dtgbasat.cc 25.7 KB
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// -*- coding: utf-8 -*-
// Copyright (C) 2013 Laboratoire de Recherche et Développement
// de l'Epita.
//
// 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 3 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 this program.  If not, see <http://www.gnu.org/licenses/>.

#include <iostream>
#include <fstream>
#include <sstream>
#include "dtgbasat.hh"
#include "reachiter.hh"
#include <map>
#include <utility>
#include "scc.hh"
#include "tgba/bddprint.hh"
#include "ltlast/constant.hh"
#include "stats.hh"
#include "ltlenv/defaultenv.hh"
#include "misc/tmpfile.hh"
Alexandre Duret-Lutz's avatar
Alexandre Duret-Lutz committed
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#include "misc/satsolver.hh"
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// If the following DEBUG macro is set to 1, the temporary files used
// to communicate with the SAT-solver will be left in the current
// directory.  (The files dtgba-sat.cnf and dtgba-sat.out contain the
// input and output for the last successful minimization attempted, or
// for the only failed attempt if the minimization failed.)
//
// Additionally, the CNF file will be output with a comment before
// each clause, and an additional output file (dtgba-sat.dbg) will be
// created with a list of all positive variables in the result and
// their meaning.
//
// Note that the code use unique temporary filenames, so it is safe to
// run several such minimizations in parallel.  It only when DEBUG=1
// that some of these files will be renamed to the above hard-coded
// names, possibly causing confusion if multiple minimizations are
// debugged in parallel and in the same directory.

#define DEBUG 0
#if DEBUG
#define dout out << "c "
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#define trace std::cerr
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#else
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#define dout while (0) std::cout
#define trace dout
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#endif

namespace spot
{
  namespace
  {
    static bdd_dict* debug_dict = 0;

    struct transition
    {
      int src;
      bdd cond;
      int dst;

      transition(int src, bdd cond, int dst)
	: src(src), cond(cond), dst(dst)
      {
      }

      bool operator<(const transition& other) const
      {
	if (this->src < other.src)
	  return true;
	if (this->src > other.src)
	  return false;
	if (this->dst < other.dst)
	  return true;
	if (this->dst > other.dst)
	  return false;
	return this->cond.id() < other.cond.id();
      }

      bool operator==(const transition& other) const
      {
	return (this->src == other.src
		&& this->dst == other.dst
		&& this->cond.id() == other.cond.id());
      }
    };

    struct transition_acc
    {
      int src;
      bdd cond;
      bdd acc;
      int dst;

      transition_acc(int src, bdd cond, bdd acc, int dst)
	: src(src), cond(cond), acc(acc), dst(dst)
      {
      }

      bool operator<(const transition_acc& other) const
      {
	if (this->src < other.src)
	  return true;
	if (this->src > other.src)
	  return false;
	if (this->dst < other.dst)
	  return true;
	if (this->dst > other.dst)
	  return false;
	if (this->cond.id() < other.cond.id())
	  return true;
	if (this->cond.id() > other.cond.id())
	  return false;
	return this->acc.id() < other.acc.id();
      }

      bool operator==(const transition_acc& other) const
      {
	return (this->src == other.src
		&& this->dst == other.dst
		&& this->cond.id() == other.cond.id()
		&& this->acc.id() == other.acc.id());
      }
    };

    struct state_pair
    {
      int a;
      int b;

      state_pair(int a, int b)
	: a(a), b(b)
      {
      }

      bool operator<(const state_pair& other) const
      {
	if (this->a < other.a)
	  return true;
	if (this->a > other.a)
	  return false;
	if (this->b < other.b)
	  return true;
	if (this->b > other.b)
	  return false;
	return false;
      }
    };

    struct path
    {
      int src_cand;
      int src_ref;
      int dst_cand;
      int dst_ref;
      bdd acc_cand;
      bdd acc_ref;

      path(int src_cand, int src_ref,
	   int dst_cand, int dst_ref,
	   bdd acc_cand, bdd acc_ref)
	: src_cand(src_cand), src_ref(src_ref),
	  dst_cand(dst_cand), dst_ref(dst_ref),
	  acc_cand(acc_cand), acc_ref(acc_ref)
      {
      }

