minimize.cc 18.6 KB
Newer Older
1
// Copyright (C) 2010, 2011, 2012 Laboratoire de Recherche et Développement
2
3
4
5
6
7
// 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
8
// the Free Software Foundation; either version 3 of the License, or
9
10
11
12
13
14
15
16
// (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
17
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
18

19
20
21
22
23
24
25
26
27

//#define TRACE

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

28
#include <queue>
29
30
31
#include <deque>
#include <set>
#include <list>
32
#include <vector>
33
#include <sstream>
34
35
36
#include "minimize.hh"
#include "ltlast/allnodes.hh"
#include "misc/hash.hh"
37
#include "misc/bddlt.hh"
38
39
#include "tgba/tgbaproduct.hh"
#include "tgba/tgbatba.hh"
40
#include "tgba/wdbacomp.hh"
41
#include "tgbaalgos/powerset.hh"
42
43
44
#include "tgbaalgos/gtec/gtec.hh"
#include "tgbaalgos/safety.hh"
#include "tgbaalgos/sccfilter.hh"
45
#include "tgbaalgos/scc.hh"
46
#include "tgbaalgos/ltl2tgba_fm.hh"
47
#include "tgbaalgos/bfssteps.hh"
48
#include "tgbaalgos/stats.hh"
49
50
51
52
53
54
55
56

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;

57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
  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();
    }
  }

82
83
  // Find all states of an automaton.
  void state_set(const tgba* a, hash_set* seen)
84
  {
Felix Abecassis's avatar
Felix Abecassis committed
85
    std::queue<const state*> tovisit;
86
    // Perform breadth-first traversal.
Felix Abecassis's avatar
Felix Abecassis committed
87
    const state* init = a->get_init_state();
88
    tovisit.push(init);
89
    seen->insert(init);
90
91
    while (!tovisit.empty())
    {
Felix Abecassis's avatar
Felix Abecassis committed
92
      const state* src = tovisit.front();
93
      tovisit.pop();
94

95
96
97
      tgba_succ_iterator* sit = a->succ_iter(src);
      for (sit->first(); !sit->done(); sit->next())
      {
Felix Abecassis's avatar
Felix Abecassis committed
98
        const state* dst = sit->current_state();
99
        // Is it a new state ?
100
101
102
103
104
105
        if (seen->find(dst) == seen->end())
	  {
	    // Register the successor for later processing.
	    tovisit.push(dst);
	    seen->insert(dst);
	  }
106
        else
107
          dst->destroy();
108
      }
Felix Abecassis's avatar
Felix Abecassis committed
109
      delete sit;
110
111
112
113
114
    }
  }

  // From the base automaton and the list of sets, build the minimal
  // resulting automaton
115
  sba_explicit_number* build_result(const tgba* a,
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
                                     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
133
    typedef state_explicit_number::transition trs;
134
    sba_explicit_number* res = new sba_explicit_number(a->get_dict());
135
136
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
137
138
    if (!final->empty())
      res->declare_acceptance_condition(ltl::constant::true_instance());
139
140
141
142
    for (sit = sets.begin(); sit != sets.end(); ++sit)
    {
      hash_set::iterator hit;
      hash_set* h = *sit;
143
144
145
146
147
148
149
150
151

      // 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())
152
        {
Felix Abecassis's avatar
Felix Abecassis committed
153
          const state* dst = succit->current_state();
154
	  hash_map::const_iterator i = state_num.find(dst);
155
          dst->destroy();
156
157
158
	  if (i == state_num.end()) // Ignore useless destinations.
	    continue;
          trs* t = res->create_transition(src_num, i->second);
159
160
161
162
          res->add_conditions(t, succit->current_condition());
          if (accepting)
            res->add_acceptance_condition(t, ltl::constant::true_instance());
        }
163
      delete succit;
164
165
166
167
    }
    res->merge_transitions();
    const state* init_state = a->get_init_state();
    unsigned init_num = state_num[init_state];
168
    init_state->destroy();
169
170
171
172
    res->set_init_state(init_num);
    return res;
  }

173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194

  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;
195
	    (*old)->destroy();
196
197
198
199
200
201
202
203
204
205
206
207
208
209
	  }
      }

      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
	  {
210
	    s->destroy();
211
212
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
	    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;
255
	  i->s->destroy();
256
257
258
	}
      assert(i != loop.end());
      loop_a.create_transition(n - 1, 0)->condition = i->label;
259
      i->s->destroy();
260
261
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
      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;
	}

289
      loop_a_init->destroy();
290
291
292
293
294
      return accepting;
    }

  }

295
296
  sba_explicit_number* minimize_dfa(const tgba_explicit_number* det_a,
				    hash_set* final, hash_set* non_final)
297
  {
298
299
300
    typedef std::list<hash_set*> partition_t;
    partition_t cur_run;
    partition_t next_run;
301

302
303
    // The list of equivalent states.
    partition_t done;
304

305
    hash_map state_set_map;
306

307
308
    // Size of det_a
    unsigned size = final->size() + non_final->size();
309
310
    // Use bdd variables to number sets.  set_num is the first variable
    // available.
311
312
    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
313
314
315
316
317
318

    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
319
320
    hash_set* final_copy;

321
322
323
324
325
326
    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
327
	  cur_run.push_back(final);
328
329
330
331
332
	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
333
334

	final_copy = new hash_set(*final);
335
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
336
337
338
339
340
    else
      {
	final_copy = final;
      }

341
342
343
344
345
346
347
    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)
348
	  cur_run.push_back(non_final);
349
350
351
352
353
354
	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
355
356
357
358
    else
      {
	delete non_final;
      }
359

