2));
}
{
VLOG(1) << "Check: ShortestDistance(T- prune(T))"
<< " > ShortestDistance(T) times Thresold";
Weight thresold = (*weight_generator_)();
VectorFst<Arc> P;
Prune(A, &P, thresold);
DifferenceFst<Arc> C(A, DeterminizeFst<Arc>
(RmEpsilonFst<Arc>
(ArcMapFst<Arc, Arc,
RmWeightMapper<Arc> >
(P, RmWeightMapper<Arc>()))));
Weight sum1 = Times(ShortestDistance(A), thresold);
Weight sum2 = ShortestDistance(C);
CHECK(Plus(sum1, sum2) == sum1);
}
}
if (tprops & kAcyclic) {
VLOG(1) << "Check synchronize(T) equiv T";
SynchronizeFst<Arc> S(T);
CHECK(Equiv(T, S));
}
}
// Tests search operations
void TestSearch(const Fst<Arc> &T) {
uint64 wprops = Weight::Properties();
VectorFst<Arc> A(T);
Project(&A, PROJECT_INPUT);
if ((wprops & (kPath | kRightSemiring)) == (kPath | kRightSemiring)) {
VLOG(1) << "Check 1-best weight.";
VectorFst<Arc> path;
ShortestPath(T, &path);
Weight tsum = ShortestDistance(T);
Weight psum = ShortestDistance(path);
CHECK(ApproxEqual(tsum, psum, kTestDelta));
}
if ((wprops & (kPath | kSemiring)) == (kPath | kSemiring)) {
VLOG(1) << "Check n-best weights";
VectorFst<Arc> R(A);
RmEpsilon(&R);
int nshortest = rand() % kNumRandomShortestPaths + 2;
VectorFst<Arc> paths;
ShortestPath(R, &paths, nshortest, true, false,
Weight::Zero(), kNumShortestStates);
vector<Weight> distance;
ShortestDistance(paths, &distance, true);
StateId pstart = paths.Start();
if (pstart != kNoStateId) {
ArcIterator< Fst<Arc> > piter(paths, pstart);
for (; !piter.Done(); piter.Next()) {
StateId s = piter.Value().nextstate;
Weight nsum = s < distance.size() ?
Times(piter.Value().weight, distance[s]) : Weight::Zero();
VectorFst<Arc> path;
ShortestPath(R, &path);
Weight dsum = ShortestDistance(path);
CHECK(ApproxEqual(nsum, dsum, kTestDelta));
ArcMap(&path, RmWeightMapper<Arc>());
VectorFst<Arc> S;
Difference(R, path, &S);
R = S;
}
}
}
}
// Tests if two FSTS are equivalent by checking if random
// strings from one FST are transduced the same by both FSTs.
bool Equiv(const Fst<Arc> &fst1, const Fst<Arc> &fst2) {
VLOG(1) << "Check FSTs for sanity (including property bits).";
CHECK(Verify(fst1));
CHECK(Verify(fst2));
UniformArcSelector<Arc> uniform_selector(seed_);
RandGenOptions< UniformArcSelector<Arc> >
opts(uniform_selector, kRandomPathLength);
return RandEquivalent(fst1, fst2, kNumRandomPaths, kTestDelta, opts);
}
// Random seed
int seed_;
// FST with no states
VectorFst<Arc> zero_fst_;
// FST with one state that accepts epsilon.
VectorFst<Arc> one_fst_;
// FST with one state that accepts all strings.
VectorFst<Arc> univ_fst_;
// Generates weights used in testing.
WeightGenerator *weight_generator_;
// Maximum random path length.
static const int kRandomPathLength;
// Number of random paths to explore.
static const int kNumRandomPaths;
// Maximum number of nshortest paths.
static const int kNumRandomShortestPaths;
// Maximum number of nshortest states.
static const int kNumShortestStates;
// Delta for equivalence tests.
static const float kTestDelta;
DISALLOW_COPY_AND_ASSIGN(WeightedTester);
};
template <class A, class WG>
const int WeightedTester<A, WG>::kRandomPathLength = 25;
template <class A, class WG>
const int WeightedTester<A, WG>::kNumRandomPaths = 100;
template <class A, class WG>
const int WeightedTester<A, WG>::kNumRandomShortestPaths = 100;
template <class A, class WG>
const int WeightedTester<A, WG>::kNumShortestStates = 10000;
template <class A, class WG>
const float WeightedTester<A, WG>::kTestDelta = .05;
// This class tests a variety of identities and properties that must
// hold for various algorithms on unweighted FSAs and that are not tested
// by WeightedTester. Only the specialization does anything interesting.
