ltl2tgba_fm.cc 44.5 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
36
#include "ltlvisit/mark.hh"
#include "ltlvisit/tostring.hh"
37
#include <cassert>
38
#include <memory>
39
#include "ltl2tgba_fm.hh"
40
#include "ltlvisit/contain.hh"
41
42
#include "ltlvisit/consterm.hh"
#include "tgba/bddprint.hh"
43
44
45
46
47
48
49
50

namespace spot
{
  using namespace ltl;

  namespace
  {

51
52
    // Helper dictionary.  We represent formulae using BDDs to
    // simplify them, and then translate BDDs back into formulae.
53
54
55
56
57
    //
    // 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.
58
    class translate_dict
59
60
61
    {
    public:

62
63
      translate_dict(bdd_dict* dict)
	: dict(dict),
64
65
66
67
68
69
70
71
72
73
	  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)
74
	  i->first->destroy();
75
	dict->unregister_all_my_variables(this);
76
77
      }

78
79
      bdd_dict* dict;

80
81
      typedef bdd_dict::fv_map fv_map;
      typedef bdd_dict::vf_map vf_map;
82
83
84
85
86
87
88
89
90

      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
91
      register_proposition(const formula* f)
92
      {
93
	int num = dict->register_proposition(f, this);
94
95
96
97
98
	var_set &= bdd_ithvar(num);
	return num;
      }

      int
99
      register_a_variable(const formula* f)
100
      {
101
	int num = dict->register_acceptance_variable(f, this);
102
103
104
105
106
	a_set &= bdd_ithvar(num);
	return num;
      }

      int
107
      register_next_variable(const formula* f)
108
109
110
111
112
113
114
115
116
117
      {
	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
	  {
118
	    f = f->clone();
119
	    num = dict->register_anonymous_variables(1, this);
120
121
122
123
124
125
126
	    next_map[f] = num;
	    next_formula_map[num] = f;
	  }
	next_set &= bdd_ithvar(num);
	return num;
      }

127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
      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;
      }

142
      formula*
143
144
145
146
      var_to_formula(int var) const
      {
	vf_map::const_iterator isi = next_formula_map.find(var);
	if (isi != next_formula_map.end())
147
	  return isi->second->clone();
148
149
	isi = dict->acc_formula_map.find(var);
	if (isi != dict->acc_formula_map.end())
150
	  return isi->second->clone();
151
152
	isi = dict->var_formula_map.find(var);
	if (isi != dict->var_formula_map.end())
153
	  return isi->second->clone();
154
	assert(0);
155
156
157
	// Never reached, but some GCC versions complain about
	// a missing return otherwise.
	return 0;
158
159
      }

160
      formula*
161
      conj_bdd_to_formula(bdd b, multop::type op = multop::And) const
162
163
      {
	if (b == bddfalse)
164
165
	  return constant::false_instance();
	multop::vec* v = new multop::vec;
166
167
168
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
169
	    formula* res = var_to_formula(var);
170
171
172
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
173
		res = unop::instance(unop::Not, res);
174
175
176
177
		b = bdd_low(b);
	      }
	    else
	      {
178
		assert(bdd_low(b) == bddfalse);
179
180
181
182
183
		b = high;
	      }
	    assert(b != bddfalse);
	    v->push_back(res);
	  }
184
	return multop::instance(op, v);
185
186
      }

187
      formula*
188
      bdd_to_formula(bdd f)
189
      {
190
	if (f == bddfalse)
191
	  return constant::false_instance();
192

193
194
195
196
197
198
199
200
201
	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);
      }
202
203

      void
204
      conj_bdd_to_acc(tgba_explicit_formula* a, bdd b,
Pierre PARUTTO's avatar
Pierre PARUTTO committed
205
		      state_explicit_formula::transition* t)
206
207
208
209
210
211
212
213
      {
	assert(b != bddfalse);
	while (b != bddtrue)
	  {
	    int var = bdd_var(b);
	    bdd high = bdd_high(b);
	    if (high == bddfalse)
	      {
214
		// Simply ignore negated acceptance variables.
215
216
217
218
		b = bdd_low(b);
	      }
	    else
	      {
219
		formula* ac = var_to_formula(var);
220

221
		if (!a->has_acceptance_condition(ac))
222
		  a->declare_acceptance_condition(ac->clone());
223
		a->add_acceptance_condition(t, ac);
224
225
226
227
228
229
230
231
		b = high;
	      }
	    assert(b != bddfalse);
	  }
      }
    };


232
233
234
235
236
237
238
239
240
241
242
    // Debugging function.
    std::ostream&
    trace_ltl_bdd(const translate_dict& d, bdd f)
    {
      minato_isop isop(f);
      bdd cube;
      while ((cube = isop.next()) != bddfalse)
	{
	  bdd label = bdd_exist(cube, d.next_set);
	  bdd dest_bdd = bdd_existcomp(cube, d.next_set);
	  const formula* dest = d.conj_bdd_to_formula(dest_bdd);
243
244
245
246
	  bdd_print_set(std::cerr, d.dict, label) << " => ";
	  bdd_print_set(std::cerr, d.dict, dest_bdd) << " = "
						     << to_string(dest)
						     << std::endl;
247
248
249
250
251
252
	  dest->destroy();
	}
      return std::cerr;
    }


