ltl2tgba_fm.cc 25.6 KB
Newer Older
1
2
3
// Copyright (C) 2008, 2009, 2010 Laboratoire de Recherche et
// Dveloppement de l'Epita (LRDE).
// Copyright (C) 2003, 2004, 2005, 2006 Laboratoire
4
5
// d'Informatique de Paris 6 (LIP6), dpartement Systmes Rpartis
// Coopratifs (SRC), Universit Pierre et Marie Curie.
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
//
// 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.

24
#include "misc/hash.hh"
25
#include "misc/bddalloc.hh"
26
#include "misc/bddlt.hh"
27
#include "misc/minato.hh"
28
29
#include "ltlast/visitor.hh"
#include "ltlast/allnodes.hh"
30
31
32
#include "ltlvisit/lunabbrev.hh"
#include "ltlvisit/nenoform.hh"
#include "ltlvisit/tostring.hh"
33
#include "ltlvisit/postfix.hh"
34
#include "ltlvisit/apcollect.hh"
35
#include <cassert>
36
#include <memory>
37
#include "ltl2tgba_fm.hh"
38
#include "ltlvisit/contain.hh"
39
40
41
42
43
44
45
46

namespace spot
{
  using namespace ltl;

  namespace
  {

47
48
    // Helper dictionary.  We represent formulae using BDDs to
    // simplify them, and then translate BDDs back into formulae.
49
50
51
52
53
    //
    // The name of the variables are inspired from Couvreur's FM paper.
    //   "a" variables are promises (written "a" in the paper)
    //   "next" variables are X's operands (the "r_X" variables from the paper)
    //   "var" variables are atomic propositions.
54
    class translate_dict
55
56
57
    {
    public:

58
59
      translate_dict(bdd_dict* dict)
	: dict(dict),
60
61
62
63
64
65
66
67
68
69
	  a_set(bddtrue),
	  var_set(bddtrue),
	  next_set(bddtrue)
      {
      }

      ~translate_dict()
      {
	fv_map::iterator i;
	for (i = next_map.begin(); i != next_map.end(); ++i)
70
	  i->first->destroy();
71
	dict->unregister_all_my_variables(this);
72
73
      }

74
75
      bdd_dict* dict;

76
77
      typedef bdd_dict::fv_map fv_map;
      typedef bdd_dict::vf_map vf_map;
78
79
80
81
82
83
84
85
86

      fv_map next_map;	       ///< Maps "Next" variables to BDD variables
      vf_map next_formula_map; ///< Maps BDD variables to "Next" variables

      bdd a_set;
      bdd var_set;
      bdd next_set;

      int
87
      register_proposition(const formula* f)
88
      {
89
	int num = dict->register_proposition(f, this);
90
91
92
93
94
	var_set &= bdd_ithvar(num);
	return num;
      }

      int
95
      register_a_variable(const formula* f)
96
      {
97
	int num = dict->register_acceptance_variable(f, this);
98
99
100
101
102
	a_set &= bdd_ithvar(num);
	return num;
      }

      int
103
      register_next_variable(const formula* f)
104
105
106
107
108
109
110
111
112
113
      {
	int num;
	// Do not build a Next variable that already exists.
	fv_map::iterator sii = next_map.find(f);
	if (sii != next_map.end())
	  {
	    num = sii->second;
	  }
	else
	  {
114
	    f = f->clone();
115
	    num = dict->register_anonymous_variables(1, this);
116
117
118
119
120
121
122
	    next_map[f] = num;
	    next_formula_map[num] = f;
	  }
	next_set &= bdd_ithvar(num);
	return num;
      }

123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
      std::ostream&
      dump(std::ostream& os) const
      {
	fv_map::const_iterator fi;
	os << "Next Variables:" << std::endl;
	for (fi = next_map.begin(); fi != next_map.end(); ++fi)
	{
	  os << "  " << fi->second << ": Next[";
	  to_string(fi->first, os) << "]" << std::endl;
	}
	os << "Shared Dict:" << std::endl;
	dict->dump(os);
	return os;
      }