template <class Arc>
class UnweightedTester {
public:
UnweightedTester(const Fst<Arc> &zero_fsa, const Fst<Arc> &one_fsa,
const Fst<Arc> &univ_fsa) {}
void Test(const Fst<Arc> &A1, const Fst<Arc> &A2, const Fst<Arc> &A3) {}
};
// Specialization for StdArc. This should work for any commutative,
// idempotent semiring when restricted to the unweighted case
// (being isomorphic to the boolean semiring).
template <>
class UnweightedTester<StdArc> {
public:
typedef StdArc Arc;
typedef Arc::Label Label;
typedef Arc::StateId StateId;
typedef Arc::Weight Weight;
UnweightedTester(const Fst<Arc> &zero_fsa, const Fst<Arc> &one_fsa,
const Fst<Arc> &univ_fsa)
: zero_fsa_(zero_fsa), one_fsa_(one_fsa), univ_fsa_(univ_fsa) {}
void Test(const Fst<Arc> &A1, const Fst<Arc> &A2, const Fst<Arc> &A3) {
TestRational(A1, A2, A3);
TestIntersect(A1, A2, A3);
TestOptimize(A1);
}
private:
// Tests rational operations with identities
void TestRational(const Fst<Arc> &A1, const Fst<Arc> &A2,
const Fst<Arc> &A3) {
{
VLOG(1) << "Check the union contains its arguments (destructive).";
VectorFst<Arc> U(A1);
Union(&U, A2);
CHECK(Subset(A1, U));
CHECK(Subset(A2, U));
}
{
VLOG(1) << "Check the union contains its arguments (delayed).";
UnionFst<Arc> U(A1, A2);
CHECK(Subset(A1, U));
CHECK(Subset(A2, U));
}
{
VLOG(1) << "Check if A^n c A* (destructive).";
VectorFst<Arc> C(one_fsa_);
int n = rand() % 5;
for (int i = 0; i < n; ++i)
Concat(&C, A1);
VectorFst<Arc> S(A1);
Closure(&S, CLOSURE_STAR);
CHECK(Subset(C, S));
}
{
VLOG(1) << "Check if A^n c A* (delayed).";
int n = rand() % 5;
Fst<Arc> *C = new VectorFst<Arc>(one_fsa_);
for (int i = 0; i < n; ++i) {
ConcatFst<Arc> *F = new ConcatFst<Arc>(*C, A1);
delete C;
C = F;
}
ClosureFst<Arc> S(A1, CLOSURE_STAR);
CHECK(Subset(*C, S));
delete C;
}
}
// Tests intersect-based operations.
void TestIntersect(const Fst<Arc> &A1, const Fst<Arc> &A2,
const Fst<Arc> &A3) {
VectorFst<Arc> S1(A1);
VectorFst<Arc> S2(A2);
VectorFst<Arc> S3(A3);
ILabelCompare<Arc> comp;
ArcSort(&S1, comp);
ArcSort(&S2, comp);
ArcSort(&S3, comp);
{
VLOG(1) << "Check the intersection is contained in its arguments.";
IntersectFst<Arc> I1(S1, S2);
CHECK(Subset(I1, S1));
CHECK(Subset(I1, S2));
}
{
VLOG(1) << "Check union distributes over intersection.";
IntersectFst<Arc> I1(S1, S2);
UnionFst<Arc> U1(I1, S3);
UnionFst<Arc> U2(S1, S3);
UnionFst<Arc> U3(S2, S3);
ArcSortFst< Arc, ILabelCompare<Arc> > S4(U3, comp);
IntersectFst<Arc> I2(U2, S4);
CHECK(Equiv(U1, I2));
}
VectorFst<Arc> C1;
VectorFst<Arc> C2;
Complement(S1, &C1);
Complement(S2, &C2);
ArcSort(&C1, comp);
ArcSort(&C2, comp);
{
VLOG(1) << "Check S U S' = Sigma*";
UnionFst<Arc> U(S1, C1);
CHECK(Equiv(U, univ_fsa_));
}
{
VLOG(1) << "Check S n S' = {}";
IntersectFst<Arc> I(S1, C1);
CHECK(Equiv(I, zero_fsa_));
}
{
VLOG(1) << "Check (S1' U S2') == (S1 n S2)'";
UnionFst<Arc> U(C1, C2);
IntersectFst<Arc> I(S1, S2);
VectorFst<Arc> C3;
Complement(I, &C3);
CHECK(Equiv(U, C3));
}
{
VLOG(1) << "Check (S1' n S2') == (S1 U S2)'";
IntersectFst<Arc> I(C1, C2);
UnionFst<Arc> U(S1, S2);
VectorFst<Arc> C3;
Complement(U, &C3);
CHECK(Equiv(I, C3));
}
}
// Tests optimization operations
void TestOptimize(const Fst<Arc> &A) {
{
VLOG(1) << "Check determinized FSA is equivalent to its input.";
DeterminizeFst<Arc> D(A);
CHECK(Equiv(A, D));
}
{
VLOG(1) << "Check minimized FSA is equivalent to its input.";
int n;
{
RmEpsilonFst<Arc> R(A);
DeterminizeFst<Arc> D(R);
VectorFst<Arc> M(D);
Minimize(&M);
CHECK(Equiv(A, M));
n = M.NumStates();
}
if (n) { // Skip test if A is the empty machine
VLOG(1) << "Check that Hopcroft's and Revuz's algorithms lead to the"
<< " same number of states as Brozozowski's algorithm";
VectorFst<Arc> R;
Reverse(A, &R);
RmEpsilon(&R);
DeterminizeFst<Arc> DR(R);
VectorFst<Arc> RD;
Reverse(DR, &RD);
DeterminizeFst<Arc> DRD(RD);
VectorFst<Arc> M(DRD);
CHECK_EQ(n + 1, M.NumStates()); // Accounts for the epsilon transition
// to the initial state
}
}
}
// Tests if two FSAS are equivalent.