253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295

    // 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_;
    };

296
297
298
299
    // Rewrite rule for rational operators.
    class ratexp_trad_visitor: public const_visitor
    {
    public:
300
301
      ratexp_trad_visitor(translate_dict& dict, formula* to_concat = 0)
	: dict_(dict), to_concat_(to_concat)
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
      {
      }

      virtual
      ~ratexp_trad_visitor()
      {
	if (to_concat_)
	  to_concat_->destroy();
      }

      bdd
      result() const
      {
	return res_;
      }

      bdd next_to_concat()
      {
	if (!to_concat_)
	  to_concat_ = constant::empty_word_instance();
	int x = dict_.register_next_variable(to_concat_);
	return bdd_ithvar(x);
      }

      bdd now_to_concat()
      {
328
329
330
	if (to_concat_ && to_concat_ != constant::empty_word_instance())
	  return recurse(to_concat_);

331
	return bddfalse;
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
      }

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

      void
      visit(const constant* node)
      {
	switch (node->val())
	  {
	  case constant::True:
	    res_ = next_to_concat();
	    return;
	  case constant::False:
	    res_ = bddfalse;
	    return;
	  case constant::EmptyWord:
	    res_ = now_to_concat();
	    return;
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const unop* node)
      {
	switch (node->op())
	  {
	  case unop::F:
	  case unop::G:
	  case unop::X:
	  case unop::Finish:
369
370
	  case unop::Closure:
	  case unop::NegClosure:
371
372
	    assert(!"not a rational operator");
	    return;
373
374
375
376
377
378
379
380
381
382
	  case unop::Not:
	    {
	      // Not can only appear in front of constants or atomic
	      // propositions.
	      const formula* f = node->child();
	      assert(dynamic_cast<const atomic_prop*>(f)
		     || dynamic_cast<const constant*>(f));
	      res_ = !recurse(f) & next_to_concat();
	      return;
	    }
383
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
412
413
414
	  case unop::Star:
	    {
	      formula* f;
	      if (to_concat_)
		f = multop::instance(multop::Concat, node->clone(),
				     to_concat_->clone());
	      else
		f = node->clone();

	      res_ = recurse(node->child(), f) | now_to_concat();
	      return;
	    }
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const binop*)
      {
	assert(!"not a rational operator");
      }

      void
      visit(const automatop*)
      {
	assert(!"not a rational operator");
      }

      void
      visit(const multop* node)
      {
415
416
	multop::type op = node->op();
	switch (op)
417
	  {
418
	  case multop::AndNLM:
419
420
421
	  case multop::And:
	    {
	      unsigned s = node->size();
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
458
459
460
461
462
463
464
465
466
467
468
469
470
471
472
473
474
475
476
477

	      if (op == multop::AndNLM)
		{
		  multop::vec* final = new multop::vec;
		  multop::vec* non_final = new multop::vec;

		  for (unsigned n = 0; n < s; ++n)
		    {
		      const formula* f = node->nth(n);
		      if (constant_term_as_bool(f))
			final->push_back(f->clone());
		      else
			non_final->push_back(f->clone());
		    }

		  if (non_final->empty())
		    {
		      delete non_final;
		      // (a* & b*);c = (a*|b*);c
		      formula* f = multop::instance(multop::Or, final);
		      res_ = recurse_and_concat(f);
		      f->destroy();
		      break;
		    }
		  if (!final->empty())
		    {
		      // let F_i be final formulae
		      //     N_i be non final formula
		      // (F_1 & ... & F_n & N_1 & ... & N_m)
		      // =   (F_1 | ... | F_n);[*] && (N_1 & ... & N_m)
		      //   | (F_1 | ... | F_n) && (N_1 & ... & N_m);[*]
		      formula* f = multop::instance(multop::Or, final);
		      formula* n = multop::instance(multop::AndNLM, non_final);
		      formula* t = unop::instance(unop::Star,
						  constant::true_instance());
		      formula* ft = multop::instance(multop::Concat,
						     f->clone(), t->clone());
		      formula* nt = multop::instance(multop::Concat,
						     n->clone(), t);
		      formula* ftn = multop::instance(multop::And, ft, n);
		      formula* fnt = multop::instance(multop::And, f, nt);
		      formula* all = multop::instance(multop::Or, ftn, fnt);
		      res_ = recurse_and_concat(all);
		      all->destroy();
		      break;
		    }
		  // No final formula.
		  // Apply same rule as &&, until we reach a point where
		  // we have final formulae.
		  delete final;
		  for (unsigned n = 0; n < s; ++n)
		    (*non_final)[n]->destroy();
		  delete non_final;
		}

	      res_ = bddtrue;
478
	      for (unsigned n = 0; n < s; ++n)
479
480
481
482
483
		{
		  bdd res = recurse(node->nth(n));
		  // trace_ltl_bdd(dict_, res);
		  res_ &= res;
		}
484
485
486
487
488
489

