492 lines
16 KiB
C++
492 lines
16 KiB
C++
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/****************************************************************************
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**
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** Copyright (C) 2016 The Qt Company Ltd.
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** Contact: https://www.qt.io/licensing/
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**
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** This file is part of the utils of the Qt Toolkit.
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**
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** $QT_BEGIN_LICENSE:GPL-EXCEPT$
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** Commercial License Usage
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** Licensees holding valid commercial Qt licenses may use this file in
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** accordance with the commercial license agreement provided with the
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** Software or, alternatively, in accordance with the terms contained in
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** a written agreement between you and The Qt Company. For licensing terms
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** and conditions see https://www.qt.io/terms-conditions. For further
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** information use the contact form at https://www.qt.io/contact-us.
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**
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** GNU General Public License Usage
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** Alternatively, this file may be used under the terms of the GNU
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** General Public License version 3 as published by the Free Software
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** Foundation with exceptions as appearing in the file LICENSE.GPL3-EXCEPT
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** included in the packaging of this file. Please review the following
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** information to ensure the GNU General Public License requirements will
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** be met: https://www.gnu.org/licenses/gpl-3.0.html.
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**
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** $QT_END_LICENSE$
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**
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****************************************************************************/
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#include "nfa.h"
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#include <QSet>
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#include <limits.h>
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NFA NFA::createSingleInputNFA(InputType input)
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{
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NFA result;
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result.initialize(2);
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result.addTransition(result.initialState, input, result.finalState);
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return result;
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}
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NFA NFA::createSymbolNFA(const QString &symbol)
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{
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NFA result = NFA::createSingleInputNFA(Epsilon);
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result.states[result.finalState].symbol = symbol;
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return result;
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}
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void NFA::initialize(int size)
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{
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states.resize(size);
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states.fill(State());
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initialState = 0;
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finalState = size - 1;
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}
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void NFA::addTransition(int from, InputType input, int to)
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{
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assertValidState(from);
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assertValidState(to);
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states[from].transitions.insertMulti(input, to);
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}
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void NFA::copyFrom(const NFA &other, int baseState)
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{
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assertValidState(baseState);
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assertValidState(baseState + other.states.count() - 1);
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for (int i = 0; i < other.states.count(); ++i) {
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State s = other.states.at(i);
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for (TransitionMap::Iterator it = s.transitions.begin(),
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end = s.transitions.end(); it != end; ++it)
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*it += baseState;
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states[baseState + i] = s;
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}
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}
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void NFA::initializeFromPair(const NFA &a, const NFA &b,
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int *initialA, int *finalA,
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int *initialB, int *finalB)
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{
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initialize(a.states.count() + b.states.count() + 2);
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int baseIdxA = 1;
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int baseIdxB = 1 + a.states.count();
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*initialA = a.initialState + baseIdxA;
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*finalA = a.finalState + baseIdxA;
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*initialB = b.initialState + baseIdxB;
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*finalB = b.finalState + baseIdxB;
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copyFrom(a, baseIdxA);
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copyFrom(b, baseIdxB);
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}
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NFA NFA::createAlternatingNFA(const NFA &a, const NFA &b)
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{
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NFA result;
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int newInitialA, newFinalA,
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newInitialB, newFinalB;
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result.initializeFromPair(a, b, &newInitialA, &newFinalA,
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&newInitialB, &newFinalB);
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result.addTransition(result.initialState, Epsilon, newInitialA);
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result.addTransition(result.initialState, Epsilon, newInitialB);
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result.addTransition(newFinalA, Epsilon, result.finalState);
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result.addTransition(newFinalB, Epsilon, result.finalState);
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return result;
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}
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NFA NFA::createConcatenatingNFA(const NFA &a, const NFA &b)
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{
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NFA result;
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int initialA, finalA,
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initialB, finalB;
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result.initializeFromPair(a, b, &initialA, &finalA, &initialB, &finalB);
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result.addTransition(result.initialState, Epsilon, initialA);
