minimize.cc 17.8 KB
Newer Older
1
// -*- coding: utf-8 -*-
2
3
// Copyright (C) 2010, 2011, 2012, 2013, 2014 Laboratoire de Recherche
// et Développement de l'Epita (LRDE).
4
5
6
7
8
//
// 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
9
// the Free Software Foundation; either version 3 of the License, or
10
11
12
13
14
15
16
17
// (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
18
// along with this program.  If not, see <http://www.gnu.org/licenses/>.
19

20
21
22
23
24
25
26
27
28

//#define TRACE

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

29
#include <queue>
30
31
32
#include <deque>
#include <set>
#include <list>
33
#include <vector>
34
#include <sstream>
35
36
37
#include "minimize.hh"
#include "ltlast/allnodes.hh"
#include "misc/hash.hh"
38
#include "misc/bddlt.hh"
39
#include "tgba/tgbaproduct.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/isdet.hh"
49
#include "tgbaalgos/dtgbacomp.hh"
50
51
52

namespace spot
{
53
54
  // FIXME: do we really want to use unordered_set instead of set here?
  // This calls for benchmarking.
55
56
57
58
  typedef std::unordered_set<const state*,
			     state_ptr_hash, state_ptr_equal> hash_set;
  typedef std::unordered_map<const state*, unsigned,
			     state_ptr_hash, state_ptr_equal> hash_map;
59

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

    static std::string
79
    format_hash_set(const hash_set* hs, const_tgba_ptr aut)
80
81
82
83
84
85
86
    {
      std::ostringstream s;
      dump_hash_set(hs, aut, s);
      return s.str();
    }
  }

87
  // Find all states of an automaton.
88
  void build_state_set(const const_tgba_ptr& a, hash_set* seen)
89
  {
Felix Abecassis's avatar
Felix Abecassis committed
90
    std::queue<const state*> tovisit;
91
    // Perform breadth-first traversal.
Felix Abecassis's avatar
Felix Abecassis committed
92
    const state* init = a->get_init_state();
93
    tovisit.push(init);
94
    seen->insert(init);
95
96
    while (!tovisit.empty())
      {
97
98
99
100
	const state* src = tovisit.front();
	tovisit.pop();

	for (auto sit: a->succ(src))
101
	  {
102
103
104
105
106
107
108
109
110
111
	    const state* dst = sit->current_state();
	    // Is it a new state ?
	    if (seen->find(dst) == seen->end())
	      {
		// Register the successor for later processing.
		tovisit.push(dst);
		seen->insert(dst);
	      }
	    else
	      dst->destroy();
112
	  }
113
114
115
116
117
      }
  }

  // From the base automaton and the list of sets, build the minimal
  // resulting automaton
118
119
120
  tgba_digraph_ptr build_result(const const_tgba_ptr& a,
				std::list<hash_set*>& sets,
				hash_set* final)
121
  {
122
    auto dict = a->get_dict();
123
    auto res = make_tgba_digraph(dict);
124
    res->copy_ap_of(a);
125
126
    res->set_bprop(tgba_digraph::StateBasedAcc);

127
128
129
130
131
132
    // 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;
    for (sit = sets.begin(); sit != sets.end(); ++sit)
133
134
135
      {
	hash_set::iterator hit;
	hash_set* h = *sit;
136
	unsigned num = res->new_state();
137
138
139
	for (hit = h->begin(); hit != h->end(); ++hit)
	  state_num[*hit] = num;
      }
140

141
142
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
143

144
    if (!final->empty())
145
      res->set_single_acceptance_set();
146

147
    for (sit = sets.begin(); sit != sets.end(); ++sit)
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
      {
	hash_set::iterator hit;
	hash_set* h = *sit;

	// 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.
	for (auto succit: a->succ(src))
	  {
	    const state* dst = succit->current_state();
	    hash_map::const_iterator i = state_num.find(dst);
	    dst->destroy();
	    if (i == state_num.end()) // Ignore useless destinations.
	      continue;
165
166
	    res->new_acc_transition(src_num, i->second,
				    succit->current_condition(), accepting);
167
168
	  }
      }
169
    res->merge_transitions();
170
171
172
173
174
175
176
    if (res->num_states() > 0)
      {
	const state* init_state = a->get_init_state();
	unsigned init_num = state_num[init_state];
	init_state->destroy();
	res->set_init_state(init_num);
      }
177
178
179
    return res;
  }

180
181
182
183
184
185

  namespace
  {

    struct wdba_search_acc_loop : public bfs_steps
    {
186
      wdba_search_acc_loop(const const_tgba_ptr& det_a,
187
188
189
190
			   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)
      {
191
	seen(dest);
192
193
194
195
196
      }

      virtual const state*
      filter(const state* s)
      {
197
	s = seen(s);
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
	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;
213
      state_unicity_table seen;
214
215
216
217
    };


    bool
218
219
220
    wdba_scc_is_accepting(const const_tgba_digraph_ptr& det_a, unsigned scc_n,
			  const const_tgba_ptr& orig_a, scc_map& sm,
			  power_map& pm)
221
    {
222

