util/lexgen/nfa.cpp

   1 /****************************************************************************
   2 **
   3 ** Copyright (C) 2010 Nokia Corporation and/or its subsidiary(-ies).
   4 ** All rights reserved.
   5 ** Contact: Nokia Corporation (qt-info@nokia.com)
   6 **
   7 ** This file is part of the utils of the Qt Toolkit.
   8 **
   9 ** $QT_BEGIN_LICENSE:LGPL$
  10 ** No Commercial Usage
  11 ** This file contains pre-release code and may not be distributed.
  12 ** You may use this file in accordance with the terms and conditions
  13 ** contained in the Technology Preview License Agreement accompanying
  14 ** this package.
  15 **
  16 ** GNU Lesser General Public License Usage
  17 ** Alternatively, this file may be used under the terms of the GNU Lesser
  18 ** General Public License version 2.1 as published by the Free Software
  19 ** Foundation and appearing in the file LICENSE.LGPL included in the
  20 ** packaging of this file.  Please review the following information to
  21 ** ensure the GNU Lesser General Public License version 2.1 requirements
  22 ** will be met: http://www.gnu.org/licenses/old-licenses/lgpl-2.1.html.
  23 **
  24 ** In addition, as a special exception, Nokia gives you certain additional
  25 ** rights.  These rights are described in the Nokia Qt LGPL Exception
  26 ** version 1.1, included in the file LGPL_EXCEPTION.txt in this package.
  27 **
  28 ** If you have questions regarding the use of this file, please contact
  29 ** Nokia at qt-info@nokia.com.
  30 **
  31 **
  32 **
  33 **
  34 **
  35 **
  36 **
  37 **
  38 ** $QT_END_LICENSE$
  39 **
  40 ****************************************************************************/
  41 #include "nfa.h"
  42 #include <QSet>
  43 #include <limits.h>
  44
  45 NFA NFA::createSingleInputNFA(InputType input)
  46 {
  47     NFA result;
  48     result.initialize(2);
  49     result.addTransition(result.initialState, input, result.finalState);
  50     return result;
  51 }
  52
  53 NFA NFA::createSymbolNFA(const QString &symbol)
  54 {
  55     NFA result = NFA::createSingleInputNFA(Epsilon);
  56     result.states[result.finalState].symbol = symbol;
  57     return result;
  58 }
  59
  60 void NFA::initialize(int size)
  61 {
  62     states.resize(size);
  63     states.fill(State());
  64     initialState = 0;
  65     finalState = size - 1;
  66 }
  67
  68 void NFA::addTransition(int from, InputType input, int to)
  69 {
  70     assertValidState(from);
  71     assertValidState(to);
  72
  73     states[from].transitions.insertMulti(input, to);
  74 }
  75
  76 void NFA::copyFrom(const NFA &other, int baseState)
  77 {
  78     assertValidState(baseState);
  79     assertValidState(baseState + other.states.count() - 1);
  80
  81     for (int i = 0; i < other.states.count(); ++i) {
  82         State s = other.states.at(i);
  83
  84         for (TransitionMap::Iterator it = s.transitions.begin(),
  85              end = s.transitions.end(); it != end; ++it)
  86             *it += baseState;
  87
  88         states[baseState + i] = s;
  89     }
  90 }
  91
  92 void NFA::initializeFromPair(const NFA &a, const NFA &b,
  93                              int *initialA, int *finalA,
  94                              int *initialB, int *finalB)
  95 {
  96     initialize(a.states.count() + b.states.count() + 2);
  97
  98     int baseIdxA = 1;
  99     int baseIdxB = 1 + a.states.count();
 100
 101     *initialA = a.initialState + baseIdxA;
 102     *finalA = a.finalState + baseIdxA;
 103
 104     *initialB = b.initialState + baseIdxB;
 105     *finalB = b.finalState + baseIdxB;
 106
 107     copyFrom(a, baseIdxA);
 108     copyFrom(b, baseIdxB);
 109 }
 110
 111 NFA NFA::createAlternatingNFA(const NFA &a, const NFA &b)
 112 {
 113     NFA result;
 114
 115     int newInitialA, newFinalA,
 116         newInitialB, newFinalB;
 117
 118     result.initializeFromPair(a, b, &newInitialA, &newFinalA,
 119                               &newInitialB, &newFinalB);
 120
 121     result.addTransition(result.initialState, Epsilon, newInitialA);
 122     result.addTransition(result.initialState, Epsilon, newInitialB);
 123
 124     result.addTransition(newFinalA, Epsilon, result.finalState);
 125     result.addTransition(newFinalB, Epsilon, result.finalState);
 126
 127     return result;
 128 }
 129
 130 NFA NFA::createConcatenatingNFA(const NFA &a, const NFA &b)
 131 {
 132     NFA result;
 133
 134     int initialA, finalA,
 135         initialB, finalB;
 136
 137     result.initializeFromPair(a, b, &initialA, &finalA, &initialB, &finalB);
 138