138
      formula*
139
140
141
142
      var_to_formula(int var) const
      {
	vf_map::const_iterator isi = next_formula_map.find(var);
	if (isi != next_formula_map.end())
143
	  return isi->second->clone();
144
145
	isi = dict->acc_formula_map.find(var);
	if (isi != dict->acc_formula_map.end())
146
	  return isi->second->clone();
147
148
	isi = dict->var_formula_map.find(var);
	if (isi != dict->var_formula_map.end())
149
	  return isi->second->clone();
150
	assert(0);
151
152
153
	// Never reached, but some GCC versions complain about
	// a missing return otherwise.
	return 0;
154
155
      }

156
      formula*
157
158
159
      conj_bdd_to_formula(bdd b)
      {
	if (b == bddfalse)
160
161
	  return constant::false_instance();
	multop::vec* v = new multop::vec;
162
163
164
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
165
	    formula* res = var_to_formula(var);
166
167
168
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
169
		res = unop::instance(unop::Not, res);
170
171
172
173
		b = bdd_low(b);
	      }
	    else
	      {
174
		assert(bdd_low(b) == bddfalse);
175
176
177
178
179
		b = high;
	      }
	    assert(b != bddfalse);
	    v->push_back(res);
	  }
180
	return multop::instance(multop::And, v);
181
182
      }

183
184
      const formula*
      bdd_to_formula(bdd f)
185
      {
186
	if (f == bddfalse)
187
	  return constant::false_instance();
188

189
190
191
192
193
194
195
196
197
	multop::vec* v = new multop::vec;

	minato_isop isop(f);
	bdd cube;
	while ((cube = isop.next()) != bddfalse)
	  v->push_back(conj_bdd_to_formula(cube));

	return multop::instance(multop::Or, v);
      }
198
199

      void
200
      conj_bdd_to_acc(tgba_explicit_formula* a, bdd b,
Pierre PARUTTO's avatar
Pierre PARUTTO committed
201
		      state_explicit_formula::transition* t)
202
203
204
205
206
207
208
209
      {
	assert(b != bddfalse);
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
210
		// Simply ignore negated acceptance variables.
211
212
213
214
		b = bdd_low(b);
	      }
	    else
	      {
215
		formula* ac = var_to_formula(var);
216

217
		if (!a->has_acceptance_condition(ac))
218
		  a->declare_acceptance_condition(ac->clone());
219
		a->add_acceptance_condition(t, ac);
220
221
222
223
224
225
226
227
		b = high;
	      }
	    assert(b != bddfalse);
	  }
      }
    };


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
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271

    // Gather all promises of a formula.  These are the
    // right-hand sides of U or F operators.
    class ltl_promise_visitor: public postfix_visitor
    {
    public:
      ltl_promise_visitor(translate_dict& dict)
	: dict_(dict), res_(bddtrue)
      {
      }

      virtual
      ~ltl_promise_visitor()
      {
      }

      bdd
      result() const
      {
	return res_;
      }

      using postfix_visitor::doit;

      virtual void
      doit(unop* node)
      {
	if (node->op() == unop::F)
	  res_ &= bdd_ithvar(dict_.register_a_variable(node->child()));
      }

      virtual void
      doit(binop* node)
      {
	if (node->op() == binop::U)
	  res_ &= bdd_ithvar(dict_.register_a_variable(node->second()));
      }

    private:
      translate_dict& dict_;
      bdd res_;
    };


272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
    // The rewrite rules used here are adapted from Jean-Michel
    // Couvreur's FM paper.
    class ltl_trad_visitor: public const_visitor
    {
    public:
      ltl_trad_visitor(translate_dict& dict)
	: dict_(dict)
      {
      }

      virtual
      ~ltl_trad_visitor()
      {
      }

287
288
      bdd
      result() const
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
      {
	return res_;
      }

      void
      visit(const atomic_prop* node)
      {
	res_ = bdd_ithvar(dict_.register_proposition(node));
      }

