--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/util/lexgen/nfa.cpp Mon Jan 11 14:00:40 2010 +0000
@@ -0,0 +1,508 @@
+/****************************************************************************
+**
+** Copyright (C) 2009 Nokia Corporation and/or its subsidiary(-ies).
+** All rights reserved.
+** Contact: Nokia Corporation (qt-info@nokia.com)
+**
+** This file is part of the utils of the Qt Toolkit.
+**
+** $QT_BEGIN_LICENSE:LGPL$
+** No Commercial Usage
+** This file contains pre-release code and may not be distributed.
+** You may use this file in accordance with the terms and conditions
+** contained in the Technology Preview License Agreement accompanying
+** this package.
+**
+** GNU Lesser General Public License Usage
+** Alternatively, this file may be used under the terms of the GNU Lesser
+** General Public License version 2.1 as published by the Free Software
+** Foundation and appearing in the file LICENSE.LGPL included in the
+** packaging of this file. Please review the following information to
+** ensure the GNU Lesser General Public License version 2.1 requirements
+** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
+**
+** In addition, as a special exception, Nokia gives you certain additional
+** rights. These rights are described in the Nokia Qt LGPL Exception
+** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
+**
+** If you have questions regarding the use of this file, please contact
+** Nokia at qt-info@nokia.com.
+**
+**
+**
+**
+**
+**
+**
+**
+** $QT_END_LICENSE$
+**
+****************************************************************************/
+#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 uint qHash(const DFAState &state)
+{
+ uint 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());
+ qCopy(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;
+}
+
+