qt6windows7/util/lexgen/nfa.cpp

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2023-10-30 06:33:08 +08:00
// Copyright (C) 2016 The Qt Company Ltd.
// SPDX-License-Identifier: LicenseRef-Qt-Commercial OR GPL-3.0-only WITH Qt-GPL-exception-1.0
#include "nfa.h"
#include <QSet>
#include <limits.h>
NFA NFA::createSingleInputNFA(InputType input)
{
NFA result;
result.initialize(2);
result.addTransition(result.initialState, input, result.finalState);
return result;
}
NFA NFA::createSymbolNFA(const QString &symbol)
{
NFA result = NFA::createSingleInputNFA(Epsilon);
result.states[result.finalState].symbol = symbol;
return result;
}
void NFA::initialize(int size)
{
states.resize(size);
states.fill(State());
initialState = 0;
finalState = size - 1;
}
void NFA::addTransition(int from, InputType input, int to)
{
assertValidState(from);
assertValidState(to);
states[from].transitions.insertMulti(input, to);
}
void NFA::copyFrom(const NFA &other, int baseState)
{
assertValidState(baseState);
assertValidState(baseState + other.states.count() - 1);
for (int i = 0; i < other.states.count(); ++i) {
State s = other.states.at(i);
for (TransitionMap::Iterator it = s.transitions.begin(),
end = s.transitions.end(); it != end; ++it)
*it += baseState;
states[baseState + i] = s;
}
}
void NFA::initializeFromPair(const NFA &a, const NFA &b,
int *initialA, int *finalA,
int *initialB, int *finalB)
{
initialize(a.states.count() + b.states.count() + 2);
int baseIdxA = 1;
int baseIdxB = 1 + a.states.count();
*initialA = a.initialState + baseIdxA;
*finalA = a.finalState + baseIdxA;
*initialB = b.initialState + baseIdxB;
*finalB = b.finalState + baseIdxB;
copyFrom(a, baseIdxA);
copyFrom(b, baseIdxB);
}
NFA NFA::createAlternatingNFA(const NFA &a, const NFA &b)
{
NFA result;
int newInitialA, newFinalA,
newInitialB, newFinalB;
result.initializeFromPair(a, b, &newInitialA, &newFinalA,
&newInitialB, &newFinalB);
result.addTransition(result.initialState, Epsilon, newInitialA);
result.addTransition(result.initialState, Epsilon, newInitialB);
result.addTransition(newFinalA, Epsilon, result.finalState);
result.addTransition(newFinalB, Epsilon, result.finalState);
return result;
}
NFA NFA::createConcatenatingNFA(const NFA &a, const NFA &b)
{
NFA result;
int initialA, finalA,
initialB, finalB;
result.initializeFromPair(a, b, &initialA, &finalA, &initialB, &finalB);
result.addTransition(result.initialState, Epsilon, initialA);
result.addTransition(finalA, Epsilon, initialB);
result.addTransition(finalB, Epsilon, result.finalState);
return result;
}
NFA NFA::createOptionalNFA(const NFA &a)
{
NFA result;
result.initialize(a.states.count() + 2);
int baseIdxA = 1;
int initialA = a.initialState + baseIdxA;
int finalA = a.finalState + baseIdxA;
result.copyFrom(a, baseIdxA);
result.addTransition(result.initialState, Epsilon, initialA);
result.addTransition(result.initialState, Epsilon, result.finalState);
result.addTransition(finalA, Epsilon, initialA);
result.addTransition(finalA, Epsilon, result.finalState);
return result;
}
NFA NFA::createStringNFA(const QByteArray &str)
{
NFA result;
foreach (char c, str) {
NFA ch = NFA::createSingleInputNFA(c);
if (result.isEmpty())
result = ch;
else
result = NFA::createConcatenatingNFA(result, ch);
}
return result;
}
NFA NFA::createSetNFA(const QSet<InputType> &set)
{
NFA result;
result.initialize(set.count() + 2);
int state = 1;
for (QSet<InputType>::ConstIterator it = set.constBegin(), end = set.constEnd();
it != end; ++it, ++state) {
result.addTransition(result.initialState, Epsilon, state);
result.addTransition(state, *it, result.finalState);
}
/*
foreach (InputType input, set) {