      void
      visit(const constant* node)
      {
	switch (node->val())
	  {
	  case constant::True:
	    res_ = bddtrue;
	    return;
	  case constant::False:
	    res_ = bddfalse;
	    return;
310
311
	  case constant::EmptyWord:
	    assert(!"unsupported operator");
312
313
314
315
316
317
318
319
320
321
322
323
324
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const unop* node)
      {
	switch (node->op())
	  {
	  case unop::F:
	    {
	      // r(Fy) = r(y) + a(y)r(XFy)
325
326
327
	      const formula* child = node->child();
	      bdd y = recurse(child);
	      int a = dict_.register_a_variable(child);
328
329
330
331
332
333
	      int x = dict_.register_next_variable(node);
	      res_ = y | (bdd_ithvar(a) & bdd_ithvar(x));
	      return;
	    }
	  case unop::G:
	    {
334
335
336
337
338
339
340
341
342
343
344
345
	      // The paper suggests that we optimize GFy
	      // as
	      //   r(GFy) = (r(y) + a(y))r(XGFy)
	      // instead of
	      //   r(GFy) = (r(y) + a(y)r(XFy)).r(XGFy)
	      // but this is just a particular case
	      // of the "merge all states with the same
	      // symbolic rewriting" optimization we do later.
	      // (r(Fy).r(GFy) and r(GFy) have the same symbolic
	      // rewriting.)  Let's keep things simple here.

	      // r(Gy) = r(y)r(XGy)
346
	      const formula* child = node->child();
347
	      int x = dict_.register_next_variable(node);
348
349
	      bdd y = recurse(child);
	      res_ = y & bdd_ithvar(x);
350
351
352
353
	      return;
	    }
	  case unop::Not:
	    {
354
	      // r(!y) = !r(y)
355
356
357
358
359
	      res_ = bdd_not(recurse(node->child()));
	      return;
	    }
	  case unop::X:
	    {
360
	      // r(Xy) = Next[y]
361
362
363
364
	      int x = dict_.register_next_variable(node->child());
	      res_ = bdd_ithvar(x);
	      return;
	    }
365
	  case unop::Finish:
366
	  case unop::Star:
367
	    assert(!"unsupported operator");
368
369
370
371
372
373
374
375
376
377
378
379
380
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const binop* node)
      {
	bdd f1 = recurse(node->first());
	bdd f2 = recurse(node->second());

	switch (node->op())
	  {
381
	    // r(f1 logical-op f2) = r(f1) logical-op r(f2)
382
383
384
385
386
387
388
389
390
391
392
393
394
395
396
397
398
	  case binop::Xor:
	    res_ = bdd_apply(f1, f2, bddop_xor);
	    return;
	  case binop::Implies:
	    res_ = bdd_apply(f1, f2, bddop_imp);
	    return;
	  case binop::Equiv:
	    res_ = bdd_apply(f1, f2, bddop_biimp);
	    return;
	  case binop::U:
	    {
	      // r(f1 U f2) = r(f2) + a(f2)r(f1)r(X(f1 U f2))
	      int a = dict_.register_a_variable(node->second());
	      int x = dict_.register_next_variable(node);
	      res_ = f2 | (bdd_ithvar(a) & f1 & bdd_ithvar(x));
	      return;
	    }
399
400
401
402
403
404
405
	  case binop::W:
	    {
	      // r(f1 W f2) = r(f2) + r(f1)r(X(f1 U f2))
	      int x = dict_.register_next_variable(node);
	      res_ = f2 | (f1 & bdd_ithvar(x));
	      return;
	    }
406
407
408
409
410
411
412
	  case binop::R:
	    {
	      // r(f1 R f2) = r(f1)r(f2) + r(f2)r(X(f1 U f2))
	      int x = dict_.register_next_variable(node);
	      res_ = (f1 & f2) | (f2 & bdd_ithvar(x));
	      return;
	    }
413
414
415
416
417
418
419
420
	  case binop::M:
	    {
	      // r(f1 M f2) = r(f1)r(f2) + a(f1)r(f2)r(X(f1 M f2))
	      int a = dict_.register_a_variable(node->first());
	      int x = dict_.register_next_variable(node);
	      res_ = (f1 & f2) | (bdd_ithvar(a) & f2 & bdd_ithvar(x));
	      return;
	    }
421
422
423
424
425
	  }
	/* Unreachable code.  */
	assert(0);
      }

