minimize.cc 17.9 KB
Newer Older
1
// -*- coding: utf-8 -*-
2
3
// Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015 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 "tgbaalgos/product.hh"
40
#include "tgbaalgos/powerset.hh"
41
42
43
#include "tgbaalgos/gtec/gtec.hh"
#include "tgbaalgos/safety.hh"
#include "tgbaalgos/sccfilter.hh"
44
#include "tgbaalgos/sccinfo.hh"
45
#include "tgbaalgos/ltl2tgba_fm.hh"
46
#include "tgbaalgos/bfssteps.hh"
47
#include "tgbaalgos/isdet.hh"
48
#include "tgbaalgos/dtgbacomp.hh"
49
50
51

namespace spot
{
52
53
  // FIXME: do we really want to use unordered_set instead of set here?
  // This calls for benchmarking.
54
55
56
57
  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;
58

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

    static std::string
78
    format_hash_set(const hash_set* hs, const_tgba_ptr aut)
79
80
81
82
83
84
85
    {
      std::ostringstream s;
      dump_hash_set(hs, aut, s);
      return s.str();
    }
  }

86
  // Find all states of an automaton.
87
  void build_state_set(const const_tgba_ptr& a, hash_set* seen)
88
  {
Felix Abecassis's avatar
Felix Abecassis committed
89
    std::queue<const state*> tovisit;
90
    // Perform breadth-first traversal.
Felix Abecassis's avatar
Felix Abecassis committed
91
    const state* init = a->get_init_state();
92
    tovisit.push(init);
93
    seen->insert(init);
94
95
    while (!tovisit.empty())
      {
96
97
98
99
	const state* src = tovisit.front();
	tovisit.pop();

	for (auto sit: a->succ(src))
100
	  {
101
102
103
104
105
106
107
108
109
110
	    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();
111
	  }
112
113
114
115
116
      }
  }

  // From the base automaton and the list of sets, build the minimal
  // resulting automaton
117
118
119
  tgba_digraph_ptr build_result(const const_tgba_ptr& a,
				std::list<hash_set*>& sets,
				hash_set* final)
120
  {
121
    auto dict = a->get_dict();
122
    auto res = make_tgba_digraph(dict);
123
    res->copy_ap_of(a);
124
    res->prop_state_based_acc();
125

126
127
128
129
130
131
    // 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)
132
133
134
      {
	hash_set::iterator hit;
	hash_set* h = *sit;
135
	unsigned num = res->new_state();
136
137
138
	for (hit = h->begin(); hit != h->end(); ++hit)
	  state_num[*hit] = num;
      }
139

140
141
    // For each transition in the initial automaton, add the corresponding
    // transition in res.
142

143
    if (!final->empty())
144
      res->set_single_acceptance_set();
145

146
    for (sit = sets.begin(); sit != sets.end(); ++sit)
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
      {
	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;
164
165
	    res->new_acc_transition(src_num, i->second,
				    succit->current_condition(), accepting);
166
167
	  }
      }
168
    res->merge_transitions();
169
170
171
172
173
174
175
    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);
      }
176
177
178
    return res;
  }

179
180
181
182
183
184

  namespace
  {

    struct wdba_search_acc_loop : public bfs_steps
    {
185
      wdba_search_acc_loop(const const_tgba_ptr& det_a,
186
			   unsigned scc_n, scc_info& sm,
187
188
189
			   power_map& pm, const state* dest)
	: bfs_steps(det_a), scc_n(scc_n), sm(sm), pm(pm), dest(dest)
      {
190
	seen(dest);
191
192
193
194
195
      }

      virtual const state*
      filter(const state* s)
      {
196
	s = seen(s);
197
198
	if (sm.scc_of(std::static_pointer_cast<const tgba_digraph>(a_)
		      ->state_number(s)) != scc_n)
199
200
201
202
203
204
205
206
207
208
209
	  return 0;
	return s;
      }

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

      unsigned scc_n;
210
      scc_info& sm;
211
212
      power_map& pm;
      const state* dest;
213
      state_unicity_table seen;
214
215
216
217
    };


    bool
218
    wdba_scc_is_accepting(const const_tgba_digraph_ptr& det_a, unsigned scc_n,
219
			  const const_tgba_digraph_ptr& orig_a, scc_info& sm,
220
			  power_map& pm)
221
222
    {
      // Get some state from the SCC #n.
223
      const state* start = det_a->state_from_number(sm.one_state_of(scc_n));
224
225
226
227
228
229
230
231
232

