minimize.cc 18.3 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
40
#include "tgba/tgbaproduct.hh"
#include "tgba/tgbatba.hh"
41
#include "tgba/wdbacomp.hh"
42
#include "tgbaalgos/powerset.hh"
43
44
45
#include "tgbaalgos/gtec/gtec.hh"
#include "tgbaalgos/safety.hh"
#include "tgbaalgos/sccfilter.hh"
46
#include "tgbaalgos/scc.hh"
47
#include "tgbaalgos/ltl2tgba_fm.hh"
48
#include "tgbaalgos/bfssteps.hh"
49
#include "tgbaalgos/isdet.hh"
50
#include "tgbaalgos/dtgbacomp.hh"
51
#include "priv/countstates.hh"
52
53
54

namespace spot
{
55
56
  // FIXME: do we really want to use unordered_set instead of set here?
  // This calls for benchmarking.
57
58
59
60
  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;
61

62
63
64
65
66
  namespace
  {
    static std::ostream&
    dump_hash_set(const hash_set* hs, const tgba* aut, std::ostream& out)
    {
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
79
80
81
82
83
84
85
86
      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();
    }
  }

87
  // Find all states of an automaton.
88
  void build_state_set(const tgba* 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
  sba_explicit_number* build_result(const tgba* a,
119
120
121
122
123
124
125
126
127
128
                                     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)
129
130
131
132
133
134
135
      {
	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
136
    typedef state_explicit_number::transition trs;
137
    sba_explicit_number* res = new sba_explicit_number(a->get_dict());
138
139
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
140
141
    if (!final->empty())
      res->declare_acceptance_condition(ltl::constant::true_instance());
142
    for (sit = sets.begin(); sit != sets.end(); ++sit)
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
      {
	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;
	    trs* t = res->create_transition(src_num, i->second);
	    res->add_conditions(t, succit->current_condition());
	    if (accepting)
	      res->add_acceptance_condition(t, ltl::constant::true_instance());
	  }
      }
166
167
168
    res->merge_transitions();
    const state* init_state = a->get_init_state();
    unsigned init_num = state_num[init_state];
169
    init_state->destroy();
170
171
172
173
    res->set_init_state(init_num);
    return res;
  }

174
175
176
177
178
179
180
181
182
183
184

  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)
      {
185
	seen(dest);
186
187
188
189
190
      }

      virtual const state*
      filter(const state* s)
      {
191
	s = seen(s);
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
	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;
207
      state_unicity_table seen;
208
209
210
211
    };


    bool
212
    wdba_scc_is_accepting(const tgba_digraph* det_a, unsigned scc_n,
213
214
215
216
217
218
219
220
221
222
223
224
225
			  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.
226
      tgba_digraph loop_a(det_a->get_dict());
227
228
      tgba_run::steps::const_iterator i;
      int loop_size = loop.size();
229
      loop_a.new_states(loop_size);
230
231
232
      int n;
      for (n = 1, i = loop.begin(); n < loop_size; ++n, ++i)
	{
233
	  loop_a.new_transition(n - 1, n, i->label);
234
	  i->s->destroy();
235
236
	}
      assert(i != loop.end());
237
      loop_a.new_transition(n - 1, 0, i->label);
238
      i->s->destroy();
239
240
      assert(++i == loop.end());

241
      loop_a.set_init_state(0U);
242
243
244
245
246
247
      const state* loop_a_init = loop_a.get_init_state();

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

      // Iterate on each original state corresponding to start.
248
249
250
      const power_map::power_state& ps =
	pm.states_of(det_a->state_number(start));
      for (auto& it: ps)
251
252
253
	{
	  // Contrustruct a product between
	  // LOOP_A, and ORIG_A starting in *IT.
254
	  // FIXME: This could be sped up a lot!
255
	  tgba* p = new tgba_product_init(&loop_a, orig_a, loop_a_init, it);
256
257
258
259
260
	  emptiness_check* ec = couvreur99(p);
	  emptiness_check_result* res = ec->check();
	  delete res;
	  delete ec;
	  delete p;
261
262
263
264
265
266

	  if (res)
	    {
	      accepting = true;
	      break;
	    }
267
268
	}

269
      loop_a_init->destroy();
270
271
272
273
274
      return accepting;
    }