426
427
428
429
430
431
      void
      visit(const automatop*)
      {
	assert(!"unsupported operator");
      }

432
433
434
435
436
437
438
439
440
441
442
443
444
445
      void
      visit(const multop* node)
      {
	int op = -1;
	switch (node->op())
	  {
	  case multop::And:
	    op = bddop_and;
	    res_ = bddtrue;
	    break;
	  case multop::Or:
	    op = bddop_or;
	    res_ = bddfalse;
	    break;
446
447
	  case multop::Concat:
	    assert(!"unsupported operator");
448
449
450
451
452
453
454
455
456
457
458
459
460
461
462
463
464
465
466
467
468
469
470
	  }
	assert(op != -1);
	unsigned s = node->size();
	for (unsigned n = 0; n < s; ++n)
	  {
	    res_ = bdd_apply(res_, recurse(node->nth(n)), op);
	  }
      }

      bdd
      recurse(const formula* f)
      {
	ltl_trad_visitor v(dict_);
	f->accept(v);
	return v.result();
      }


    private:
      translate_dict& dict_;
      bdd res_;
    };

471

472
473
    // Check whether a formula has a R, W, or G operator at its
    // top-level (preceding logical operators do not count).
474
475
476
477
478
479
480
481
482
483
484
485
486
487
488
489
490
491
492
493
494
495
496
497
498
499
500
501
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
523
    class ltl_possible_fair_loop_visitor: public const_visitor
    {
    public:
      ltl_possible_fair_loop_visitor()
	: res_(false)
      {
      }

      virtual
      ~ltl_possible_fair_loop_visitor()
      {
      }

      bool
      result() const
      {
	return res_;
      }

      void
      visit(const atomic_prop*)
      {
      }

      void
      visit(const constant*)
      {
      }

      void
      visit(const unop* node)
      {
	if (node->op() == unop::G)
	  res_ = true;
      }

      void
      visit(const binop* node)
      {
	switch (node->op())
	  {
	    // r(f1 logical-op f2) = r(f1) logical-op r(f2)
	  case binop::Xor:
	  case binop::Implies:
	  case binop::Equiv:
	    node->first()->accept(*this);
	    if (!res_)
	      node->second()->accept(*this);
	    return;
	  case binop::U:
524
	  case binop::M:
525
526
	    return;
	  case binop::R:
527
	  case binop::W:
528
529
530
531
532
533
534
	    res_ = true;
	    return;
	  }
	/* Unreachable code.  */
	assert(0);
      }

535
536
537
538
539
540
      void
      visit(const automatop*)
      {
	assert(!"unsupported operator");
      }

541
542
543
544
545
546
547
548
549
550
551
552
553
554
555
556
557
558
559
560
561
562
      void
      visit(const multop* node)
      {
	unsigned s = node->size();
	for (unsigned n = 0; n < s && !res_; ++n)
	  {
	    node->nth(n)->accept(*this);
	  }
      }

    private:
      bool res_;
    };

    // Check whether a formula can be part of a fair loop.
    // Cache the result for efficiency.
    class possible_fair_loop_checker
    {
    public:
      bool
      check(const formula* f)
      {
563
564
	pfl_map::const_iterator i = pfl_.find(f);
	if (i != pfl_.end())
565
566
567
568
	  return i->second;
	ltl_possible_fair_loop_visitor v;
	f->accept(v);
	bool rel = v.result();
569
	pfl_[f] = rel;
570
571
572
573
	return rel;
      }

    private:
574
      typedef Sgi::hash_map<const formula*, bool, formula_ptr_hash> pfl_map;
575
      pfl_map pfl_;
576
577
    };

