minimize.cc 18.7 KB
Newer Older
1
// Copyright (C) 2010, 2011, 2012 Laboratoire de Recherche et Développement
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
// de l'Epita (LRDE).
//
// This file is part of Spot, a model checking library.
//
// Spot is free software; you can redistribute it and/or modify it
// under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 2 of the License, or
// (at your option) any later version.
//
// Spot is distributed in the hope that it will be useful, but WITHOUT
// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
// License for more details.
//
// You should have received a copy of the GNU General Public License
// along with Spot; see the file COPYING.  If not, write to the Free
// Software Foundation, Inc., 59 Temple Place - Suite 330, Boston, MA
// 02111-1307, USA.

21
22
23
24
25
26
27
28
29

//#define TRACE

#ifdef TRACE
#  define trace std::cerr
#else
#  define trace while (0) std::cerr
#endif

30
#include <queue>
31
32
33
#include <deque>
#include <set>
#include <list>
34
#include <vector>
35
#include <sstream>
36
37
38
#include "minimize.hh"
#include "ltlast/allnodes.hh"
#include "misc/hash.hh"
39
#include "misc/bddlt.hh"
40
41
#include "tgba/tgbaproduct.hh"
#include "tgba/tgbatba.hh"
42
#include "tgba/wdbacomp.hh"
43
#include "tgbaalgos/powerset.hh"
44
45
46
#include "tgbaalgos/gtec/gtec.hh"
#include "tgbaalgos/safety.hh"
#include "tgbaalgos/sccfilter.hh"
47
#include "tgbaalgos/scc.hh"
48
#include "tgbaalgos/ltl2tgba_fm.hh"
49
#include "tgbaalgos/bfssteps.hh"
50
#include "tgbaalgos/stats.hh"
51
52
53
54
55
56
57
58

namespace spot
{
  typedef Sgi::hash_set<const state*,
                        state_ptr_hash, state_ptr_equal> hash_set;
  typedef Sgi::hash_map<const state*, unsigned,
                        state_ptr_hash, state_ptr_equal> hash_map;

59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
  namespace
  {
    static std::ostream&
    dump_hash_set(const hash_set* hs, const tgba* aut, std::ostream& out)
    {
      out << "{";
      const char* sep = "";
      for (hash_set::const_iterator i = hs->begin(); i != hs->end(); ++i)
	{
	  out << sep << aut->format_state(*i);
	  sep = ", ";
	}
      out << "}";
      return out;
    }

    static std::string
    format_hash_set(const hash_set* hs, const tgba* aut)
    {
      std::ostringstream s;
      dump_hash_set(hs, aut, s);
      return s.str();
    }
  }

84
85
  // Find all states of an automaton.
  void state_set(const tgba* a, hash_set* seen)
86
  {
Felix Abecassis's avatar
Felix Abecassis committed
87
    std::queue<const state*> tovisit;
88
    // Perform breadth-first traversal.
Felix Abecassis's avatar
Felix Abecassis committed
89
    const state* init = a->get_init_state();
90
    tovisit.push(init);
91
    seen->insert(init);
92
93
    while (!tovisit.empty())
    {
Felix Abecassis's avatar
Felix Abecassis committed
94
      const state* src = tovisit.front();
95
      tovisit.pop();
96

97
98
99
      tgba_succ_iterator* sit = a->succ_iter(src);
      for (sit->first(); !sit->done(); sit->next())
      {
Felix Abecassis's avatar
Felix Abecassis committed
100
        const state* dst = sit->current_state();
101
        // Is it a new state ?
102
103
104
105
106
107
        if (seen->find(dst) == seen->end())
	  {
	    // Register the successor for later processing.
	    tovisit.push(dst);
	    seen->insert(dst);
	  }
108
        else
109
          dst->destroy();
110
      }
Felix Abecassis's avatar
Felix Abecassis committed
111
      delete sit;
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
    }
  }

  // From the base automaton and the list of sets, build the minimal
  // resulting automaton
  tgba_explicit_number* build_result(const tgba* a,
                                     std::list<hash_set*>& sets,
                                     hash_set* final)
  {
    // For each set, create a state in the resulting automaton.
    // For a state s, state_num[s] is the number of the state in the minimal
    // automaton.
    hash_map state_num;
    std::list<hash_set*>::iterator sit;
    unsigned num = 0;
    for (sit = sets.begin(); sit != sets.end(); ++sit)
    {
      hash_set::iterator hit;
      hash_set* h = *sit;
      for (hit = h->begin(); hit != h->end(); ++hit)
        state_num[*hit] = num;
      ++num;
    }
Pierre PARUTTO's avatar
Pierre PARUTTO committed
135
    typedef state_explicit_number::transition trs;
136
137
138
    tgba_explicit_number* res = new tgba_explicit_number(a->get_dict());
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
139
140
    if (!final->empty())
      res->declare_acceptance_condition(ltl::constant::true_instance());
141
142
143
144
    for (sit = sets.begin(); sit != sets.end(); ++sit)
    {
      hash_set::iterator hit;
      hash_set* h = *sit;
145
146
147
148
149
150
151
152
153