	      //std::cerr << "Pre-Concat:" << std::endl;
	      //trace_ltl_bdd(dict_, res_);

	      if (to_concat_)
		{
490
		  // If we have translated (a* && b*) in (a* && b*);c, we
491
492
493
494
495
496
497
498
499
		  // have to append ";c" to all destinations.

		  minato_isop isop(res_);
		  bdd cube;
		  res_ = bddfalse;
		  while ((cube = isop.next()) != bddfalse)
		    {
		      bdd label = bdd_exist(cube, dict_.next_set);
		      bdd dest_bdd = bdd_existcomp(cube, dict_.next_set);
500
501
		      formula* dest =
			dict_.conj_bdd_to_formula(dest_bdd, op);
502
503
504
505
506
507
508
509
510
511
512
513
514
515
516
517
518
519
520
521
522
		      formula* dest2;
		      int x;
		      if (dest == constant::empty_word_instance())
			{
			  res_ |= label & next_to_concat();
			}
		      else
			{
			  dest2 = multop::instance(multop::Concat, dest,
						   to_concat_->clone());
			  if (dest2 != constant::false_instance())
			    {
			      x = dict_.register_next_variable(dest2);
			      dest2->destroy();
			      res_ |= label & bdd_ithvar(x);
			    }
			  if (constant_term_as_bool(node))
			    res_ |= label & next_to_concat();
			}
		    }
		}
523
524
	      if (constant_term_as_bool(node))
		res_ |= now_to_concat();
525
526
527
528
529
530
531

	      break;
	    }
	  case multop::Or:
	    {
	      res_ = bddfalse;
	      unsigned s = node->size();
532
533
	      for (unsigned n = 0; n < s; ++n)
		res_ |= recurse_and_concat(node->nth(n));
534
535
536
537
538
539
540
541
542
543
544
545
546
547
548
	      break;
	    }
	  case multop::Concat:
	    {
	      multop::vec* v = new multop::vec;
	      unsigned s = node->size();
	      v->reserve(s);
	      for (unsigned n = 1; n < s; ++n)
		v->push_back(node->nth(n)->clone());
	      if (to_concat_)
		v->push_back(to_concat_->clone());
	      res_ = recurse(node->nth(0),
			     multop::instance(multop::Concat, v));
	      break;
	    }
549
550
551
552
553
554
555
556
557
558
559
560
561
562
563
564
565
566
567
568
569
570
571
572
573
574
575
576
577
578
579
580
581
582
	  case multop::Fusion:
	    {
	      assert(node->size() >= 2);

	      // the head
	      bdd res = recurse(node->nth(0));

	      // the tail
	      multop::vec* v = new multop::vec;
	      unsigned s = node->size();
	      v->reserve(s - 1);
	      for (unsigned n = 1; n < s; ++n)
		v->push_back(node->nth(n)->clone());
	      formula* tail = multop::instance(multop::Fusion, v);
	      bdd tail_bdd;
	      bool tail_computed = false;

	      //trace_ltl_bdd(dict_, res);

	      minato_isop isop(res);
	      bdd cube;
	      res_ = bddfalse;
	      while ((cube = isop.next()) != bddfalse)
		{
		  bdd label = bdd_exist(cube, dict_.next_set);
		  bdd dest_bdd = bdd_existcomp(cube, dict_.next_set);
		  formula* dest = dict_.conj_bdd_to_formula(dest_bdd);

		  if (constant_term_as_bool(dest))
		    {
		      // The destination is a final state.  Make sure we
		      // can also exit if tail is satisfied.
		      if (!tail_computed)
			{
583
			  tail_bdd = recurse_and_concat(tail);
584
585
586
587
588
589
590
591
592
593
594
595
596
597
598
599
600
601
602
603
604
605
606
607
608
609
610
			  tail_computed = true;
			}
		      res_ |= label & tail_bdd;
		    }

		  if (dynamic_cast<constant*>(dest) == 0)
		    {
		      // If the destination is not a constant, it
		      // means it can have successors.  Fusion the
		      // tail and append anything to concatenate.
		      formula* dest2 = multop::instance(multop::Fusion, dest,
							tail->clone());
		      if (to_concat_)
			 dest2 = multop::instance(multop::Concat, dest2,
						 to_concat_->clone());
		      if (dest2 != constant::false_instance())
			{
			  int x = dict_.register_next_variable(dest2);
			  dest2->destroy();
			  res_ |= label & bdd_ithvar(x);
			}
		    }
		}

	      tail->destroy();
	      break;
	    }
611
612
613
614
615
616
	  }
      }

      bdd
      recurse(const formula* f, formula* to_concat = 0)
      {
617
	ratexp_trad_visitor v(dict_, to_concat);
618
619
620
621
	f->accept(v);
	return v.result();
      }