  }

275
  sba_explicit_number* minimize_dfa(const tgba_digraph* det_a,
276
				    hash_set* final, hash_set* non_final)
277
  {
278
279
280
    typedef std::list<hash_set*> partition_t;
    partition_t cur_run;
    partition_t next_run;
281

282
283
    // The list of equivalent states.
    partition_t done;
284

285
    hash_map state_set_map;
286

287
288
    // Size of det_a
    unsigned size = final->size() + non_final->size();
289
290
    // Use bdd variables to number sets.  set_num is the first variable
    // available.
291
292
    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
293
294
295
296
297
298

    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
299
300
    hash_set* final_copy;

301
302
303
304
305
306
    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
307
	  cur_run.push_back(final);
308
309
310
311
312
	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
313
314

	final_copy = new hash_set(*final);
315
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
316
317
318
319
320
    else
      {
	final_copy = final;
      }

321
322
323
324
325
326
327
    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)
328
	  cur_run.push_back(non_final);
329
330
331
332
333
334
	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
335
336
337
338
    else
      {
	delete non_final;
      }
339

340
341
    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
342
343
344
345
346
    typedef std::map<bdd, hash_set*, bdd_less_than> bdd_states_map;

    bool did_split = true;

    while (did_split)
347
      {
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
	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;
363
		for (auto si: det_a->succ(src))
364
365
		  {
		    const state* dst = si->current_state();
366
		    hash_map::const_iterator i = state_set_map.find(dst);
367
		    dst->destroy();
368
369
370
371
372
373
374
375
376
		    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());
377
378
379
380
381
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
399
400
401
402
403
404
		  }

		// 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
	      {
405
		did_split = true;
406
407
408
409
410
411
412
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
		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);
451
      }
452
453
454
455
456
457

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

#ifdef TRACE
    trace << "Final partition: ";
    for (partition_t::const_iterator i = done.begin(); i != done.end(); ++i)
458
      trace << format_hash_set(*i, det_a) << ' ';
459
460
    trace << std::endl;
#endif
Felix Abecassis's avatar
Felix Abecassis committed
461
462

    // Build the result.
463
    sba_explicit_number* res = build_result(det_a, done, final_copy);
Felix Abecassis's avatar
Felix Abecassis committed
464
465
466
467

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
468
469
470
    for (hit = state_set_map.begin(); hit != state_set_map.end();)
      {
	hash_map::iterator old = hit++;
471
	old->first->destroy();
472
      }
Felix Abecassis's avatar
Felix Abecassis committed
473
474
475
476
477
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;
    delete det_a;

478
479
    return res;
  }
480

481

482
  sba_explicit_number* minimize_monitor(const tgba* a)
483
484
  {
    hash_set* final = new hash_set;
485
    hash_set* non_final = new hash_set;
486
    tgba_digraph* det_a;
487
488
489
490
491

    {
      power_map pm;
      det_a = tgba_powerset(a, pm);
    }
492
493

    // non_final contain all states.
494
    // final is empty: there is no acceptance condition
495
    build_state_set(det_a, non_final);
496
497

    return minimize_dfa(det_a, final, non_final);
498
499
  }

500
  sba_explicit_number* minimize_wdba(const tgba* a)
501
502
  {
    hash_set* final = new hash_set;
503
504
    hash_set* non_final = new hash_set;

505
    tgba_digraph* det_a;
506
507
508
509
510

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

511
512
513
514
515
      // 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
516
      // Christof Löding and published in Information Processing
517
518
519
520
521
      // 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).