578
579
580
    class formula_canonizer
    {
    public:
581
      formula_canonizer(translate_dict& d,
582
			bool fair_loop_approx, bdd all_promises)
583
584
	: v_(d),
	  fair_loop_approx_(fair_loop_approx),
585
	  all_promises_(all_promises)
586
587
588
589
590
      {
	// For cosmetics, register 1 initially, so the algorithm will
	// not register an equivalent formula first.
	b2f_[bddtrue] = constant::true_instance();
      }
591

592
593
      ~formula_canonizer()
      {
594
	while (!f2b_.empty())
595
	  {
596
597
598
	    formula_to_bdd_map::iterator i = f2b_.begin();
	    const formula* f = i->first;
	    f2b_.erase(i);
599
	    f->destroy();
600
	  }
601
602
603
      }

      bdd
604
      translate(const formula* f, bool* new_flag = 0)
605
606
607
608
609
610
      {
	// Use the cached result if available.
	formula_to_bdd_map::const_iterator i = f2b_.find(f);
	if (i != f2b_.end())
	  return i->second;

611
612
613
	if (new_flag)
	  *new_flag = true;

614
615
616
	// Perform the actual translation.
	f->accept(v_);
	bdd res = v_.result();
617
618
619
620
621
622
623
624
625
626
627
628

	// Apply the fair-loop approximation if requested.
	if (fair_loop_approx_)
	  {
	    // If the source cannot possibly be part of a fair
	    // loop, make all possible promises.
	    if (fair_loop_approx_
		&& f != constant::true_instance()
		&& !pflc_.check(f))
	      res &= all_promises_;
	  }

629
	f2b_[f->clone()] = res;
630
631
632
633
634
635
636
637
638
639

	// Register the reverse mapping if it is not already done.
	if (b2f_.find(res) == b2f_.end())
	  b2f_[res] = f;
	return res;
      }

      const formula*
      canonize(const formula* f)
      {
640
641
	bool new_variable = false;
	bdd b = translate(f, &new_variable);
642
643

	bdd_to_formula_map::iterator i = b2f_.find(b);
644
645
	// Since we have just translated the formula, it is
	// necessarily in b2f_.
646
647
648
	assert(i != b2f_.end());

	if (i->second != f)
649
	  {
650
	    // The translated bdd maps to an already seen formula.
651
	    f->destroy();
652
	    f = i->second->clone();
653
	  }
654
	return f;
655
656
      }

657
658
659
660
661
662
663
664
665
666
667
668
669
    private:
      ltl_trad_visitor v_;
      // Map each formula to its associated bdd.  This speed things up when
      // the same formula is translated several times, which especially
      // occurs when canonize() is called repeatedly inside exprop.
      typedef std::map<bdd, const formula*, bdd_less_than> bdd_to_formula_map;
      bdd_to_formula_map b2f_;
      // Map a representation of successors to a canonical formula.
      // We do this because many formulae (such as `aR(bRc)' and
      // `aR(bRc).(bRc)') are equivalent, and are trivially identified
      // by looking at the set of successors.
      typedef std::map<const formula*, bdd> formula_to_bdd_map;
      formula_to_bdd_map f2b_;
670
671
672
673

      possible_fair_loop_checker pflc_;
      bool fair_loop_approx_;
      bdd all_promises_;
674
675
676
677
678
    };

  }

  typedef std::map<bdd, bdd, bdd_less_than> prom_map;
679
  typedef Sgi::hash_map<const formula*, prom_map, formula_ptr_hash> dest_map;
680
681
682
683

  static void
  fill_dests(translate_dict& d, dest_map& dests, bdd label, const formula* dest)
  {
684
    bdd conds = bdd_existcomp(label, d.var_set);
685
686
    bdd promises = bdd_existcomp(label, d.a_set);

687
688
689
690
691
692
693
694
    dest_map::iterator i = dests.find(dest);
    if (i == dests.end())
      {
	dests[dest][promises] = conds;
      }
    else
      {
	i->second[promises] |= conds;
695
	dest->destroy();
696
697
698
699
      }
  }