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

248
      loop_a->set_init_state(0U);
249
250
251
252
253

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

      // Iterate on each original state corresponding to start.
254
255
      const power_map::power_state& ps =
	pm.states_of(det_a->state_number(start));
256
      for (auto& s: ps)
257
	{
258
	  // Construct a product between LOOP_A and ORIG_A starting in
259
260
	  // S.  FIXME: This could be sped up a lot!
	  if (!product(loop_a, orig_a, 0U, s)->is_empty())
261
262
263
264
	    {
	      accepting = true;
	      break;
	    }
265
266
267
268
269
270
271
	}

      return accepting;
    }

  }

272
273
  tgba_digraph_ptr minimize_dfa(const const_tgba_digraph_ptr& det_a,
				hash_set* final, hash_set* non_final)
274
  {
275
276
277
    typedef std::list<hash_set*> partition_t;
    partition_t cur_run;
    partition_t next_run;
278

279
280
    // The list of equivalent states.
    partition_t done;
281

282
    hash_map state_set_map;
283

284
285
    // Size of det_a
    unsigned size = final->size() + non_final->size();
286
287
    // Use bdd variables to number sets.  set_num is the first variable
    // available.
288
289
    unsigned set_num =
      det_a->get_dict()->register_anonymous_variables(size, det_a);
290
291
292
293
294
295

    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
296
297
    hash_set* final_copy;

298
299
300
301
302
303
    if (!final->empty())
      {
	unsigned s = final->size();
	used_var[set_num] = s;
	free_var.erase(set_num);
	if (s > 1)
304
	  cur_run.push_back(final);
305
306
307
308
309
	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
310
311

	final_copy = new hash_set(*final);
312
      }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
313
314
315
316
317
    else
      {
	final_copy = final;
      }

318
319
320
321
322
323
324
    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)
325
	  cur_run.push_back(non_final);
326
327
328
329
330
331
	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
332
333
334
335
    else
      {
	delete non_final;
      }
336

337
338
    // A bdd_states_map is a list of formulae (in a BDD form) associated with a
    // destination set of states.
339
340
341
342
343
    typedef std::map<bdd, hash_set*, bdd_less_than> bdd_states_map;

    bool did_split = true;

    while (did_split)
344
      {
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
	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;
360
		for (auto si: det_a->succ(src))
361
362
		  {
		    const state* dst = si->current_state();
363
		    hash_map::const_iterator i = state_set_map.find(dst);
364
		    dst->destroy();
365
366
367
368
369
370
371
372
373
		    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());
374
375
376
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
		  }

		// 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
	      {
402
		did_split = true;
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
429
430
431
432
433
434
435
436
437
438
439
440
441
442
443
444
445
446
447
		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);
448
      }
449
450
451
452
453
454

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

#ifdef TRACE
    trace << "Final partition: ";
    for (partition_t::const_iterator i = done.begin(); i != done.end(); ++i)
455
      trace << format_hash_set(*i, det_a) << ' ';
456
457
    trace << std::endl;
#endif
Felix Abecassis's avatar
Felix Abecassis committed
458
459

    // Build the result.
460
    auto res = build_result(det_a, done, final_copy);
Felix Abecassis's avatar
Felix Abecassis committed
461
462
463
464

    // Free all the allocated memory.
    delete final_copy;
    hash_map::iterator hit;
465
466
467
    for (hit = state_set_map.begin(); hit != state_set_map.end();)
      {
	hash_map::iterator old = hit++;
468
	old->first->destroy();
469
      }
Felix Abecassis's avatar
Felix Abecassis committed
470
471
472
473
    std::list<hash_set*>::iterator it;
    for (it = done.begin(); it != done.end(); ++it)
      delete *it;

474
475
    return res;
  }
476

477

478
  tgba_digraph_ptr minimize_monitor(const const_tgba_digraph_ptr& a)
479
480
  {
    hash_set* final = new hash_set;
481
    hash_set* non_final = new hash_set;
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
482
    tgba_digraph_ptr det_a = tgba_powerset(a);
483
484

    // non_final contain all states.
485
    // final is empty: there is no acceptance condition
486
    build_state_set(det_a, non_final);
487
    auto res = minimize_dfa(det_a, final, non_final);
488
    res->prop_copy(a, { false, false, false, false, true });
489
490
    res->prop_deterministic();
    res->prop_inherently_weak();
491
    res->prop_state_based_acc();
492
    return res;
493
494
  }

495
  tgba_digraph_ptr minimize_wdba(const const_tgba_digraph_ptr& a)
496
  {
497
498
499
500
    if (a->acc().uses_fin_acceptance())
      throw std::runtime_error
	("minimize_wdba cannot work with Fin acceptance");

501
    hash_set* final = new hash_set;
502
503
    hash_set* non_final = new hash_set;

504
    tgba_digraph_ptr det_a;
505
506
507
508
509

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

510
511
512
513
514
      // 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
515
      // Christof Löding and published in Information Processing
516
517
518
519
520
      // 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).