360
361
    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
362
363
364
365
366
    typedef std::map<bdd, hash_set*, bdd_less_than> bdd_states_map;

    bool did_split = true;

    while (did_split)
367
      {
368
369
370
371
372
373
374
375
376
377
378
379
380
381
382
383
384
385
386
	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();
387
		    hash_map::const_iterator i = state_set_map.find(dst);
388
		    dst->destroy();
389
390
391
392
393
394
395
396
397
		    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());
398
399
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
		  }
		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
	      {
427
		did_split = true;
428
429
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
		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);
473
      }
474
475
476
477
478
479
480
481
482

    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
483
484

    // Build the result.
485
    sba_explicit_number* res = build_result(det_a, done, final_copy);
Felix Abecassis's avatar
Felix Abecassis committed
486
487
488
489

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
490
491
492
    for (hit = state_set_map.begin(); hit != state_set_map.end();)
      {
	hash_map::iterator old = hit++;
493
	old->first->destroy();
494
      }
Felix Abecassis's avatar
Felix Abecassis committed
495
496
497
498
499
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;
    delete det_a;

500
501
    return res;
  }
502

503

504
  sba_explicit_number* minimize_monitor(const tgba* a)
505
506
  {
    hash_set* final = new hash_set;
507
    hash_set* non_final = new hash_set;
508
509
510
511
512
513
    tgba_explicit_number* det_a;

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);
    }
514
515

    // non_final contain all states.
516
    // final is empty: there is no acceptance condition
517
    state_set(det_a, non_final);
518
519

    return minimize_dfa(det_a, final, non_final);
520
521
  }

522
  sba_explicit_number* minimize_wdba(const tgba* a)
523
524
  {
    hash_set* final = new hash_set;
525
526
    hash_set* non_final = new hash_set;

527
528
529
530
531
532
    tgba_explicit_number* det_a;

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

533
534
535
536
537
538
539
540
541
542
543
      // 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).

544
545
546
      scc_map sm(det_a);
      sm.build_map();
      unsigned scc_count = sm.scc_count();
547
548
      // SCC that have been marked as useless.
      std::vector<bool> useless(scc_count);
549
550
551
552
553
554
555
      // 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;

556
      // SCC are numbered in topological order
557
558
      // (but in the reverse order as Löding's)
      for (unsigned m = 0; m < scc_count; ++m)
559
	{
560
	  bool is_useless = true;
561
562
	  bool transient = sm.trivial(m);
	  const scc_map::succ_type& succ = sm.succ(m);
563

564
	  if (transient && succ.empty())
565
	    {
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
583
584
585
586
587
	      // 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;
588
589
590
591
	    }
	  else
	    {
	      // Regular SCCs are accepting if any of their loop
592
593
	      // corresponds to an accepted word in the original
	      // automaton.
594
	      if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
595
596
		{
		  is_useless = false;
597
		  d[m] = l & ~1; // largest even number inferior or equal
598
599
600
		}
	      else
		{
601
		  d[m] = (l - 1) | 1; // largest odd number inferior or equal
602
		}
603
	    }
604

605
	  useless[m] = is_useless;
606

607
608
	  if (!is_useless)
	    {
609
	      hash_set* dest_set = (d[m] & 1) ? non_final : final;
610
	      const std::list<const state*>& l = sm.states_of(m);
611
612
613
614
	      std::list<const state*>::const_iterator il;
	      for (il = l.begin(); il != l.end(); ++il)
		dest_set->insert((*il)->clone());
	    }
615
616
617
	}
    }

618
    return minimize_dfa(det_a, final, non_final);
619
620
  }

621
  tgba*
622
  minimize_obligation(const tgba* aut_f,
623
624
		      const ltl::formula* f, const tgba* aut_neg_f,
		      bool reject_bigger)
625
  {
626
    sba_explicit_number* min_aut_f = minimize_wdba(aut_f);
627

628
629
630
631
632
633
634
635
636
637
638
    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);
	  }
      }

639
640
641
642
643
    // if f is a syntactic obligation formula, the WDBA minimization
    // must be correct.
    if (f && f->is_syntactic_obligation())
      return min_aut_f;

644
    // If aut_f is a guarantee automaton, the WDBA minimization must be
645
    // correct.
646
    if (is_guarantee_automaton(aut_f))
647
      return min_aut_f;
648
649
650
651

    if (!f && !aut_neg_f)
      {
	// We do not now if the minimization is safe.
652
	delete min_aut_f;
653
654
655
656
657
658
659
660
661
662
	return 0;
      }

    const tgba* to_free = 0;

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

663
664
	const ltl::formula* neg_f =
	  ltl::unop::instance(ltl::unop::Not, f->clone());
665
666
667
668
669
670
671
672
673
	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;
      }

674
    // If the negation is a guarantee automaton, then the
675
    // minimization is correct.
676
    if (is_guarantee_automaton(aut_neg_f))
677
678
679
680
681
682
683
684
685
686
687
688
689
690
      {
	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;
691

692
	// Complement the minimized WDBA.
693
694
695
	tgba* neg_min_aut_f = wdba_complement(min_aut_f);

	tgba* p = new tgba_product(aut_f, neg_min_aut_f);
696
697
698
699
	emptiness_check* ec = couvreur99(p);
	res = ec->check();

	if (!res)
700
701
702
703
704
	  {
	    // Finally, we are now sure that it was safe
	    // to minimize the automaton.
	    ok = true;
	  }
705
706
707
708

	delete res;
	delete ec;
	delete p;
709
	delete neg_min_aut_f;
710
711
712
713
714
715
716
717
718
719
720
721
      }
    else
      {
	delete res;
	delete ec;
	delete p;
      }
    delete to_free;

    if (ok)
      return min_aut_f;
    delete min_aut_f;
722
    return const_cast<tgba*>(aut_f);
723
  }
724
}