622
623
624
625
626
      bdd
      recurse_and_concat(const formula* f)
      {
	return recurse(f, to_concat_ ? to_concat_->clone() : 0);
      }
627
628
629
630
631
632
633

    private:
      translate_dict& dict_;
      bdd res_;
      formula* to_concat_;
    };

634

635
    // The rewrite rules used here are adapted from Jean-Michel
636
    // Couvreur's FM paper, augmented to support rational operators.
637
638
639
    class ltl_trad_visitor: public const_visitor
    {
    public:
640
641
642
643
      ltl_trad_visitor(translate_dict& dict, bool mark_all = false,
		       bool exprop = false)
	: dict_(dict), rat_seen_(false), has_marked_(false),
	  mark_all_(mark_all), exprop_(exprop)
644
645
646
647
648
649
650
651
      {
      }

      virtual
      ~ltl_trad_visitor()
      {
      }

652
653
654
655
656
657
658
659
      void
      reset(bool mark_all)
      {
	rat_seen_ = false;
	has_marked_ = false;
	mark_all_ = mark_all;
      }

660
661
      bdd
      result() const
662
663
664
665
      {
	return res_;
      }

666
667
668
669
670
671
672
673
674
675
676
677
678
679
680
681
682
683
      const translate_dict&
      get_dict() const
      {
	return dict_;
      }

      bool
      has_rational() const
      {
	return rat_seen_;
      }

      bool
      has_marked() const
      {
	return has_marked_;
      }

684
685
686
687
688
689
690
691
692
693
694
695
696
697
698
699
700
      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;
701
	  case constant::EmptyWord:
702
703
	    assert(!"Not an LTL operator");
	    return;
704
705
706
707
708
709
710
711
	  }
	/* Unreachable code.  */
	assert(0);
      }

      void
      visit(const unop* node)
      {
712
713
714
	unop::type op = node->op();

	switch (op)
715
716
717
718
	  {
	  case unop::F:
	    {
	      // r(Fy) = r(y) + a(y)r(XFy)
719
720
721
	      const formula* child = node->child();
	      bdd y = recurse(child);
	      int a = dict_.register_a_variable(child);
722
723
	      int x = dict_.register_next_variable(node);
	      res_ = y | (bdd_ithvar(a) & bdd_ithvar(x));
724
	      break;
725
726
727
	    }
	  case unop::G:
	    {
728
729
730
731
732
733
734
735
736
737
738
739
	      // 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)
740
	      const formula* child = node->child();
741
	      int x = dict_.register_next_variable(node);
742
743
	      bdd y = recurse(child);
	      res_ = y & bdd_ithvar(x);
744
	      break;
745
746
747
	    }
	  case unop::Not:
	    {
748
	      // r(!y) = !r(y)
749
	      res_ = bdd_not(recurse(node->child()));
750
	      break;
751
752
753
	    }
	  case unop::X:
	    {
754
	      // r(Xy) = Next[y]
755
756
	      int x = dict_.register_next_variable(node->child());
	      res_ = bdd_ithvar(x);
757
	      break;
758
	    }
759
760
761
	  case unop::Closure:
	    {
	      rat_seen_ = true;
762
763
764
765
766
767
768
	      if (constant_term_as_bool(node->child()))
		{
		  res_ = bddtrue;
		  return;
		}

	      ratexp_trad_visitor v(dict_);
769
770
771
772
	      node->child()->accept(v);
	      bdd f1 = v.result();
	      res_ = bddfalse;

773

774
775
776
777
778
779
780
781
782
783
784
785
786
787
788
789
790
791
792
793
794
795
796
797
798
799
800
801
802
803
804
805
806
807
808
809
810
811
812
813
814
815
816
817
818
819
820
821
822
823
824
825
826
827
828
829
830
831
832
833
834
835
836
837
	      if (exprop_)
		{
		  bdd var_set = bdd_existcomp(bdd_support(f1), dict_.var_set);
		  bdd all_props = bdd_existcomp(f1, dict_.var_set);
		  while (all_props != bddfalse)
		    {
		      bdd label = bdd_satoneset(all_props, var_set, bddtrue);
		      all_props -= label;

		      formula* dest =
			dict_.bdd_to_formula(bdd_exist(f1 & label,
						       dict_.var_set));

		      const formula* dest2;
		      if (constant_term_as_bool(dest))
			{
			  dest->destroy();
			  res_ |= label;
			}
		      else
			{
			  dest2 = unop::instance(op, dest);
			  if (dest2 == constant::false_instance())
			    continue;
			  int x = dict_.register_next_variable(dest2);
			  dest2->destroy();
			  res_ |= label & bdd_ithvar(x);
			}
		    }
		}
	      else
		{
		  minato_isop isop(f1);
		  bdd cube;
		  while ((cube = isop.next()) != bddfalse)
		    {
		      bdd label = bdd_exist(cube, dict_.next_set);
		      bdd dest_bdd = bdd_existcomp(cube, dict_.next_set);
		      formula* dest = dict_.conj_bdd_to_formula(dest_bdd);