NFA ch = NFA::createSingleInputNFA(input);
if (result.isEmpty())
result = ch;
else
result = NFA::createAlternatingNFA(result, ch);
}
*/
return result;
}
NFA NFA::createZeroOrOneNFA(const NFA &a)
{
NFA epsilonNFA = createSingleInputNFA(Epsilon);
return NFA::createAlternatingNFA(a, epsilonNFA);
}
NFA NFA::applyQuantity(const NFA &a, int minOccurrences, int maxOccurrences)
{
NFA result = a;
NFA epsilonNFA = createSingleInputNFA(Epsilon);
if (minOccurrences == 0) {
result = NFA::createAlternatingNFA(result, epsilonNFA);
} else {
minOccurrences--;
}
maxOccurrences--;
for (int i = 0; i < minOccurrences; ++i)
result = NFA::createConcatenatingNFA(result, a);
for (int i = minOccurrences; i < maxOccurrences; ++i)
result = NFA::createConcatenatingNFA(result, NFA::createAlternatingNFA(a, epsilonNFA));
return result;
}
void NFA::debug()
{
qDebug() << "NFA has" << states.count() << "states";
qDebug() << "initial state is" << initialState;
qDebug() << "final state is" << finalState;
for (int i = 0; i < states.count(); ++i) {
const State &s = states.at(i);
for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
end = s.transitions.constEnd(); it != end; ++it)
qDebug() << "transition from state" << i << "to" << it.value() << "through"
<< (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));
if (!s.symbol.isEmpty())
qDebug() << "State" << i << "leads to symbol" << s.symbol;
}
}
// helper
typedef QSet<int> DFAState;
// that's a bad hash, but it's good enough for us
// and it allows us to use the nice QHash API :)
inline size_t qHash(const DFAState &state)
{
size_t val = 0;
foreach (int s, state)
val ^= qHash(s);
return val;
}
DFA NFA::toDFA() const
{
DFA result;
result.reserve(states.count());
QHash<QString, int> symbolReferenceCounts;
{
QSet<int> symbolStates;
for (int i = 0; i < states.count(); ++i)
if (!states.at(i).symbol.isEmpty())
symbolStates.insert(i);
QHash<int, QString> epsilonStates;
for (int i = 0; i < states.count(); ++i) {
const State &s = states.at(i);
for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
transition != end; ++transition)
if (transition.key() == Epsilon && symbolStates.contains(transition.value()))
epsilonStates.insert(i, states.at(transition.value()).symbol);
}
int lastCount;
do {
lastCount = epsilonStates.count();
for (int i = 0; i < states.count(); ++i) {
const State &s = states.at(i);
for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
transition != end; ++transition)
if (transition.key() == Epsilon && epsilonStates.contains(transition.value()))
epsilonStates.insert(i, epsilonStates.value(transition.value()));
}
} while (lastCount != epsilonStates.count());
for (int i = 0; i < states.count(); ++i) {
const State &s = states.at(i);
for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
transition != end; ++transition) {
if (transition.key() == Epsilon)
continue;
if (symbolStates.contains(transition.value())) {
const QString symbol = states.at(transition.value()).symbol;
symbolReferenceCounts[symbol]++;
} else if (epsilonStates.contains(transition.value())) {
const QString symbol = epsilonStates.value(transition.value());
symbolReferenceCounts[symbol]++;
}
}
}
/*
for (QHash<QString, int>::ConstIterator symIt = symbolReferenceCounts.constBegin(), symEnd = symbolReferenceCounts.constEnd();
symIt != symEnd; ++symIt)
qDebug() << "symbol" << symIt.key() << "is reached" << symIt.value() << "times";
*/
}
QSet<InputType> validInput;
foreach (const State &s, states)
for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
end = s.transitions.constEnd(); it != end; ++it)
if (it.key() != Epsilon)
validInput.insert(it.key());
// A DFA state can consist of multiple NFA states.