521
      scc_info sm(det_a);
522
      unsigned scc_count = sm.scc_count();
523
524
      // SCC that have been marked as useless.
      std::vector<bool> useless(scc_count);
525
526
527
528
529
530
531
      // 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;

532
      // SCC are numbered in topological order
533
      // (but in the reverse order as Löding's)
534
      for (unsigned m = 0; m < scc_count; ++m)
535
	{
536
	  bool is_useless = true;
537
538
	  bool transient = sm.is_trivial(m);
	  auto& succ = sm.succ(m);
539

540
	  if (transient && succ.empty())
541
	    {
542
543
544
545
546
547
548
549
550
551
	      // 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;
552
	  for (auto& j: succ)
553
	    {
554
555
	      is_useless &= useless[j.dst];
	      unsigned dj = d[j.dst];
556
557
558
559
560
561
562
	      if (dj < l)
		l = dj;
	    }

	  if (transient)
	    {
	      d[m] = l;
563
564
565
566
	    }
	  else
	    {
	      // Regular SCCs are accepting if any of their loop
567
568
	      // corresponds to an accepted word in the original
	      // automaton.
569
	      if (wdba_scc_is_accepting(det_a, m, a, sm, pm))
570
571
		{
		  is_useless = false;
572
		  d[m] = l & ~1; // largest even number inferior or equal
573
574
575
		}
	      else
		{
576
		  d[m] = (l - 1) | 1; // largest odd number inferior or equal
577
		}
578
	    }
579

580
	  useless[m] = is_useless;
581

582
583
	  if (!is_useless)
	    {
584
	      hash_set* dest_set = (d[m] & 1) ? non_final : final;
585
586
	      for (auto s: sm.states_of(m))
		dest_set->insert(det_a->state_from_number(s));
587
	    }
588
589
590
	}
    }

591
    auto res = minimize_dfa(det_a, final, non_final);
592
    res->prop_copy(a, { false, false, false, false, true });
593
594
595
    res->prop_deterministic();
    res->prop_inherently_weak();
    return res;
596
597
  }

598
599
600
601
  tgba_digraph_ptr
  minimize_obligation(const const_tgba_digraph_ptr& aut_f,
		      const ltl::formula* f,
		      const_tgba_digraph_ptr aut_neg_f,
602
		      bool reject_bigger)
603
  {
604
    auto 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
	unsigned orig_states = aut_f->num_states();
610
	if (orig_states < min_aut_f->num_states())
611
	  return std::const_pointer_cast<tgba_digraph>(aut_f);
612
613
      }

614
615
616
617
618
    // If the input automaton was already weak and deterministic, the
    // output is necessary correct.
    if (aut_f->is_inherently_weak() && aut_f->is_deterministic())
      return min_aut_f;

619
620
621
622
623
    // if f is a syntactic obligation formula, the WDBA minimization
    // must be correct.
    if (f && f->is_syntactic_obligation())
      return min_aut_f;

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

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

656
    // If the negation is a guarantee automaton, then the
657
    // minimization is correct.
658
    if (is_guarantee_automaton(aut_neg_f))
659
660
661
662
663
664
      {
	return min_aut_f;
      }

    bool ok = false;

665
    if (product(min_aut_f, aut_neg_f)->is_empty())
666
      {
667
	// Complement the minimized WDBA.
668
669
	assert(min_aut_f->is_inherently_weak());
	auto neg_min_aut_f = dtgba_complement(min_aut_f);
670
671
672
673
	if (product(aut_f, neg_min_aut_f)->is_empty())
	  // Finally, we are now sure that it was safe
	  // to minimize the automaton.
	  ok = true;
674
675
676
677
      }

    if (ok)
      return min_aut_f;
678
    return std::const_pointer_cast<tgba_digraph>(aut_f);
679
  }
680
}