      // Pick one state.
      const state* src = *h->begin();
      unsigned src_num = state_num[src];
      bool accepting = (final->find(src) != final->end());

      // Connect it to all destinations.
      tgba_succ_iterator* succit = a->succ_iter(src);
      for (succit->first(); !succit->done(); succit->next())
154
        {
Felix Abecassis's avatar
Felix Abecassis committed
155
          const state* dst = succit->current_state();
156
	  hash_map::const_iterator i = state_num.find(dst);
157
          dst->destroy();
158
159
160
	  if (i == state_num.end()) // Ignore useless destinations.
	    continue;
          trs* t = res->create_transition(src_num, i->second);
161
162
163
164
          res->add_conditions(t, succit->current_condition());
          if (accepting)
            res->add_acceptance_condition(t, ltl::constant::true_instance());
        }
165
      delete succit;
166
167
168
169
    }
    res->merge_transitions();
    const state* init_state = a->get_init_state();
    unsigned init_num = state_num[init_state];
170
    init_state->destroy();
171
172
173
174
    res->set_init_state(init_num);
    return res;
  }

175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196

  namespace
  {

    struct wdba_search_acc_loop : public bfs_steps
    {
      wdba_search_acc_loop(const tgba* det_a,
			   unsigned scc_n, scc_map& sm,
			   power_map& pm, const state* dest)
	: bfs_steps(det_a), scc_n(scc_n), sm(sm), pm(pm), dest(dest)
      {
	seen.insert(dest);
      }

      virtual
      ~wdba_search_acc_loop()
      {
	hash_set::const_iterator i = seen.begin();
	while (i != seen.end())
	  {
	    hash_set::const_iterator old = i;
	    ++i;
197
	    (*old)->destroy();
198
199
200
201
202
203
204
205
206
207
208
209
210
211
	  }
      }

      virtual const state*
      filter(const state* s)
      {
	// Use the state from seen.
	hash_set::const_iterator i = seen.find(s);
	if (i == seen.end())
	  {
	    seen.insert(s);
	  }
	else
	  {
212
	    s->destroy();
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
	    s = *i;
	  }
	// Ignore states outside SCC #n.
	if (sm.scc_of_state(s) != scc_n)
	  return 0;
	return s;
      }

      virtual bool
      match(tgba_run::step&, const state* to)
      {
	return to == dest;
      }

      unsigned scc_n;
      scc_map& sm;
      power_map& pm;
      const state* dest;
      hash_set seen;
    };


    bool
    wdba_scc_is_accepting(const tgba_explicit_number* det_a, unsigned scc_n,
			  const tgba* orig_a, scc_map& sm, power_map& pm)
    {
      // Get some state from the SCC #n.
      const state* start = sm.one_state_of(scc_n)->clone();

      // Find a loop around START in SCC #n.
      wdba_search_acc_loop wsal(det_a, scc_n, sm, pm, start);
      tgba_run::steps loop;
      const state* reached = wsal.search(start, loop);
      assert(reached == start);
      (void)reached;

      // Build an automaton representing this loop.
      tgba_explicit_number loop_a(det_a->get_dict());
      tgba_run::steps::const_iterator i;
      int loop_size = loop.size();
      int n;
      for (n = 1, i = loop.begin(); n < loop_size; ++n, ++i)
	{
	  loop_a.create_transition(n - 1, n)->condition = i->label;
257
	  i->s->destroy();
258
259
260
	}
      assert(i != loop.end());
      loop_a.create_transition(n - 1, 0)->condition = i->label;
261
      i->s->destroy();
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
      assert(++i == loop.end());

      const state* loop_a_init = loop_a.get_init_state();
      assert(loop_a.get_label(loop_a_init) == 0);

      // Check if the loop is accepting in the original automaton.
      bool accepting = false;

      // Iterate on each original state corresponding to start.
      const power_map::power_state& ps = pm.states_of(det_a->get_label(start));
      for (power_map::power_state::const_iterator it = ps.begin();
	   it != ps.end() && !accepting; ++it)
	{
	  // Contrustruct a product between
	  // LOOP_A, and ORIG_A starting in *IT.