		      const formula* dest2;
		      if (constant_term_as_bool(dest))
			{
			  dest->destroy();
			  res_ |= label;
			}
		      else
			{
			  dest2 = unop::instance(op, dest);
			  if (dest2 == constant::false_instance())
			    continue;
			  int x = dict_.register_next_variable(dest2);
			  dest2->destroy();
			  res_ |= label & bdd_ithvar(x);
			}
		    }
		}
	    }
	    break;

	  case unop::NegClosure:
	    {
	      rat_seen_ = true;
	      has_marked_ = true;
838
839
840
841
842
843
844
845

	      if (constant_term_as_bool(node->child()))
		{
		  res_ = bddfalse;
		  return;
		}

	      ratexp_trad_visitor v(dict_);
846
847
848
849
850
851
852
853
854
855
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
876
877
878
879
880
881
882
883
884
885
886
	      node->child()->accept(v);
	      bdd f1 = v.result();

	      // trace_ltl_bdd(dict_, f1);

	      bdd var_set = bdd_existcomp(bdd_support(f1), dict_.var_set);
	      bdd all_props = bdd_existcomp(f1, dict_.var_set);

	      res_ = !all_props &
		// stick X(1) to preserve determinism.
		bdd_ithvar(dict_.register_next_variable
			   (constant::true_instance()));

	      while (all_props != bddfalse)
		{
		  bdd label = bdd_satoneset(all_props, var_set, bddtrue);
		  all_props -= label;

		  formula* dest =
		    dict_.bdd_to_formula(bdd_exist(f1 & label,
						   dict_.var_set));

		  // !{ Exp } is false if Exp accepts the empty word.
		  if (constant_term_as_bool(dest))
		    {
		      dest->destroy();
		      continue;
		    }

		  const formula* dest2 = unop::instance(op, dest);

		  if (dest == constant::false_instance())
		    continue;

		  int x = dict_.register_next_variable(dest2);
		  dest2->destroy();
		  res_ |= label & bdd_ithvar(x);
		}
	    }
	    break;

887
888
	  case unop::Finish:
	    assert(!"unsupported operator");
889
890
891
892
	    break;
	  case unop::Star:
	    assert(!"Not an LTL operator");
	    break;
893
894
895
896
897
898
	  }
      }

      void
      visit(const binop* node)
      {
899
	binop::type op = node->op();
900

901
	switch (op)
902
	  {
903
	    // r(f1 logical-op f2) = r(f1) logical-op r(f2)
904
	  case binop::Xor:
905
906
907
908
909
910
	    {
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
	      res_ = bdd_apply(f1, f2, bddop_xor);
	      return;
	    }
911
	  case binop::Implies:
912
913
914
915
916
917
	    {
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
	      res_ = bdd_apply(f1, f2, bddop_imp);
	      return;
	    }
918
	  case binop::Equiv:
919
920
921
922
923
924
	    {
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
	      res_ = bdd_apply(f1, f2, bddop_biimp);
	      return;
	    }
925
926
	  case binop::U:
	    {
927
928
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
929
930
931
932
	      // 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));
933
	      break;
934
	    }
935
936
	  case binop::W:
	    {
937
938
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
939
940
941
	      // 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));
942
	      break;
943
	    }
944
945
	  case binop::R:
	    {
946
947
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
948
949
950
	      // 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));
951
	      break;
952
	    }
953
954
	  case binop::M:
	    {
955
956
	      bdd f1 = recurse(node->first());
	      bdd f2 = recurse(node->second());
957
958
959
960
	      // 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));
961
	      break;
962
	    }
963
964
965
	  case binop::EConcatMarked:
	    has_marked_ = true;
	    /* fall through */
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
966
	  case binop::EConcat:
967
968
	    rat_seen_ = true;
	    {
969
970
	      // Recognize f2 on transitions going to destinations
	      // that accept the empty word.
971
	      bdd f2 = recurse(node->second());
972
	      ratexp_trad_visitor v(dict_);
973
974
	      node->first()->accept(v);
	      bdd f1 = v.result();
975
	      res_ = bddfalse;
976
977
978
979
980
981
982

	      if (mark_all_)
		{
		  op = binop::EConcatMarked;
		  has_marked_ = true;
		}

983
	      if (exprop_)
984
		{
985
986
987
		  bdd var_set = bdd_existcomp(bdd_support(f1), dict_.var_set);
		  bdd all_props = bdd_existcomp(f1, dict_.var_set);
		  while (all_props != bddfalse)
988
		    {
989
		      bdd label = bdd_satoneset(all_props, var_set, bddtrue);
990
991
992
993
994
995
996
997
998
		      all_props -= label;

		      formula* dest =
			dict_.bdd_to_formula(bdd_exist(f1 & label,
						       dict_.var_set));

		      const formula* dest2 =
			binop::instance(op, dest, node->second()->clone());