bool Equiv(const Fst<Arc> &fsa1, const Fst<Arc> &fsa2) {
VLOG(1) << "Check FSAs for sanity (including property bits).";
CHECK(Verify(fsa1));
CHECK(Verify(fsa2));
VectorFst<Arc> vfsa1(fsa1);
VectorFst<Arc> vfsa2(fsa2);
RmEpsilon(&vfsa1);
RmEpsilon(&vfsa2);
DeterminizeFst<Arc> dfa1(vfsa1);
DeterminizeFst<Arc> dfa2(vfsa2);
// Test equivalence using union-find algorithm
bool equiv1 = Equivalent(dfa1, dfa2);
// Test equivalence by checking if (S1 - S2) U (S2 - S1) is empty
ILabelCompare<Arc> comp;
VectorFst<Arc> sdfa1(dfa1);
ArcSort(&sdfa1, comp);
VectorFst<Arc> sdfa2(dfa2);
ArcSort(&sdfa2, comp);
DifferenceFst<Arc> dfsa1(sdfa1, sdfa2);
DifferenceFst<Arc> dfsa2(sdfa2, sdfa1);
VectorFst<Arc> ufsa(dfsa1);
Union(&ufsa, dfsa2);
Connect(&ufsa);
bool equiv2 = ufsa.NumStates() == 0;
// Check two equivalence tests match
CHECK((equiv1 && equiv2) || (!equiv1 && !equiv2));
return equiv1;
}
// Tests if FSA1 is a subset of FSA2 (disregarding weights).
bool Subset(const Fst<Arc> &fsa1, const Fst<Arc> &fsa2) {
VLOG(1) << "Check FSAs (incl. property bits) for sanity";
CHECK(Verify(fsa1));
CHECK(Verify(fsa2));
VectorFst<StdArc> vfsa1;
VectorFst<StdArc> vfsa2;
RmEpsilon(&vfsa1);
RmEpsilon(&vfsa2);
ILabelCompare<StdArc> comp;
ArcSort(&vfsa1, comp);
ArcSort(&vfsa2, comp);
IntersectFst<StdArc> ifsa(vfsa1, vfsa2);
DeterminizeFst<StdArc> dfa1(vfsa1);
DeterminizeFst<StdArc> dfa2(ifsa);
return Equivalent(dfa1, dfa2);
}
// Returns complement Fsa
void Complement(const Fst<Arc> &ifsa, MutableFst<Arc> *ofsa) {
RmEpsilonFst<Arc> rfsa(ifsa);
DeterminizeFst<Arc> dfa(rfsa);
DifferenceFst<Arc> cfsa(univ_fsa_, dfa);
*ofsa = cfsa;
}
// FSA with no states
VectorFst<Arc> zero_fsa_;
// FSA with one state that accepts epsilon.
VectorFst<Arc> one_fsa_;
// FSA with one state that accepts all strings.
VectorFst<Arc> univ_fsa_;
DISALLOW_COPY_AND_ASSIGN(UnweightedTester);
};
// This class tests a variety of identities and properties that must
// hold for various FST algorithms. It randomly generates FSTs, using
// function object 'weight_generator' to select weights. 'WeightTester'
// and 'UnweightedTester' are then called.