	  tgba* p = new tgba_product_init(&loop_a, orig_a,
					  loop_a_init, *it);

	  emptiness_check* ec = couvreur99(p);
	  emptiness_check_result* res = ec->check();

	  if (res)
	    accepting = true;
	  delete res;
	  delete ec;
	  delete p;
	}

291
      loop_a_init->destroy();
292
293
294
295
296
      return accepting;
    }

  }

297
  tgba_explicit_number* minimize_dfa(const tgba_explicit_number* det_a,
298
				     hash_set* final, hash_set* non_final)
299
  {
300
301
302
    typedef std::list<hash_set*> partition_t;
    partition_t cur_run;
    partition_t next_run;
303

304
305
    // The list of equivalent states.
    partition_t done;
306

307
    hash_map state_set_map;
308

309
310
    // Size of det_a
    unsigned size = final->size() + non_final->size();
311
312
    // Use bdd variables to number sets.  set_num is the first variable
    // available.
313
314
    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
315
316
317
318
319
320

    std::set<int> free_var;
    for (unsigned i = set_num; i < set_num + size; ++i)
      free_var.insert(i);
    std::map<int, int> used_var;

Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
321
322
    hash_set* final_copy;

323
324
325
326
327
328
    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
329
	  cur_run.push_back(final);
330
331
332
333
334
	else
	  done.push_back(final);
	for (hash_set::const_iterator i = final->begin();
	     i != final->end(); ++i)
	  state_set_map[*i] = set_num;
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
335
336

	final_copy = new hash_set(*final);
337
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
338
339
340
341
342
    else
      {
	final_copy = final;
      }

343
344
345
346
347
348
349
    if (!non_final->empty())
      {
	unsigned s = non_final->size();
	unsigned num = set_num + 1;
	used_var[num] = s;
	free_var.erase(num);
	if (s > 1)
350
	  cur_run.push_back(non_final);
351
352
353
354
355
356
	else
	  done.push_back(non_final);
	for (hash_set::const_iterator i = non_final->begin();
	     i != non_final->end(); ++i)
	  state_set_map[*i] = num;
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
357
358
359
360
    else
      {
	delete non_final;
      }
361

362
363
    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
364
365
366
367
368
    typedef std::map<bdd, hash_set*, bdd_less_than> bdd_states_map;

    bool did_split = true;

    while (did_split)
369
      {
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
387
388
	did_split = false;
	while (!cur_run.empty())
	  {
	    // Get a set to process.
	    hash_set* cur = cur_run.front();
	    cur_run.pop_front();

	    trace << "processing " << format_hash_set(cur, det_a) << std::endl;

	    hash_set::iterator hi;
	    bdd_states_map bdd_map;
	    for (hi = cur->begin(); hi != cur->end(); ++hi)
	      {
		const state* src = *hi;
		bdd f = bddfalse;
		tgba_succ_iterator* si = det_a->succ_iter(src);
		for (si->first(); !si->done(); si->next())
		  {
		    const state* dst = si->current_state();
389
		    hash_map::const_iterator i = state_set_map.find(dst);
390
		    dst->destroy();
391
392
393
394
395
396
397
398
399
		    if (i == state_set_map.end())
		      // The destination state is not in our
		      // partition.  This can happen if the initial
		      // FINAL and NON_FINAL supplied to the algorithm
		      // do not cover the whole automaton (because we
		      // want to ignore some useless states).  Simply
		      // ignore these states here.
		      continue;
		    f |= (bdd_ithvar(i->second) & si->current_condition());
400
401
402
403
404
405
406
407
408
409
410
411
412
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
428
		  }
		delete si;

		// Have we already seen this formula ?
		bdd_states_map::iterator bsi = bdd_map.find(f);
		if (bsi == bdd_map.end())
		  {
		    // No, create a new set.
		    hash_set* new_set = new hash_set;
		    new_set->insert(src);
		    bdd_map[f] = new_set;
		  }
		else
		  {
		    // Yes, add the current state to the set.
		    bsi->second->insert(src);
		  }
	      }