Pierre PARUTTO's avatar
Pierre PARUTTO committed
700
  tgba_explicit_formula*
701
  ltl_to_tgba_fm(const formula* f, bdd_dict* dict,
702
		 bool exprop, bool symb_merge, bool branching_postponement,
703
		 bool fair_loop_approx, const atomic_prop_set* unobs,
704
		 int reduce_ltl)
705
706
707
708
709
  {
    // Normalize the formula.  We want all the negations on
    // the atomic propositions.  We also suppress logic
    // abbreviations such as <=>, =>, or XOR, since they
    // would involve negations at the BDD level.
710
711
    formula* f1 = unabbreviate_logic(f);
    formula* f2 = negative_normal_form(f1);
712
    f1->destroy();
713

714
715
716
717
    // Simplify the formula, if requested.
    if (reduce_ltl)
      {
	formula* tmp = reduce(f2, reduce_ltl);
718
	f2->destroy();
719
720
721
	f2 = tmp;
      }

722
723
    typedef std::set<const formula*, formula_ptr_less_than> set_type;
    set_type formulae_to_translate;
724

725
    translate_dict d(dict);
726

727
728
    // Compute the set of all promises that can possibly occurre
    // inside the formula.
729
    bdd all_promises = bddtrue;
730
    if (fair_loop_approx || unobs)
731
732
733
734
735
736
      {
	ltl_promise_visitor pv(d);
	f2->accept(pv);
	all_promises = pv.result();
      }

737
    formula_canonizer fc(d, fair_loop_approx, all_promises);
738

739
740
741
742
743
744
745
746
747
748
    // These are used when atomic propositions are interpreted as
    // events.  There are two kinds of events: observable events are
    // those used in the formula, and unobservable events or other
    // events that can occur at anytime.  All events exclude each
    // other.
    bdd observable_events = bddfalse;
    bdd unobservable_events = bddfalse;
    if (unobs)
      {
	bdd neg_events = bddtrue;
749
750
	std::auto_ptr<atomic_prop_set> aps(atomic_prop_collect(f));
	for (atomic_prop_set::const_iterator i = aps->begin();
751
752
753
754
755
756
757
758
	     i != aps->end(); ++i)
	  {
	    int p = d.register_proposition(*i);
	    bdd pos = bdd_ithvar(p);
	    bdd neg = bdd_nithvar(p);
	    observable_events = (observable_events & neg) | (neg_events & pos);
	    neg_events &= neg;
	  }
759
	for (atomic_prop_set::const_iterator i = unobs->begin();
760
761
762
763
764
765
766
767
768
769
770
771
772
	     i != unobs->end(); ++i)
	  {
	    int p = d.register_proposition(*i);
	    bdd pos = bdd_ithvar(p);
	    bdd neg = bdd_nithvar(p);
	    unobservable_events = ((unobservable_events & neg)
				   | (neg_events & pos));
	    observable_events &= neg;
	    neg_events &= neg;
	  }
      }
    bdd all_events = observable_events | unobservable_events;

773

774
    tgba_explicit_formula* a = new tgba_explicit_formula(dict);
775

776
777
    formulae_to_translate.insert(f2);
    a->set_init_state(f2);
778
779
780
781

    while (!formulae_to_translate.empty())
      {
	// Pick one formula.
782
	const formula* now = *formulae_to_translate.begin();
783
784
785
	formulae_to_translate.erase(formulae_to_translate.begin());

	// Translate it into a BDD to simplify it.
786
	bdd res = fc.translate(now);
787

788
789
790
791
	// Handle exclusive events.
	if (unobs)
	  {
	    res &= observable_events;
792
	    int n = d.register_next_variable(now);
793
794
795
	    res |= unobservable_events & bdd_ithvar(n) & all_promises;
	  }