223
224
225
226
227
228
229
230
231
232
233
      // 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.
234
      auto loop_a = make_tgba_digraph(det_a->get_dict());
235
236
      tgba_run::steps::const_iterator i;
      int loop_size = loop.size();
237
      loop_a->new_states(loop_size);
238
239
240
      int n;
      for (n = 1, i = loop.begin(); n < loop_size; ++n, ++i)
	{
241
	  loop_a->new_transition(n - 1, n, i->label);
242
	  i->s->destroy();
243
244
	}
      assert(i != loop.end());
245
      loop_a->new_transition(n - 1, 0, i->label);
246
      i->s->destroy();
247
248
      assert(++i == loop.end());

249
250
      loop_a->set_init_state(0U);
      const state* loop_a_init = loop_a->get_init_state();
251
252
253
254
255

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

      // Iterate on each original state corresponding to start.
256
257
258
      const power_map::power_state& ps =
	pm.states_of(det_a->state_number(start));
      for (auto& it: ps)
259
260
261
	{
	  // Contrustruct a product between
	  // LOOP_A, and ORIG_A starting in *IT.
262
	  // FIXME: This could be sped up a lot!
263
264
	  emptiness_check* ec = couvreur99(product_at(loop_a, orig_a,
						      loop_a_init, it));
265
266
267
	  emptiness_check_result* res = ec->check();
	  delete res;
	  delete ec;
268
269
270
271
272
273

	  if (res)
	    {
	      accepting = true;
	      break;
	    }
274
275
	}

276
      loop_a_init->destroy();
277
278
279
280
281
      return accepting;
    }

  }

282
283
  tgba_digraph_ptr minimize_dfa(const const_tgba_digraph_ptr& det_a,
				hash_set* final, hash_set* non_final)
284
  {
285
286
287
    typedef std::list<hash_set*> partition_t;
    partition_t cur_run;
    partition_t next_run;
288

289
290
    // The list of equivalent states.
    partition_t done;
291

292
    hash_map state_set_map;
293

294
295
    // Size of det_a
    unsigned size = final->size() + non_final->size();
296
297
    // Use bdd variables to number sets.  set_num is the first variable
    // available.
298
299
    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
300
301
302
303
304
305

    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
306
307
    hash_set* final_copy;

308
309
310
311
312
313
    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
314
	  cur_run.push_back(final);
315
316
317
318
319
	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
320
321

	final_copy = new hash_set(*final);
322
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
323
324
325
326
327
    else
      {
	final_copy = final;
      }

328
329
330
331
332
333
334
    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)
335
	  cur_run.push_back(non_final);
336
337
338
339
340
341
	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
342
343
344
345
    else
      {
	delete non_final;
      }
346

347
348
    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
349
350
351
352
353
    typedef std::map<bdd, hash_set*, bdd_less_than> bdd_states_map;

    bool did_split = true;

    while (did_split)
354
      {
355
356
357
358
359
360
361
362
363
364
365
366
367
368
369
	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;
370
		for (auto si: det_a->succ(src))
371
372
		  {
		    const state* dst = si->current_state();
373
		    hash_map::const_iterator i = state_set_map.find(dst);
374
		    dst->destroy();
375
376
377
378
379
380
381
382
383
		    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());
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
405
406
407
408
409
410
411
		  }

		// 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
	      {
412
		did_split = true;
413
414
415
416
417
418
419
420
421
422
423
424
425
426
427
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
		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);
458
      }
459
460
461
462
463
464

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

#ifdef TRACE
    trace << "Final partition: ";
    for (partition_t::const_iterator i = done.begin(); i != done.end(); ++i)
465
      trace << format_hash_set(*i, det_a) << ' ';
466
467
    trace << std::endl;
#endif
Felix Abecassis's avatar
Felix Abecassis committed
468
469

    // Build the result.
470
    auto res = build_result(det_a, done, final_copy);
Felix Abecassis's avatar
Felix Abecassis committed
471
472
473
474

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
475
476
477
    for (hit = state_set_map.begin(); hit != state_set_map.end();)
      {
	hash_map::iterator old = hit++;
478
	old->first->destroy();
479
      }
Felix Abecassis's avatar
Felix Abecassis committed
480
481
482
483
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;

484
485
    return res;
  }
486

487

488
  tgba_digraph_ptr minimize_monitor(const const_tgba_ptr& a)
489
490
  {
    hash_set* final = new hash_set;
491
    hash_set* non_final = new hash_set;
492
    tgba_digraph_ptr det_a;
493
494
495
496
497

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);
    }
498
499

    // non_final contain all states.
500
    // final is empty: there is no acceptance condition
501
    build_state_set(det_a, non_final);
502
503

    return minimize_dfa(det_a, final, non_final);
504
505
  }

506
  tgba_digraph_ptr minimize_wdba(const const_tgba_ptr& a)
507
508
  {
    hash_set* final = new hash_set;
509
510
    hash_set* non_final = new hash_set;

511
    tgba_digraph_ptr det_a;
512
513
514
515
516

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

517
518
519
520
521
      // 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
522
      // Christof Löding and published in Information Processing
523
524
525
526
527
      // 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).