template <class Arc, class WeightGenerator>
class AlgoTester {
public:
typedef typename Arc::Label Label;
typedef typename Arc::StateId StateId;
typedef typename Arc::Weight Weight;
AlgoTester(WeightGenerator generator, int seed) :
weight_generator_(generator), seed_(seed) {
one_fst_.AddState();
one_fst_.SetStart(0);
one_fst_.SetFinal(0, Weight::One());
univ_fst_.AddState();
univ_fst_.SetStart(0);
univ_fst_.SetFinal(0, Weight::One());
for (int i = 0; i < kNumRandomLabels; ++i)
univ_fst_.AddArc(0, Arc(i, i, Weight::One(), 0));
}
void Test() {
VLOG(1) << "weight type = " << Weight::Type();
for (int i = 0; i < FLAGS_repeat; ++i) {
// Random transducers
VectorFst<Arc> T1;
VectorFst<Arc> T2;
VectorFst<Arc> T3;
RandFst(&T1);
RandFst(&T2);
RandFst(&T3);
WeightedTester<Arc, WeightGenerator>
weighted_tester(seed_, zero_fst_, one_fst_,
univ_fst_, &weight_generator_);
weighted_tester.Test(T1, T2, T3);
VectorFst<Arc> A1(T1);
VectorFst<Arc> A2(T2);
VectorFst<Arc> A3(T3);
Project(&A1, PROJECT_OUTPUT);
Project(&A2, PROJECT_INPUT);
Project(&A3, PROJECT_INPUT);
ArcMap(&A1, rm_weight_mapper);
ArcMap(&A2, rm_weight_mapper);
ArcMap(&A3, rm_weight_mapper);
UnweightedTester<Arc> unweighted_tester(zero_fst_, one_fst_, univ_fst_);
unweighted_tester.Test(A1, A2, A3);
}
}
private:
// Generates a random FST.
void RandFst(MutableFst<Arc> *fst) {
// Determines direction of the arcs wrt state numbering. This way we
// can force acyclicity when desired.
enum ArcDirection { ANY_DIRECTION = 0, FORWARD_DIRECTION = 1,
REVERSE_DIRECTION = 2, NUM_DIRECTIONS = 3 };
ArcDirection arc_direction = ANY_DIRECTION;
if (rand()/(RAND_MAX + 1.0) < kAcyclicProb)
arc_direction = rand() % 2 ? FORWARD_DIRECTION : REVERSE_DIRECTION;
fst->DeleteStates();
StateId ns = rand() % kNumRandomStates;
if (ns == 0)
return;
for (StateId s = 0; s < ns; ++s)
fst->AddState();
StateId start = rand() % ns;
fst->SetStart(start);
size_t na = rand() % kNumRandomArcs;
for (size_t n = 0; n < na; ++n) {
StateId s = rand() % ns;
Arc arc;
arc.ilabel = rand() % kNumRandomLabels;
arc.olabel = rand() % kNumRandomLabels;
arc.weight = weight_generator_();
arc.nextstate = rand() % ns;
if (arc_direction == ANY_DIRECTION ||
(arc_direction == FORWARD_DIRECTION && arc.ilabel > arc.olabel) ||
(arc_direction == REVERSE_DIRECTION && arc.ilabel < arc.olabel))
fst->AddArc(s, arc);
}
StateId nf = rand() % (ns + 1);
for (StateId n = 0; n < nf; ++n) {
StateId s = rand() % ns;
Weight final = weight_generator_();
fst->SetFinal(s, final);
}
VLOG(1) << "Check FST for sanity (including property bits).";
CHECK(Verify(*fst));
// Get/compute all properties.
uint64 props = fst->Properties(kFstProperties, true);
// Select random set of properties to be unknown.
uint64 mask = 0;
for (int n = 0; n < 8; ++n) {
mask |= rand() & 0xff;
mask <<= 8;
}
mask &= ~kTrinaryProperties;
fst->SetProperties(props & ~mask, mask);
}
// Generates weights used in testing.
WeightGenerator weight_generator_;
// Random seed
int seed_;
// FST with no states
VectorFst<Arc> zero_fst_;
// FST with one state that accepts epsilon.
VectorFst<Arc> one_fst_;
// FST with one state that accepts all strings.
VectorFst<Arc> univ_fst_;
// Mapper to remove weights from an Fst
RmWeightMapper<Arc> rm_weight_mapper;
// Maximum number of states in random test Fst.
static const int kNumRandomStates;
// Maximum number of arcs in random test Fst.
static const int kNumRandomArcs;
// Number of alternative random labels.
static const int kNumRandomLabels;
// Probability to force an acyclic Fst
static const float kAcyclicProb;
// Maximum random path length.
static const int kRandomPathLength;
// Number of random paths to explore.
static const int kNumRandomPaths;
DISALLOW_COPY_AND_ASSIGN(AlgoTester);
};
template <class A, class G> const int AlgoTester<A, G>::kNumRandomStates = 10;
template <class A, class G> const int AlgoTester<A, G>::kNumRandomArcs = 25;
template <class A, class G> const int AlgoTester<A, G>::kNumRandomLabels = 5;
template <class A, class G> const float AlgoTester<A, G>::kAcyclicProb = .25;
template <class A, class G> const int AlgoTester<A, G>::kRandomPathLength = 25;
template <class A, class G> const int AlgoTester<A, G>::kNumRandomPaths = 100;
} // namespace fst
#endif // FST_TEST_ALGO_TEST_H__