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result.addTransition(finalA, Epsilon, initialB);
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result.addTransition(finalB, Epsilon, result.finalState);
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return result;
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}
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NFA NFA::createOptionalNFA(const NFA &a)
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{
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NFA result;
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result.initialize(a.states.count() + 2);
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int baseIdxA = 1;
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int initialA = a.initialState + baseIdxA;
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int finalA = a.finalState + baseIdxA;
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result.copyFrom(a, baseIdxA);
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result.addTransition(result.initialState, Epsilon, initialA);
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result.addTransition(result.initialState, Epsilon, result.finalState);
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result.addTransition(finalA, Epsilon, initialA);
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result.addTransition(finalA, Epsilon, result.finalState);
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return result;
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}
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NFA NFA::createStringNFA(const QByteArray &str)
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{
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NFA result;
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foreach (char c, str) {
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NFA ch = NFA::createSingleInputNFA(c);
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if (result.isEmpty())
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result = ch;
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else
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result = NFA::createConcatenatingNFA(result, ch);
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}
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return result;
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}
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NFA NFA::createSetNFA(const QSet<InputType> &set)
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{
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NFA result;
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result.initialize(set.count() + 2);
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int state = 1;
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for (QSet<InputType>::ConstIterator it = set.constBegin(), end = set.constEnd();
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it != end; ++it, ++state) {
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result.addTransition(result.initialState, Epsilon, state);
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result.addTransition(state, *it, result.finalState);
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}
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/*
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foreach (InputType input, set) {
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NFA ch = NFA::createSingleInputNFA(input);
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if (result.isEmpty())
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result = ch;
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else
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result = NFA::createAlternatingNFA(result, ch);
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}
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*/
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return result;
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}
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NFA NFA::createZeroOrOneNFA(const NFA &a)
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{
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NFA epsilonNFA = createSingleInputNFA(Epsilon);
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return NFA::createAlternatingNFA(a, epsilonNFA);
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}
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NFA NFA::applyQuantity(const NFA &a, int minOccurrences, int maxOccurrences)
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{
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NFA result = a;
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NFA epsilonNFA = createSingleInputNFA(Epsilon);
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if (minOccurrences == 0) {
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result = NFA::createAlternatingNFA(result, epsilonNFA);
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} else {
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minOccurrences--;
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}
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maxOccurrences--;
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for (int i = 0; i < minOccurrences; ++i)
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result = NFA::createConcatenatingNFA(result, a);
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for (int i = minOccurrences; i < maxOccurrences; ++i)
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result = NFA::createConcatenatingNFA(result, NFA::createAlternatingNFA(a, epsilonNFA));
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return result;
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}
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void NFA::debug()
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{
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qDebug() << "NFA has" << states.count() << "states";
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qDebug() << "initial state is" << initialState;
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qDebug() << "final state is" << finalState;
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for (int i = 0; i < states.count(); ++i) {
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const State &s = states.at(i);
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for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
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end = s.transitions.constEnd(); it != end; ++it)
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qDebug() << "transition from state" << i << "to" << it.value() << "through"
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<< (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));
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if (!s.symbol.isEmpty())
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qDebug() << "State" << i << "leads to symbol" << s.symbol;
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}
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}
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// helper
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typedef QSet<int> DFAState;
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// that's a bad hash, but it's good enough for us
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// and it allows us to use the nice QHash API :)
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inline uint qHash(const DFAState &state)
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{
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uint val = 0;
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foreach (int s, state)
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val |= qHash(s);
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return val;
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}
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DFA NFA::toDFA() const
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{
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DFA result;
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result.reserve(states.count());
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QHash<QString, int> symbolReferenceCounts;
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{
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QSet<int> symbolStates;
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for (int i = 0; i < states.count(); ++i)
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if (!states.at(i).symbol.isEmpty())
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symbolStates.insert(i);
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QHash<int, QString> epsilonStates;