 139     result.addTransition(result.initialState, Epsilon, initialA);
 140     result.addTransition(finalA, Epsilon, initialB);
 141     result.addTransition(finalB, Epsilon, result.finalState);
 142     return result;
 143 }
 144
 145 NFA NFA::createOptionalNFA(const NFA &a)
 146 {
 147     NFA result;
 148
 149     result.initialize(a.states.count() + 2);
 150
 151     int baseIdxA = 1;
 152     int initialA = a.initialState + baseIdxA;
 153     int finalA = a.finalState + baseIdxA;
 154
 155     result.copyFrom(a, baseIdxA);
 156
 157     result.addTransition(result.initialState, Epsilon, initialA);
 158     result.addTransition(result.initialState, Epsilon, result.finalState);
 159
 160     result.addTransition(finalA, Epsilon, initialA);
 161     result.addTransition(finalA, Epsilon, result.finalState);
 162
 163     return result;
 164 }
 165
 166 NFA NFA::createStringNFA(const QByteArray &str)
 167 {
 168     NFA result;
 169     foreach (char c, str) {
 170         NFA ch = NFA::createSingleInputNFA(c);
 171         if (result.isEmpty())
 172             result = ch;
 173         else
 174             result = NFA::createConcatenatingNFA(result, ch);
 175     }
 176     return result;
 177 }
 178
 179 NFA NFA::createSetNFA(const QSet<InputType> &set)
 180 {
 181     NFA result;
 182     result.initialize(set.count() + 2);
 183
 184     int state = 1;
 185     for (QSet<InputType>::ConstIterator it = set.constBegin(), end = set.constEnd();
 186          it != end; ++it, ++state) {
 187         result.addTransition(result.initialState, Epsilon, state);
 188         result.addTransition(state, *it, result.finalState);
 189     }
 190
 191     /*
 192     foreach (InputType input, set) {
 193         NFA ch = NFA::createSingleInputNFA(input);
 194         if (result.isEmpty())
 195             result = ch;
 196         else
 197             result = NFA::createAlternatingNFA(result, ch);
 198     }
 199     */
 200     return result;
 201 }
 202
 203 NFA NFA::createZeroOrOneNFA(const NFA &a)
 204 {
 205     NFA epsilonNFA = createSingleInputNFA(Epsilon);
 206     return NFA::createAlternatingNFA(a, epsilonNFA);
 207 }
 208
 209 NFA NFA::applyQuantity(const NFA &a, int minOccurrences, int maxOccurrences)
 210 {
 211     NFA result = a;
 212     NFA epsilonNFA = createSingleInputNFA(Epsilon);
 213
 214     if (minOccurrences == 0) {
 215         result = NFA::createAlternatingNFA(result, epsilonNFA);
 216     } else {
 217         minOccurrences--;
 218     }
 219     maxOccurrences--;
 220
 221     for (int i = 0; i < minOccurrences; ++i)
 222         result = NFA::createConcatenatingNFA(result, a);
 223
 224     for (int i = minOccurrences; i < maxOccurrences; ++i)
 225         result = NFA::createConcatenatingNFA(result, NFA::createAlternatingNFA(a, epsilonNFA));
 226
 227     return result;
 228 }
 229
 230 void NFA::debug()
 231 {
 232     qDebug() << "NFA has" << states.count() << "states";
 233     qDebug() << "initial state is" << initialState;
 234     qDebug() << "final state is" << finalState;
 235
 236     for (int i = 0; i < states.count(); ++i) {
 237         const State &s = states.at(i);
 238         for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
 239              end = s.transitions.constEnd(); it != end; ++it)
 240             qDebug() << "transition from state" << i << "to" << it.value() << "through"
 241                      << (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));
 242         if (!s.symbol.isEmpty())
 243             qDebug() << "State" << i << "leads to symbol" << s.symbol;
 244     }
 245 }
 246
 247 // helper
 248 typedef QSet<int> DFAState;
 249
 250 // that's a bad hash, but it's good enough for us
 251 // and it allows us to use the nice QHash API :)
 252 inline uint qHash(const DFAState &state)
 253 {
 254     uint val = 0;
 255     foreach (int s, state)
 256         val |= qHash(s);
 257     return val;
 258 }
 259
 260 DFA NFA::toDFA() const
 261 {
 262     DFA result;
 263     result.reserve(states.count());
 264
 265     QHash<QString, int> symbolReferenceCounts;
 266     {
 267         QSet<int> symbolStates;
 268         for (int i = 0; i < states.count(); ++i)
 269             if (!states.at(i).symbol.isEmpty())
 270                 symbolStates.insert(i);
 271
 272         QHash<int, QString> epsilonStates;
 273         for (int i = 0; i < states.count(); ++i) {
 274             const State &s = states.at(i);
 275             for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
 276                  transition != end; ++transition)