// the dfaStateMap maps from these to the actual
// state index within the resulting DFA vector
QHash<DFAState, int> dfaStateMap;
QStack<DFAState> pendingDFAStates;
DFAState startState = epsilonClosure(QSet<int>() << initialState);
result.resize(1);
dfaStateMap.insert(startState, 0);
pendingDFAStates.push(startState);
while (!pendingDFAStates.isEmpty()) {
DFAState state = pendingDFAStates.pop();
// qDebug() << "processing" << state << "from the stack of pending states";
foreach (InputType input, validInput) {
QSet<int> reachableStates;
foreach (int nfaState, state) {
const TransitionMap &transitions = states.at(nfaState).transitions;
TransitionMap::ConstIterator it = transitions.find(input);
while (it != transitions.constEnd() && it.key() == input) {
reachableStates.insert(it.value());
++it;
}
}
if (reachableStates.isEmpty())
continue;
// qDebug() << "can reach" << reachableStates << "from input" << char(input);
QSet<int> closure = epsilonClosure(reachableStates);
// qDebug() << "closure is" << closure;
if (!dfaStateMap.contains(closure)) {
int dfaState = result.count();
result.append(State());
QString symbol;
int refCount = INT_MAX;
foreach (int nfaState, closure)
if (!states.at(nfaState).symbol.isEmpty()) {
// qDebug() << "closure also contains symbol" << states.at(nfaState).symbol;
QString candidate = states.at(nfaState).symbol;
int candidateRefCount =symbolReferenceCounts.value(candidate, INT_MAX);
if (candidateRefCount < refCount) {
refCount = candidateRefCount;
symbol = candidate;
}
}
if (!symbol.isEmpty())
result.last().symbol = symbol;
dfaStateMap.insert(closure, dfaState);
Q_ASSERT(!pendingDFAStates.contains(closure));
pendingDFAStates.prepend(closure);
}
result[dfaStateMap.value(state)].transitions.insert(input, dfaStateMap.value(closure));
}
}
return result;
}
QSet<int> NFA::epsilonClosure(const QSet<int> &initialClosure) const
{
QSet<int> closure = initialClosure;
closure.reserve(closure.count() * 4);
QStack<int> stateStack;
stateStack.resize(closure.count());
std::copy(closure.constBegin(), closure.constEnd(), stateStack.begin());
while (!stateStack.isEmpty()) {
int t = stateStack.pop();
const TransitionMap &transitions = states.at(t).transitions;
TransitionMap::ConstIterator it = transitions.find(Epsilon);
while (it != transitions.constEnd() && it.key() == Epsilon) {
const int u = it.value();
if (!closure.contains(u)) {
closure.insert(u);
stateStack.push(u);
}
++it;
}
}
return closure;
}
void NFA::setTerminationSymbol(const QString &symbol)
{
states[finalState].symbol = symbol;
}
void DFA::debug() const
{
qDebug() << "DFA has" << count() << "states";
for (int i = 0; i < count(); ++i) {
const State &s = at(i);
if (s.transitions.isEmpty()) {
qDebug() << "State" << i << "has no transitions";
} else {
for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
end = s.transitions.constEnd(); it != end; ++it)
qDebug() << "transition from state" << i << "to" << it.value() << "through"
<< (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));
}
if (!s.symbol.isEmpty())
qDebug() << "State" << i << "leads to symbol" << s.symbol;
}
}
DFA DFA::minimize() const
{
QList<bool> inequivalentStates(count() * count());
inequivalentStates.fill(false);
for (int i = 0; i < count(); ++i)
for (int j = 0; j < i; ++j) {
if (i != j && at(i).symbol != at(j).symbol)
inequivalentStates[i * count() + j] = true;
}
bool done;
do {
done = true;
for (int i = 0; i < count(); ++i)
for (int j = 0; j < count(); ++j) {
if (i == j)
continue;
if (inequivalentStates[i * count() + j])
continue;
if (at(i).transitions.keys() != at(j).transitions.keys()) {
inequivalentStates[i * count() + j] = true;
done = false;
continue;
}
foreach (InputType a, at(i).transitions.keys()) {
int r = at(i).transitions.value(a, -1);
if (r == -1)
continue;
int s = at(j).transitions.value(a, -1);
if (s == -1)
continue;
if (inequivalentStates[r * count() + s]
|| r == s) {
inequivalentStates[i * count() + j] = true;
done = false;
break;
}
}
}
} while (!done);
QHash<int, int> statesToEliminate;
for (int i = 0; i < count(); ++i)
for (int j = 0; j < i; ++j)
if (!inequivalentStates[i * count() + j]) {
statesToEliminate.insertMulti(i, j);
}
/*
qDebug() << "states to eliminiate:" << statesToEliminate.count();;
qDebug() << "merging" << statesToEliminate;
debug();
*/
return *this;
}