528
529
530
      scc_map sm(det_a);
      sm.build_map();
      unsigned scc_count = sm.scc_count();
531
532
      // SCC that have been marked as useless.
      std::vector<bool> useless(scc_count);
533
534
535
536
537
538
539
      // 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;

540
      // SCC are numbered in topological order
541
      // (but in the reverse order as Löding's)
542
      for (unsigned m = 0; m < scc_count; ++m)
543
	{
544
	  bool is_useless = true;
545
546
	  bool transient = sm.trivial(m);
	  const scc_map::succ_type& succ = sm.succ(m);
547

548
	  if (transient && succ.empty())
549
	    {
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
	      // 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;
572
573
574
575
	    }
	  else
	    {
	      // Regular SCCs are accepting if any of their loop
576
577
	      // corresponds to an accepted word in the original
	      // automaton.
578
	      if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
579
580
		{
		  is_useless = false;
581
		  d[m] = l & ~1; // largest even number inferior or equal
582
583
584
		}
	      else
		{
585
		  d[m] = (l - 1) | 1; // largest odd number inferior or equal
586
		}
587
	    }
588

589
	  useless[m] = is_useless;
590

591
592
	  if (!is_useless)
	    {
593
	      hash_set* dest_set = (d[m] & 1) ? non_final : final;
594
	      const std::list<const state*>& l = sm.states_of(m);
595
596
597
598
	      std::list<const state*>::const_iterator il;
	      for (il = l.begin(); il != l.end(); ++il)
		dest_set->insert((*il)->clone());
	    }
599
600
601
	}
    }

602
    return minimize_dfa(det_a, final, non_final);
603
604
  }

605
606
607
608
  tgba_digraph_ptr
  minimize_obligation(const const_tgba_digraph_ptr& aut_f,
		      const ltl::formula* f,
		      const_tgba_digraph_ptr aut_neg_f,
609
		      bool reject_bigger)
610
  {
611
    auto min_aut_f = minimize_wdba(aut_f);
612

613
614
615
    if (reject_bigger)
      {
	// Abort if min_aut_f has more states than aut_f.
616
	unsigned orig_states = aut_f->num_states();
617
	if (orig_states < min_aut_f->num_states())
618
	  return std::const_pointer_cast<tgba_digraph>(aut_f);
619
620
      }

621
622
623
624
625
    // if f is a syntactic obligation formula, the WDBA minimization
    // must be correct.
    if (f && f->is_syntactic_obligation())
      return min_aut_f;

626
    // If aut_f is a guarantee automaton, the WDBA minimization must be
627
    // correct.
628
    if (is_guarantee_automaton(aut_f))
629
      return min_aut_f;
630
631
632
633

    // Build negation automaton if not supplied.
    if (!aut_neg_f)
      {
634
635
636
637
638
639
640
641
642
	if (f)
	  {
	    // If we know the formula, simply build the automaton for
	    // its negation.
	    const ltl::formula* neg_f =
	      ltl::unop::instance(ltl::unop::Not, f->clone());
	    aut_neg_f = ltl_to_tgba_fm(neg_f, aut_f->get_dict());
	    neg_f->destroy();
	    // Remove useless SCCs.
643
	    aut_neg_f = scc_filter(aut_neg_f, true);
644
645
646
647
648
	  }
	else if (is_deterministic(aut_f))
	  {
	    // If the automaton is deterministic, complementing is
	    // easy.
649
	    aut_neg_f = dtgba_complement(aut_f);
650
651
652
653
	  }
	else
	  {
	    // Otherwise, we cannot check if the minimization is safe.
654
	    return nullptr;
655
	  }
656
657
      }

658
    // If the negation is a guarantee automaton, then the
659
    // minimization is correct.
660
    if (is_guarantee_automaton(aut_neg_f))
661
662
663
664
665
666
      {
	return min_aut_f;
      }

    bool ok = false;

667
    emptiness_check* ec = couvreur99(product(min_aut_f, aut_neg_f));
668
669
670
671
    emptiness_check_result* res = ec->check();
    if (!res)
      {
	delete ec;
672

673
	// Complement the minimized WDBA.
674
675
	auto neg_min_aut_f = wdba_complement(min_aut_f);
	ec = couvreur99(product(aut_f, neg_min_aut_f));
676
677
	res = ec->check();
	if (!res)
678
679
680
681
682
	  {
	    // Finally, we are now sure that it was safe
	    // to minimize the automaton.
	    ok = true;
	  }
683
      }
684
685
    delete res;
    delete ec;
686
687
688

    if (ok)
      return min_aut_f;
689
    return std::const_pointer_cast<tgba_digraph>(aut_f);
690
  }
691
}