796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
	// We used to factor only Next and A variables while computing
	// prime implicants, with
	//    minato_isop isop(res, d.next_set & d.a_set);
	// in order to obtain transitions with formulae of atomic
	// proposition directly, but unfortunately this led to strange
	// factorizations.  For instance f U g was translated as
	//     r(f U g) = g + a(g).r(X(f U g)).(f + g)
	// instead of just
	//     r(f U g) = g + a(g).r(X(f U g)).f
	// Of course both formulae are logically equivalent, but the
	// latter is "more deterministic" than the former, so it should
	// be preferred.
	//
	// Therefore we now factor all variables.  This may lead to more
	// transitions than necessary (e.g.,  r(f + g) = f + g  will be
811
812
813
	// coded as two transitions), but we later merge all transitions
	// with same source/destination and acceptance conditions.  This
	// is the goal of the `dests' hash.
814
	//
815
	// Note that this is still not optimal.  For instance it is
816
	// better to encode `f U g' as
817
	//     r(f U g) = g + a(g).r(X(f U g)).f.!g
818
819
820
821
	// because that leads to a deterministic automaton.  In order
	// to handle this, we take the conditions of any transition
	// going to true (it's `g' here), and remove it from the other
	// transitions.
822
823
824
	//
	// In `exprop' mode, considering all possible combinations of
	// outgoing propositions generalizes the above trick.
825
	dest_map dests;
826

827
	// Compute all outgoing arcs.
828
829
830
831
832

	// If EXPROP is set, we will refine the symbolic
	// representation of the successors for all combinations of
	// the atomic properties involved in the formula.
	// VAR_SET is the set of these properties.
833
	bdd var_set = bdd_existcomp(bdd_support(res), d.var_set);
834
835
836
837
838
	// ALL_PROPS is the combinations we have yet to consider.
	// We used to start with `all_props = bddtrue', but it is
	// more efficient to start with the set of all satisfiable
	// variables combinations.
	bdd all_props = bdd_existcomp(res, d.var_set);
839
	while (all_props != bddfalse)
840
	  {
841
842
843
	    bdd one_prop_set = bddtrue;
	    if (exprop)
	      one_prop_set = bdd_satoneset(all_props, var_set, bddtrue);
844
	    all_props -= one_prop_set;
845

846
	    typedef std::map<bdd, const formula*, bdd_less_than> succ_map;
847
848
	    succ_map succs;

849
850
851
852
853
854
855
856
857
858
859
860
861
862
	    // Compute prime implicants.
	    // The reason we use prime implicants and not bdd_satone()
	    // is that we do not want to get any negation in front of Next
	    // or Acc variables.  We wouldn't know what to do with these.
	    // We never added negations in front of these variables when
	    // we built the BDD, so prime implicants will not "invent" them.
	    //
	    // FIXME: minato_isop is quite expensive, and I (=adl)
	    // don't think we really care that much about getting the
	    // smalled sum of products that minato_isop strives to
	    // compute.  Given that Next and Acc variables should
	    // always be positive, maybe there is a faster way to
	    // compute the successors?  E.g. using bdd_satone() and
	    // ignoring negated Next and Acc variables.
863
864
865
	    minato_isop isop(res & one_prop_set);
	    bdd cube;
	    while ((cube = isop.next()) != bddfalse)
866
	      {
867
		bdd label = bdd_exist(cube, d.next_set);
868
		bdd dest_bdd = bdd_existcomp(cube, d.next_set);
869
870
		const formula* dest = d.conj_bdd_to_formula(dest_bdd);

871
872
873
874
		// Simplify the formula, if requested.
		if (reduce_ltl)
		  {
		    formula* tmp = reduce(dest, reduce_ltl);
875
		    dest->destroy();
876
877
878
879
880
881
		    dest = tmp;
		    // Ignore the arc if the destination reduces to false.
		    if (dest == constant::false_instance())
		      continue;
		  }

882
883
884
885
		// If we already know a state with the same
		// successors, use it in lieu of the current one.
		if (symb_merge)
		  dest = fc.canonize(dest);
886