	    bdd_states_map::iterator bsi = bdd_map.begin();
	    if (bdd_map.size() == 1)
	      {
		// The set was not split.
		trace << "set " << format_hash_set(bsi->second, det_a)
		      << " was not split" << std::endl;
		next_run.push_back(bsi->second);
	      }
	    else
	      {
429
		did_split = true;
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
		for (; bsi != bdd_map.end(); ++bsi)
		  {
		    hash_set* set = bsi->second;
		    // Free the number associated to these states.
		    unsigned num = state_set_map[*set->begin()];
		    assert(used_var.find(num) != used_var.end());
		    unsigned left = (used_var[num] -= set->size());
		    // Make sure LEFT does not become negative (hence bigger
		    // than SIZE when read as unsigned)
		    assert(left < size);
		    if (left == 0)
		      {
			used_var.erase(num);
			free_var.insert(num);
		      }
		    // Pick a free number
		    assert(!free_var.empty());
		    num = *free_var.begin();
		    free_var.erase(free_var.begin());
		    used_var[num] = set->size();
		    for (hash_set::iterator hit = set->begin();
			 hit != set->end(); ++hit)
		      state_set_map[*hit] = num;
		    // Trivial sets can't be splitted any further.
		    if (set->size() == 1)
		      {
			trace << "set " << format_hash_set(set, det_a)
			      << " is minimal" << std::endl;
			done.push_back(set);
		      }
		    else
		      {
			trace << "set " << format_hash_set(set, det_a)
			      << " should be processed further" << std::endl;
			next_run.push_back(set);
		      }
		  }
	      }
	    delete cur;
	  }
	if (did_split)
	  trace << "splitting did occur during this pass." << std::endl;
	else
	  trace << "splitting did not occur during this pass." << std::endl;
	std::swap(cur_run, next_run);
475
      }
476
477
478
479
480
481
482
483
484

    done.splice(done.end(), cur_run);

#ifdef TRACE
    trace << "Final partition: ";
    for (partition_t::const_iterator i = done.begin(); i != done.end(); ++i)
      trace << format_hash_set(*i, det_a) << " ";
    trace << std::endl;
#endif
Felix Abecassis's avatar
Felix Abecassis committed
485
486
487
488
489
490
491

    // Build the result.
    tgba_explicit_number* res = build_result(det_a, done, final_copy);

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
492
493
494
    for (hit = state_set_map.begin(); hit != state_set_map.end();)
      {
	hash_map::iterator old = hit++;
495
	old->first->destroy();
496
      }
Felix Abecassis's avatar
Felix Abecassis committed
497
498
499
500
501
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;
    delete det_a;

502
503
    return res;
  }
504

505

506
507
508
  tgba_explicit_number* minimize_monitor(const tgba* a)
  {
    hash_set* final = new hash_set;
509
    hash_set* non_final = new hash_set;
510
511
512
513
514
515
    tgba_explicit_number* det_a;

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);
    }
516
517

    // non_final contain all states.
518
    // final is empty: there is no acceptance condition
519
    state_set(det_a, non_final);
520
521

    return minimize_dfa(det_a, final, non_final);
522
523
524
  }

  tgba_explicit_number* minimize_wdba(const tgba* a)
525
526
  {
    hash_set* final = new hash_set;
527
528
    hash_set* non_final = new hash_set;

529
530
531
532
533
534
    tgba_explicit_number* det_a;

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);

535
536
537
538
539
540
541
542
543
544
545
      // For each SCC of the deterministic automaton, determine if it
      // is accepting or not.

      // This corresponds to the algorithm in Fig. 1 of "Efficient
      // minimization of deterministic weak omega-automata" written by
      // Christof Löding and published in Information Processing
      // Letters 79 (2001) pp 105--109.

      // We also keep track of whether an SCC is useless
      // (i.e., it is not the start of any accepting word).

546
547
548
      scc_map sm(det_a);
      sm.build_map();
      unsigned scc_count = sm.scc_count();
549
550
      // SCC that have been marked as useless.
      std::vector<bool> useless(scc_count);
551
552
553
554
555
556
557
      // The "color".  Even number correspond to
      // accepting SCCs.
      std::vector<unsigned> d(scc_count);

      // An even number larger than scc_count.
      unsigned k = (scc_count | 1) + 1;

558
      // SCC are numbered in topological order
559
560
      // (but in the reverse order as Löding's)
      for (unsigned m = 0; m < scc_count; ++m)
561
	{
562
	  bool is_useless = true;
563
564
	  bool transient = sm.trivial(m);
	  const scc_map::succ_type& succ = sm.succ(m);
565

566
	  if (transient && succ.empty())
567
	    {
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
588
589
	      // A trivial SCC without successor is useless.
	      useless[m] = true;
	      d[m] = k - 1;
	      continue;
	    }