 277                 if (transition.key() == Epsilon && symbolStates.contains(transition.value()))
 278                     epsilonStates.insert(i, states.at(transition.value()).symbol);
 279         }
 280
 281         int lastCount;
 282         do {
 283             lastCount = epsilonStates.count();
 284             for (int i = 0; i < states.count(); ++i) {
 285                 const State &s = states.at(i);
 286                 for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
 287                      transition != end; ++transition)
 288                     if (transition.key() == Epsilon && epsilonStates.contains(transition.value()))
 289                         epsilonStates.insert(i, epsilonStates.value(transition.value()));
 290             }
 291
 292         } while (lastCount != epsilonStates.count());
 293
 294         for (int i = 0; i < states.count(); ++i) {
 295             const State &s = states.at(i);
 296             for (TransitionMap::ConstIterator transition = s.transitions.constBegin(), end = s.transitions.constEnd();
 297                  transition != end; ++transition) {
 298                 if (transition.key() == Epsilon)
 299                     continue;
 300                 if (symbolStates.contains(transition.value())) {
 301                     const QString symbol = states.at(transition.value()).symbol;
 302                     symbolReferenceCounts[symbol]++;
 303                 } else if (epsilonStates.contains(transition.value())) {
 304                     const QString symbol = epsilonStates.value(transition.value());
 305                     symbolReferenceCounts[symbol]++;
 306                 }
 307             }
 308         }
 309         /*
 310         for (QHash<QString, int>::ConstIterator symIt = symbolReferenceCounts.constBegin(), symEnd = symbolReferenceCounts.constEnd();
 311              symIt != symEnd; ++symIt)
 312             qDebug() << "symbol" << symIt.key() << "is reached" << symIt.value() << "times";
 313             */
 314     }
 315
 316
 317     QSet<InputType> validInput;
 318     foreach (const State &s, states)
 319         for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
 320              end = s.transitions.constEnd(); it != end; ++it)
 321             if (it.key() != Epsilon)
 322                 validInput.insert(it.key());
 323
 324     // A DFA state can consist of multiple NFA states.
 325     // the dfaStateMap maps from these to the actual
 326     // state index within the resulting DFA vector
 327     QHash<DFAState, int> dfaStateMap;
 328     QStack<DFAState> pendingDFAStates;
 329
 330     DFAState startState = epsilonClosure(QSet<int>() << initialState);
 331
 332     result.resize(1);
 333     dfaStateMap.insert(startState, 0);
 334
 335     pendingDFAStates.push(startState);
 336
 337     while (!pendingDFAStates.isEmpty()) {
 338         DFAState state = pendingDFAStates.pop();
 339 //        qDebug() << "processing" << state << "from the stack of pending states";
 340
 341         foreach (InputType input, validInput) {
 342
 343             QSet<int> reachableStates;
 344
 345             foreach (int nfaState, state) {
 346                 const TransitionMap &transitions = states.at(nfaState).transitions;
 347                 TransitionMap::ConstIterator it = transitions.find(input);
 348                 while (it != transitions.constEnd() && it.key() == input) {
 349                     reachableStates.insert(it.value());
 350                     ++it;
 351                 }
 352             }
 353
 354             if (reachableStates.isEmpty())
 355                 continue;
 356
 357 //            qDebug() << "can reach" << reachableStates << "from input" << char(input);
 358
 359             QSet<int> closure = epsilonClosure(reachableStates);
 360
 361 //            qDebug() << "closure is" << closure;
 362
 363             if (!dfaStateMap.contains(closure)) {
 364                 int dfaState = result.count();
 365                 result.append(State());
 366
 367                 QString symbol;
 368                 int refCount = INT_MAX;
 369                 foreach (int nfaState, closure)
 370                     if (!states.at(nfaState).symbol.isEmpty()) {
 371 //                        qDebug() << "closure also contains symbol" << states.at(nfaState).symbol;
 372                         QString candidate = states.at(nfaState).symbol;
 373                         int candidateRefCount =symbolReferenceCounts.value(candidate, INT_MAX);
 374                         if (candidateRefCount < refCount) {
 375                             refCount = candidateRefCount;