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for (int i = 0; i < states.count(); ++i) {
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const State &s = states.at(i);
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for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
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transition != end; ++transition)
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if (transition.key() == Epsilon && symbolStates.contains(transition.value()))
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epsilonStates.insert(i, states.at(transition.value()).symbol);
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}
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int lastCount;
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do {
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lastCount = epsilonStates.count();
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for (int i = 0; i < states.count(); ++i) {
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const State &s = states.at(i);
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for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
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transition != end; ++transition)
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if (transition.key() == Epsilon && epsilonStates.contains(transition.value()))
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epsilonStates.insert(i, epsilonStates.value(transition.value()));
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}
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} while (lastCount != epsilonStates.count());
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for (int i = 0; i < states.count(); ++i) {
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const State &s = states.at(i);
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for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
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transition != end; ++transition) {
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if (transition.key() == Epsilon)
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continue;
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if (symbolStates.contains(transition.value())) {
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const QString symbol = states.at(transition.value()).symbol;
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symbolReferenceCounts[symbol]++;
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} else if (epsilonStates.contains(transition.value())) {
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const QString symbol = epsilonStates.value(transition.value());
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symbolReferenceCounts[symbol]++;
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}
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}
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}
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/*
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for (QHash<QString, int>::ConstIterator symIt = symbolReferenceCounts.constBegin(), symEnd = symbolReferenceCounts.constEnd();
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symIt != symEnd; ++symIt)
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qDebug() << "symbol" << symIt.key() << "is reached" << symIt.value() << "times";
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*/
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}
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QSet<InputType> validInput;
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foreach (const State &s, states)
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for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
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end = s.transitions.constEnd(); it != end; ++it)
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if (it.key() != Epsilon)
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validInput.insert(it.key());
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// A DFA state can consist of multiple NFA states.
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// the dfaStateMap maps from these to the actual
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// state index within the resulting DFA vector
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QHash<DFAState, int> dfaStateMap;
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QStack<DFAState> pendingDFAStates;
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DFAState startState = epsilonClosure(QSet<int>() << initialState);
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result.resize(1);
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dfaStateMap.insert(startState, 0);
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pendingDFAStates.push(startState);
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while (!pendingDFAStates.isEmpty()) {
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DFAState state = pendingDFAStates.pop();
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// qDebug() << "processing" << state << "from the stack of pending states";
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foreach (InputType input, validInput) {
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QSet<int> reachableStates;
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foreach (int nfaState, state) {
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const TransitionMap &transitions = states.at(nfaState).transitions;
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TransitionMap::ConstIterator it = transitions.find(input);
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while (it != transitions.constEnd() && it.key() == input) {
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reachableStates.insert(it.value());
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++it;
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}
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}
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if (reachableStates.isEmpty())
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continue;
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// qDebug() << "can reach" << reachableStates << "from input" << char(input);
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QSet<int> closure = epsilonClosure(reachableStates);
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// qDebug() << "closure is" << closure;
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if (!dfaStateMap.contains(closure)) {
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int dfaState = result.count();
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result.append(State());
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QString symbol;
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int refCount = INT_MAX;
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foreach (int nfaState, closure)
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if (!states.at(nfaState).symbol.isEmpty()) {
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// qDebug() << "closure also contains symbol" << states.at(nfaState).symbol;
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QString candidate = states.at(nfaState).symbol;
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int candidateRefCount =symbolReferenceCounts.value(candidate, INT_MAX);
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if (candidateRefCount < refCount) {
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refCount = candidateRefCount;
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symbol = candidate;
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}
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}
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if (!symbol.isEmpty())
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result.last().symbol = symbol;
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dfaStateMap.insert(closure, dfaState);
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Q_ASSERT(!pendingDFAStates.contains(closure));
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pendingDFAStates.prepend(closure);
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}
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result[dfaStateMap.value(state)].transitions.insert(input, dfaStateMap.value(closure));
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}
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}
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return result;
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}
|
||
|
|
|
||
|
|
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
|
||
|
|
{
|
||
|
|
QVector<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;
|
||
|
|
}
|