999
1000
		      if (dest2 != constant::false_instance())
			{
1001
			  int x = dict_.register_next_variable(dest2);
1002
1003
1004
1005
1006
1007
1008
			  dest2->destroy();
			  res_ |= label & bdd_ithvar(x);
			}
		      if (constant_term_as_bool(dest))
			res_ |= label & f2;
		    }
		}
1009
1010
1011
1012
1013
1014
1015
1016
1017
1018
1019
1020
1021
1022
1023
1024
1025
1026
1027
1028
1029
1030
1031
1032
1033
1034
1035
1036
1037
	      else
		{
		  minato_isop isop(f1);
		  bdd cube;
		  while ((cube = isop.next()) != bddfalse)
		    {
		      bdd label = bdd_exist(cube, dict_.next_set);
		      bdd dest_bdd = bdd_existcomp(cube, dict_.next_set);
		      formula* dest = dict_.conj_bdd_to_formula(dest_bdd);

		      if (dest == constant::empty_word_instance())
			{
			  res_ |= label & f2;
			}
		      else
			{
			  formula* dest2 = binop::instance(op, dest,
						  node->second()->clone());
			  if (dest2 != constant::false_instance())
			    {
			      int x = dict_.register_next_variable(dest2);
			      dest2->destroy();
			      res_ |= label & bdd_ithvar(x);
			    }
			  if (constant_term_as_bool(dest))
			    res_ |= label & f2;
			}
		    }
		}
1038
1039
1040
1041
1042
	    }
	    break;

	  case binop::UConcat:
	    {
1043
1044
1045
	      // Transitions going to destinations accepting the empty
	      // word should recognize f2, and the automaton for f1
	      // should be understood as universal.
1046
	      bdd f2 = recurse(node->second());
1047
	      ratexp_trad_visitor v(dict_);
1048
1049
1050
	      node->first()->accept(v);
	      bdd f1 = v.result();
	      res_ = bddtrue;
1051
1052

	      if (exprop_)
1053
		{
1054
1055
1056
1057
1058
1059
		  bdd var_set = bdd_existcomp(bdd_support(f1), dict_.var_set);
		  bdd all_props = bdd_existcomp(f1, dict_.var_set);
		  while (all_props != bddfalse)
		    {
		      bdd label = bdd_satoneset(all_props, var_set, bddtrue);
		      all_props -= label;
1060

1061
1062
1063
		      formula* dest =
			dict_.bdd_to_formula(bdd_exist(f1 & label,
						       dict_.var_set));
1064

1065
1066
1067
1068
		      formula* dest2 = binop::instance(op, dest,
						       node->second()->clone());
		      bdd udest =
			bdd_ithvar(dict_.register_next_variable(dest2));
1069

1070
1071
		      if (constant_term_as_bool(dest))
			udest &= f2;
1072

1073
1074
1075
1076
1077
1078
1079
1080
1081
1082
1083
1084
1085
1086
1087
1088
1089
1090
1091
1092
1093
1094
1095
1096
1097
1098
1099
1100
1101
1102
		      dest2->destroy();
		      label = bdd_apply(label, udest, bddop_imp);

		      res_ &= label;
		    }
		}
	      else
		{
		  minato_isop isop(f1);
		  bdd cube;
		  while ((cube = isop.next()) != bddfalse)
		    {
		      bdd label = bdd_exist(cube, dict_.next_set);
		      bdd dest_bdd = bdd_existcomp(cube, dict_.next_set);
		      formula* dest = dict_.conj_bdd_to_formula(dest_bdd);
		      formula* dest2;
		      bdd udest;

		      dest2 = binop::instance(op, dest,
					      node->second()->clone());
		      udest = bdd_ithvar(dict_.register_next_variable(dest2));

		      if (constant_term_as_bool(dest))
			udest &= f2;

		      dest2->destroy();
		      label = bdd_apply(label, udest, bddop_imp);

		      res_ &= label;
		    }
1103
1104
		}
	    }
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
1105
	    break;
1106
1107
1108
	  }
      }

1109
1110
1111
1112
1113
1114
      void
      visit(const automatop*)
      {
	assert(!"unsupported operator");
      }

1115
1116
1117
1118
1119
1120
      void
      visit(const multop* node)
      {
	switch (node->op())
	  {
	  case multop::And:
1121
1122
1123
1124
1125
1126
	    {
	      res_ = bddtrue;
	      unsigned s = node->size();
	      for (unsigned n = 0; n < s; ++n)
		{
		  bdd res = recurse(node->nth(n));
1127
1128
1129
		  //std::cerr << "== in And (" << to_string(node->nth(n))
		  // << ")" << std::endl;
		  // trace_ltl_bdd(dict_, res);
1130
1131
		  res_ &= res;
		}
1132
1133
	      //std::cerr << "=== And final" << std::endl;
	      // trace_ltl_bdd(dict_, res_);
1134
1135
	      break;
	    }
1136
	  case multop::Or:
1137
1138
1139
1140
1141
1142
1143
	    {
	      res_ = bddfalse;
	      unsigned s = node->size();
	      for (unsigned n = 0; n < s; ++n)
		res_ |= recurse(node->nth(n));
	      break;
	    }
1144
	  case multop::Concat:
1145
	  case multop::Fusion:
1146
	  case multop::AndNLM:
1147
1148
	    assert(!"Not an LTL operator");
	    break;
1149
	  }
1150