 376                             symbol = candidate;
 377                         }
 378                     }
 379                 if (!symbol.isEmpty())
 380                     result.last().symbol = symbol;
 381
 382                 dfaStateMap.insert(closure, dfaState);
 383
 384                 Q_ASSERT(!pendingDFAStates.contains(closure));
 385                 pendingDFAStates.prepend(closure);
 386             }
 387
 388             result[dfaStateMap.value(state)].transitions.insert(input, dfaStateMap.value(closure));
 389         }
 390     }
 391
 392     return result;
 393 }
 394
 395 QSet<int> NFA::epsilonClosure(const QSet<int> &initialClosure) const
 396 {
 397     QSet<int> closure = initialClosure;
 398     closure.reserve(closure.count() * 4);
 399
 400     QStack<int> stateStack;
 401     stateStack.resize(closure.count());
 402     qCopy(closure.constBegin(), closure.constEnd(), stateStack.begin());
 403
 404     while (!stateStack.isEmpty()) {
 405         int t = stateStack.pop();
 406         const TransitionMap &transitions = states.at(t).transitions;
 407         TransitionMap::ConstIterator it = transitions.find(Epsilon);
 408         while (it != transitions.constEnd() && it.key() == Epsilon) {
 409             const int u = it.value();
 410             if (!closure.contains(u)) {
 411                 closure.insert(u);
 412                 stateStack.push(u);
 413             }
 414             ++it;
 415         }
 416     }
 417
 418     return closure;
 419 }
 420
 421 void NFA::setTerminationSymbol(const QString &symbol)
 422 {
 423     states[finalState].symbol = symbol;
 424 }
 425
 426 void DFA::debug() const
 427 {
 428     qDebug() << "DFA has" << count() << "states";
 429
 430     for (int i = 0; i < count(); ++i) {
 431         const State &s = at(i);
 432         if (s.transitions.isEmpty()) {
 433             qDebug() << "State" << i << "has no transitions";
 434         } else {
 435             for (TransitionMap::ConstIterator it = s.transitions.constBegin(),
 436                  end = s.transitions.constEnd(); it != end; ++it)
 437                 qDebug() << "transition from state" << i << "to" << it.value() << "through"
 438                          << (it.key() == Epsilon ? QString("Epsilon") : QString(char(it.key())));
 439         }
 440         if (!s.symbol.isEmpty())
 441             qDebug() << "State" << i << "leads to symbol" << s.symbol;
 442     }
 443
 444 }
 445
 446 DFA DFA::minimize() const
 447 {
 448     QVector<bool> inequivalentStates(count() * count());
 449     inequivalentStates.fill(false);
 450
 451     for (int i = 0; i < count(); ++i)
 452         for (int j = 0; j < i; ++j) {
 453             if (i != j && at(i).symbol != at(j).symbol)
 454                 inequivalentStates[i * count() + j] = true;
 455         }
 456
 457     bool done;
 458     do {
 459         done = true;
 460         for (int i = 0; i < count(); ++i)
 461             for (int j = 0; j < count(); ++j) {
 462                 if (i == j)
 463                     continue;
 464
 465                 if (inequivalentStates[i * count() + j])
 466                     continue;
 467
 468                 if (at(i).transitions.keys() != at(j).transitions.keys()) {
 469                     inequivalentStates[i * count() + j] = true;
 470                     done = false;
 471                     continue;
 472                 }
 473
 474                 foreach (InputType a, at(i).transitions.keys()) {
 475                     int r = at(i).transitions.value(a, -1);
 476                     if (r == -1)
 477                         continue;
 478                     int s = at(j).transitions.value(a, -1);
 479                     if (s == -1)
 480                         continue;
 481
 482                     if (inequivalentStates[r * count() + s]
 483                         || r == s) {
 484                         inequivalentStates[i * count() + j] = true;
 485                         done = false;
 486                         break;
 487                     }
 488                 }
 489             }
 490     } while (!done);
 491
 492     QHash<int, int> statesToEliminate;
 493     for (int i = 0; i < count(); ++i)
 494         for (int j = 0; j < i; ++j)
 495             if (!inequivalentStates[i * count() + j]) {
 496                 statesToEliminate.insertMulti(i, j);
 497             }
 498
 499     /*
 500     qDebug() << "states to eliminiate:" << statesToEliminate.count();;
 501     qDebug() << "merging" << statesToEliminate;
 502     debug();
 503     */
 504
 505     return *this;
 506 }
 507
 508