522
523
524
      scc_map sm(det_a);
      sm.build_map();
      unsigned scc_count = sm.scc_count();
525
526
      // SCC that have been marked as useless.
      std::vector<bool> useless(scc_count);
527
528
529
530
531
532
533
      // 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;

534
      // SCC are numbered in topological order
535
      // (but in the reverse order as Löding's)
536
      for (unsigned m = 0; m < scc_count; ++m)
537
	{
538
	  bool is_useless = true;
539
540
	  bool transient = sm.trivial(m);
	  const scc_map::succ_type& succ = sm.succ(m);
541

542
	  if (transient && succ.empty())
543
	    {
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
	      // 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;
566
567
568
569
	    }
	  else
	    {
	      // Regular SCCs are accepting if any of their loop
570
571
	      // corresponds to an accepted word in the original
	      // automaton.
572
	      if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
573
574
		{
		  is_useless = false;
575
		  d[m] = l & ~1; // largest even number inferior or equal
576
577
578
		}
	      else
		{
579
		  d[m] = (l - 1) | 1; // largest odd number inferior or equal
580
		}
581
	    }
582

583
	  useless[m] = is_useless;
584

585
586
	  if (!is_useless)
	    {
587
	      hash_set* dest_set = (d[m] & 1) ? non_final : final;
588
	      const std::list<const state*>& l = sm.states_of(m);
589
590
591
592
	      std::list<const state*>::const_iterator il;
	      for (il = l.begin(); il != l.end(); ++il)
		dest_set->insert((*il)->clone());
	    }
593
594
595
	}
    }

596
    return minimize_dfa(det_a, final, non_final);
597
598
  }

599
  tgba*
600
  minimize_obligation(const tgba* aut_f,
601
602
		      const ltl::formula* f, const tgba* aut_neg_f,
		      bool reject_bigger)
603
  {
604
    sba_explicit_number* min_aut_f = minimize_wdba(aut_f);
605

606
607
608
    if (reject_bigger)
      {
	// Abort if min_aut_f has more states than aut_f.
609
610
	unsigned orig_states = count_states(aut_f);
	if (orig_states < min_aut_f->num_states())
611
612
613
614
615
616
	  {
	    delete min_aut_f;
	    return const_cast<tgba*>(aut_f);
	  }
      }

617
618
619
620
621
    // if f is a syntactic obligation formula, the WDBA minimization
    // must be correct.
    if (f && f->is_syntactic_obligation())
      return min_aut_f;

622
    // If aut_f is a guarantee automaton, the WDBA minimization must be
623
    // correct.
624
    if (is_guarantee_automaton(aut_f))
625
      return min_aut_f;
626
627
628
629
630
631

    const tgba* to_free = 0;

    // Build negation automaton if not supplied.
    if (!aut_neg_f)
      {
632
633
634
635
636
637
638
639
640
641
642
643
644
645
646
647
648
649
	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.
	    const tgba* tmp = scc_filter(aut_neg_f, true);
	    delete aut_neg_f;
	    to_free = aut_neg_f = tmp;
	  }
	else if (is_deterministic(aut_f))
	  {
	    // If the automaton is deterministic, complementing is
	    // easy.
650
	    to_free = aut_neg_f = dtgba_complement(aut_f);
651
652
653
654
655
656
657
	  }
	else
	  {
	    // Otherwise, we cannot check if the minimization is safe.
	    delete min_aut_f;
	    return 0;
	  }
658
659
      }

660
    // If the negation is a guarantee automaton, then the
661
    // minimization is correct.
662
    if (is_guarantee_automaton(aut_neg_f))
663
664
665
666
667
668
669
670
671
672
673
674
675
676
      {
	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;
677

678
	// Complement the minimized WDBA.
679
680
681
	tgba* neg_min_aut_f = wdba_complement(min_aut_f);

	tgba* p = new tgba_product(aut_f, neg_min_aut_f);
682
683
684
685
	emptiness_check* ec = couvreur99(p);
	res = ec->check();

	if (!res)
686
687
688
689
690
	  {
	    // Finally, we are now sure that it was safe
	    // to minimize the automaton.
	    ok = true;
	  }
691
692
693
694

	delete res;
	delete ec;
	delete p;
695
	delete neg_min_aut_f;
696
697
698
699
700
701
702
703
704
705
706
707
      }
    else
      {
	delete res;
	delete ec;
	delete p;
      }
    delete to_free;

    if (ok)
      return min_aut_f;
    delete min_aut_f;
708
    return const_cast<tgba*>(aut_f);
709
  }
710
}