1151
1152
1153
1154
1155
      }

      bdd
      recurse(const formula* f)
      {
1156
	ltl_trad_visitor v(dict_, mark_all_, exprop_);
1157
	f->accept(v);
1158
1159
	rat_seen_ |= v.has_rational();
	has_marked_ |= v.has_marked();
1160
1161
1162
1163
1164
1165
1166
	return v.result();
      }


    private:
      translate_dict& dict_;
      bdd res_;
1167
1168
1169
      bool rat_seen_;
      bool has_marked_;
      bool mark_all_;
1170
      bool exprop_;
1171
1172
    };

1173

1174
1175
    // Check whether a formula has a R, W, or G operator at its
    // top-level (preceding logical operators do not count).
1176
1177
1178
1179
1180
1181
1182
1183
1184
1185
1186
1187
1188
1189
1190
1191
1192
1193
1194
1195
1196
1197
1198
1199
1200
1201
1202
1203
1204
1205
1206
1207
1208
1209
1210
1211
1212
1213
1214
1215
1216
1217
1218
1219
1220
1221
1222
1223
1224
1225
    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:
1226
	  case binop::M:
1227
1228
	    return;
	  case binop::R:
1229
	  case binop::W:
1230
1231
	    res_ = true;
	    return;
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
1232
1233
	  case binop::UConcat:
	  case binop::EConcat:
1234
	  case binop::EConcatMarked:
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
1235
	    node->second()->accept(*this);
1236
	    // FIXME: we might need to add Acc[1]
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
1237
	    return;
1238
1239
1240
1241
1242
	  }
	/* Unreachable code.  */
	assert(0);
      }

1243
1244
1245
1246
1247
1248
      void
      visit(const automatop*)
      {
	assert(!"unsupported operator");
      }

1249
1250
1251
1252
1253
1254
1255
1256
1257
1258
1259
1260
1261
1262
1263
1264
1265
1266
1267
1268
1269
1270
      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)
      {
1271
1272
	pfl_map::const_iterator i = pfl_.find(f);
	if (i != pfl_.end())
1273
1274
1275
1276
	  return i->second;
	ltl_possible_fair_loop_visitor v;
	f->accept(v);
	bool rel = v.result();
1277
	pfl_[f] = rel;
1278
1279
1280
1281
	return rel;
      }

    private:
1282
      typedef Sgi::hash_map<const formula*, bool, formula_ptr_hash> pfl_map;
1283
      pfl_map pfl_;
1284
1285
    };

1286
1287
1288
    class formula_canonizer
    {
    public:
1289
      formula_canonizer(translate_dict& d,
1290
1291
			bool fair_loop_approx, bdd all_promises, bool exprop)
	: v_(d, false, exprop),
1292
	  fair_loop_approx_(fair_loop_approx),
1293
1294
	  all_promises_(all_promises),
	  d_(d)
1295
1296
1297
1298
1299
      {
	// For cosmetics, register 1 initially, so the algorithm will
	// not register an equivalent formula first.
	b2f_[bddtrue] = constant::true_instance();
      }
1300

1301
1302
      ~formula_canonizer()
      {
1303
	while (!f2b_.empty())
1304
	  {
1305
1306
1307
	    formula_to_bdd_map::iterator i = f2b_.begin();
	    const formula* f = i->first;
	    f2b_.erase(i);
1308
	    f->destroy();
1309
	  }
1310
1311
      }

1312
1313
1314
1315
1316
1317
1318
1319
      struct translated
      {
	bdd symbolic;
	bool has_rational:1;
	bool has_marked:1;
      };

      const translated&
1320
      translate(const formula* f, bool* new_flag = 0)
1321
1322
1323
1324
1325
1326
      {
	// Use the cached result if available.
	formula_to_bdd_map::const_iterator i = f2b_.find(f);
	if (i != f2b_.end())
	  return i->second;

1327
1328
1329
	if (new_flag)
	  *new_flag = true;

1330
	// Perform the actual translation.
1331
	v_.reset(!has_mark(f));
1332
	f->accept(v_);
1333
1334
1335
1336
1337
1338
1339
1340
1341
1342
1343
1344
1345
1346
1347
1348
1349
1350
1351
1352
1353
1354
1355
1356
1357
1358
1359
1360
1361
1362
1363
1364
1365
1366
1367
1368
1369
1370
1371
1372
1373
1374
1375
1376
1377
1378
1379
1380
1381
1382
1383
1384
1385
1386
	translated t;
	t.symbolic = v_.result();
	t.has_rational = v_.has_rational();
	t.has_marked = v_.has_marked();