887
888
889
890
891
892
		// If we are not postponing the branching, we can
		// declare the outgoing transitions immediately.
		// Otherwise, we merge transitions with identical
		// label, and declare the outgoing transitions in a
		// second loop.
		if (!branching_postponement)
893
		  {
894
		    fill_dests(d, dests, label, dest);
895
896
897
		  }
		else
		  {
898
899
900
901
		    succ_map::iterator si = succs.find(label);
		    if (si == succs.end())
		      succs[label] = dest;
		    else
902
903
904
905
		      si->second =
			multop::instance(multop::Or,
					 const_cast<formula*>(si->second),
					 const_cast<formula*>(dest));
906
907
		  }
	      }
908
909
910
	    if (branching_postponement)
	      for (succ_map::const_iterator si = succs.begin();
		   si != succs.end(); ++si)
911
		fill_dests(d, dests, si->first, si->second);
912
	  }
913

914
	// Check for an arc going to 1 (True).  Register it first, that
915
	// way it will be explored before others during model checking.
916
	dest_map::const_iterator i = dests.find(constant::true_instance());
917
	// COND_FOR_TRUE is the conditions of the True arc, so we
918
919
920
	// can remove them from all other arcs.  It might sounds that
	// this is not needed when exprop is used, but in fact it is
	// complementary.
921
922
	//
	// Consider
923
	//   f = r(X(1) R p) = p.(1 + r(X(1) R p))
924
	// with exprop the two outgoing arcs would be
925
926
        //         p               p
	//     f ----> 1       f ----> f
927
928
	//
	// where in fact we could output
929
930
        //         p
	//     f ----> 1
931
	//
932
	// because there is no point in looping on f if we can go to 1.
933
	bdd cond_for_true = bddfalse;
934
935
	if (i != dests.end())
	  {
936
	    // When translating LTL for an event-based logic with
937
938
	    // unobservable events, the 1 state should accept all events,
	    // even unobservable events.
939
	    if (unobs && now == constant::true_instance())
940
	      cond_for_true = all_events;
941
942
943
944
945
	    else
	      {
		// There should be only one transition going to 1 (true) ...
		assert(i->second.size() == 1);
		prom_map::const_iterator j = i->second.begin();
946
947
948
		// ... and it is not expected to make any promises (unless
		// fair loop approximations are used).
		assert(fair_loop_approx || j->first == bddtrue);
949
950
		cond_for_true = j->second;
	      }
951
952
	    if (!a->has_state(constant::true_instance()))
	      formulae_to_translate.insert(constant::true_instance());
Pierre PARUTTO's avatar
Pierre PARUTTO committed
953
	    state_explicit_formula::transition* t =
954
	      a->create_transition(now, constant::true_instance());
955
	    a->add_condition(t, d.bdd_to_formula(cond_for_true));
956
957
958
959
960
	  }
	// Register other transitions.
	for (i = dests.begin(); i != dests.end(); ++i)
	  {
	    const formula* dest = i->first;
961
962
963
964
	    // The cond_for_true optimization can cause some
	    // transitions to be removed.  So we have to remember
	    // whether a formula is actually reachable.
	    bool reachable = false;
965

966
967
968
	    // Will this be a new state?
	    bool seen = a->has_state(dest);

969
970
971
972
973
	    if (dest != constant::true_instance())
	      {
		for (prom_map::const_iterator j = i->second.begin();
		     j != i->second.end(); ++j)
		  {
974
975
976
		    bdd cond = j->second - cond_for_true;
		    if (cond == bddfalse) // Skip false transitions.
		      continue;
Pierre PARUTTO's avatar
Pierre PARUTTO committed
977
		    state_explicit_formula::transition* t =
978
		      a->create_transition(now, dest);
979
		    a->add_condition(t, d.bdd_to_formula(cond));
980
		    d.conj_bdd_to_acc(a, j->first, t);
981
		    reachable = true;
982
983
		  }
	      }
984
985
986
987
988
	    else
	      {
		// "1" is reachable.
		reachable = true;
	      }
989
990
	    if (reachable && !seen)
	      formulae_to_translate.insert(dest);
991
	    else
992
	      dest->destroy();
993
994
995
	  }
      }

996
997
    // Turn all promises into real acceptance conditions.
    a->complement_all_acceptance_conditions();
998
999
1000
1001
    return a;
  }

}