	  // Compute the minimum color l of the successors.
	  // Also SCCs are useless if all their successor are
	  // useless.
	  unsigned l = k;
	  for (scc_map::succ_type::const_iterator j = succ.begin();
	       j != succ.end(); ++j)
	    {
	      is_useless &= useless[j->first];
	      unsigned dj = d[j->first];
	      if (dj < l)
		l = dj;
	    }

	  if (transient)
	    {
	      d[m] = l;
590
591
592
593
	    }
	  else
	    {
	      // Regular SCCs are accepting if any of their loop
594
595
	      // corresponds to an accepted word in the original
	      // automaton.
596
	      if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
597
598
		{
		  is_useless = false;
599
		  d[m] = (l | 1) - 1; // largest even number inferior or equal
600
601
602
		}
	      else
		{
603
		  d[m] = (l - 1) | 1; // largest odd number inferior or equal
604
		}
605
	    }
606

607
	  useless[m] = is_useless;
608

609
610
	  if (!is_useless)
	    {
611
612
	      hash_set* dest_set = (d[m]&1) ? non_final : final;
	      const std::list<const state*>& l = sm.states_of(m);
613
614
615
616
	      std::list<const state*>::const_iterator il;
	      for (il = l.begin(); il != l.end(); ++il)
		dest_set->insert((*il)->clone());
	    }
617
618
619
	}
    }

620
    return minimize_dfa(det_a, final, non_final);
621
622
  }

623
  tgba*
624
  minimize_obligation(const tgba* aut_f,
625
626
		      const ltl::formula* f, const tgba* aut_neg_f,
		      bool reject_bigger)
627
  {
628
    tgba_explicit_number* min_aut_f = minimize_wdba(aut_f);
629

630
631
632
633
634
635
636
637
638
639
640
    if (reject_bigger)
      {
	// Abort if min_aut_f has more states than aut_f.
	tgba_statistics orig_size = stats_reachable(aut_f);
	if (orig_size.states < min_aut_f->num_states())
	  {
	    delete min_aut_f;
	    return const_cast<tgba*>(aut_f);
	  }
      }

641
642
643
644
645
    // if f is a syntactic obligation formula, the WDBA minimization
    // must be correct.
    if (f && f->is_syntactic_obligation())
      return min_aut_f;

646
    // If aut_f is a guarantee automaton, the WDBA minimization must be
647
    // correct.
648
    if (is_guarantee_automaton(aut_f))
649
      return min_aut_f;
650
651
652
653

    if (!f && !aut_neg_f)
      {
	// We do not now if the minimization is safe.
654
	delete min_aut_f;
655
656
657
658
659
660
661
662
663
664
	return 0;
      }

    const tgba* to_free = 0;

    // Build negation automaton if not supplied.
    if (!aut_neg_f)
      {
	assert(f);

665
666
	const ltl::formula* neg_f =
	  ltl::unop::instance(ltl::unop::Not, f->clone());
667
668
669
670
671
672
673
674
675
	aut_neg_f = ltl_to_tgba_fm(neg_f, aut_f->get_dict());
	neg_f->destroy();

	// Remove useless SCCs.
	const tgba* tmp = scc_filter(aut_neg_f, true);
	delete aut_neg_f;
	to_free = aut_neg_f = tmp;
      }

676
    // If the negation is a guarantee automaton, then the
677
    // minimization is correct.
678
    if (is_guarantee_automaton(aut_neg_f))
679
680
681
682
683
684
685
686
687
688
689
690
691
692
      {
	delete to_free;
	return min_aut_f;
      }

    bool ok = false;

    tgba* p = new tgba_product(min_aut_f, aut_neg_f);
    emptiness_check* ec = couvreur99(p);
    emptiness_check_result* res = ec->check();
    if (!res)
      {
	delete ec;
	delete p;
693

694
	// Complement the minimized WDBA.
695
696
697
	tgba* neg_min_aut_f = wdba_complement(min_aut_f);

	tgba* p = new tgba_product(aut_f, neg_min_aut_f);
698
699
700
701
	emptiness_check* ec = couvreur99(p);
	res = ec->check();

	if (!res)
702
703
704
705
706
	  {
	    // Finally, we are now sure that it was safe
	    // to minimize the automaton.
	    ok = true;
	  }
707
708
709
710

	delete res;
	delete ec;
	delete p;
711
	delete neg_min_aut_f;
712
713
714
715
716
717
718
719
720
721
722
723
      }
    else
      {
	delete res;
	delete ec;
	delete p;
      }
    delete to_free;

    if (ok)
      return min_aut_f;
    delete min_aut_f;
724
    return const_cast<tgba*>(aut_f);
725
  }
726
}