//	std::cerr << "-----" << std::endl;
//	std::cerr << "Formula: " << to_string(f) << std::endl;
//	std::cerr << "Rational: " << t.has_rational << std::endl;
//	std::cerr << "Marked: " << t.has_marked << std::endl;
//	std::cerr << "Mark all: " << !has_mark(f) << std::endl;
//	std::cerr << "Transitions:" << std::endl;
//	trace_ltl_bdd(v_.get_dict(), t.symbolic);

	if (t.has_rational)
	  {
	    bdd res = bddfalse;

	    minato_isop isop(t.symbolic);
	    bdd cube;
	    while ((cube = isop.next()) != bddfalse)
	      {
		bdd label = bdd_exist(cube, d_.next_set);
		bdd dest_bdd = bdd_existcomp(cube, d_.next_set);
		formula* dest =
		  d_.conj_bdd_to_formula(dest_bdd);

		// Handle a Miyano-Hayashi style unrolling for
		// rational operators.  Marked nodes correspond to
		// subformulae in the Miyano-Hayashi set.
		if (simplify_mark(dest))
		  {
		    // Make the promise that we will exit marked sets.
		    int a =
		      d_.register_a_variable(constant::true_instance());
		    label &= bdd_ithvar(a);
		  }
		else
		  {
		    // We have left marked operators, but still
		    // have other rational operator to check.
		    // Start a new marked cycle.
		    formula* dest2 = mark_concat_ops(dest);
		    dest->destroy();
		    dest = dest2;
		  }
		// Note that simplify_mark may have changed dest.
		dest_bdd = bdd_ithvar(d_.register_next_variable(dest));
		dest->destroy();
		res |= label & dest_bdd;
	      }
	    t.symbolic = res;
//	    std::cerr << "Marking rewriting:" << std::endl;
//	    trace_ltl_bdd(v_.get_dict(), t.symbolic);
	  }
1387
1388
1389
1390
1391
1392
1393
1394
1395

	// 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))
1396
	      t.symbolic &= all_promises_;
1397
1398
	  }

1399
	// Register the reverse mapping if it is not already done.
1400
1401
1402
1403
	if (b2f_.find(t.symbolic) == b2f_.end())
	  b2f_[t.symbolic] = f;

	return f2b_[f->clone()] = t;
1404
1405
1406
1407
1408
      }

      const formula*
      canonize(const formula* f)
      {
1409
	bool new_variable = false;
1410
	bdd b = translate(f, &new_variable).symbolic;
1411
1412

	bdd_to_formula_map::iterator i = b2f_.find(b);
1413
1414
	// Since we have just translated the formula, it is
	// necessarily in b2f_.
1415
1416
1417
	assert(i != b2f_.end());

	if (i->second != f)
1418
	  {
1419
	    // The translated bdd maps to an already seen formula.
1420
	    f->destroy();
1421
	    f = i->second->clone();
1422
	  }
1423
	return f;
1424
1425
      }

1426
1427
1428
1429
1430
1431
1432
1433
1434
1435
1436
    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.
1437
      typedef std::map<const formula*, translated> formula_to_bdd_map;
1438
      formula_to_bdd_map f2b_;
1439
1440
1441
1442

      possible_fair_loop_checker pflc_;
      bool fair_loop_approx_;
      bdd all_promises_;
1443
      translate_dict& d_;
1444
1445
1446
1447
1448
    };

  }

  typedef std::map<bdd, bdd, bdd_less_than> prom_map;
1449
  typedef Sgi::hash_map<const formula*, prom_map, formula_ptr_hash> dest_map;
1450
1451
1452
1453

  static void
  fill_dests(translate_dict& d, dest_map& dests, bdd label, const formula* dest)
  {
1454
    bdd conds = bdd_existcomp(label, d.var_set);
1455
1456
    bdd promises = bdd_existcomp(label, d.a_set);

1457
1458
1459
1460
1461
1462
1463
1464
    dest_map::iterator i = dests.find(dest);
    if (i == dests.end())
      {
	dests[dest][promises] = conds;
      }
    else
      {
	i->second[promises] |= conds;
1465
	dest->destroy();
1466
1467
1468
1469
      }
  }


Pierre PARUTTO's avatar
Pierre PARUTTO committed
1470
  tgba_explicit_formula*
1471
  ltl_to_tgba_fm(const formula* f, bdd_dict* dict,
1472
		 bool exprop, bool symb_merge, bool branching_postponement,
1473
		 bool fair_loop_approx, const atomic_prop_set* unobs,
1474
		 int reduce_ltl)
1475
1476
1477
1478
1479
  {
    // 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.
1480
1481
    formula* f1 = unabbreviate_logic(f);
    formula* f2 = negative_normal_form(f1);
1482
    f1->destroy();
1483

1484
1485
1486
1487
    // Simplify the formula, if requested.
    if (reduce_ltl)
      {
	formula* tmp = reduce(f2, reduce_ltl);
1488
	f2->destroy();