      bool operator<(const path& other) const
      {
	if (this->src_cand < other.src_cand)
	  return true;
	if (this->src_cand > other.src_cand)
	  return false;
	if (this->src_ref < other.src_ref)
	  return true;
	if (this->src_ref > other.src_ref)
	  return false;
	if (this->dst_cand < other.dst_cand)
	  return true;
	if (this->dst_cand > other.dst_cand)
	  return false;
	if (this->dst_ref < other.dst_ref)
	  return true;
	if (this->dst_ref > other.dst_ref)
	  return false;
	if (this->acc_ref.id() < other.acc_ref.id())
	  return true;
	if (this->acc_ref.id() > other.acc_ref.id())
	  return false;
	if (this->acc_cand.id() < other.acc_cand.id())
	  return true;
	if (this->acc_cand.id() > other.acc_cand.id())
	  return false;

	return false;
      }

    };

    std::ostream& operator<<(std::ostream& os, const state_pair& p)
    {
      os << "<" << p.a << "," << p.b << ">";
      return os;
    }

    std::ostream& operator<<(std::ostream& os, const transition& t)
    {
      os << "<" << t.src << ","
	 << bdd_format_formula(debug_dict, t.cond)
	 << "," << t.dst << ">";
      return os;
    }


    std::ostream& operator<<(std::ostream& os, const transition_acc& t)
    {
      os << "<" << t.src << ","
	 << bdd_format_formula(debug_dict, t.cond) << ","
	 << bdd_format_accset(debug_dict, t.acc)
	 << "," << t.dst << ">";
      return os;
    }

    std::ostream& operator<<(std::ostream& os, const path& p)
    {
      os << "<"
	 << p.src_cand << ","
	 << p.src_ref << ","
	 << p.dst_cand << ","
	 << p.dst_ref << ", "
	 << bdd_format_accset(debug_dict, p.acc_cand) << ", "
	 << bdd_format_accset(debug_dict, p.acc_ref) << ">";
      return os;
    }

    struct dict
    {
      dict(const tgba* a)
	: aut(a)
      {
      }

      const tgba* aut;
      typedef std::map<transition, int> trans_map;
      typedef std::map<transition_acc, int> trans_acc_map;
      trans_map transid;
      trans_acc_map transaccid;
      typedef std::map<int, transition> rev_map;
      typedef std::map<int, transition_acc> rev_acc_map;
      rev_map revtransid;
      rev_acc_map revtransaccid;

      std::map<state_pair, int> prodid;
      std::map<path, int> pathid;
      int nvars;
      typedef Sgi::hash_map<const state*, int,
			    state_ptr_hash, state_ptr_equal> state_map;
      typedef Sgi::hash_map<int, const state*> int_map;
      state_map state_to_int;
      int_map int_to_state;
      int cand_size;
      unsigned int cand_nacc;
      std::vector<bdd> cand_acc; // size cand_nacc

      std::vector<bdd> all_cand_acc;
      std::vector<bdd> all_ref_acc;

      bdd cand_all_acc;
      bdd ref_all_acc;

      ~dict()
      {
	state_map::const_iterator s = state_to_int.begin();
	while (s != state_to_int.end())
	  // Always advance the iterator before deleting the key.
	  s++->first->destroy();

	aut->get_dict()->unregister_all_my_variables(this);
      }
    };


    class filler_dfs: public tgba_reachable_iterator_depth_first
    {
    protected:
      dict& d;
      int size_;
      bdd ap_;
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      bool state_based_;
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      scc_map& sm_;
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    public:
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      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based,
		 scc_map& sm)
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	: tgba_reachable_iterator_depth_first(aut), d(d), ap_(ap),
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	  state_based_(state_based), sm_(sm)
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      {
	d.nvars = 0;

	bdd_dict* bd = aut->get_dict();
	ltl::default_environment& env = ltl::default_environment::instance();

	d.cand_acc.resize(d.cand_nacc);
	d.all_cand_acc.push_back(bddfalse);

	bdd allneg = bddtrue;
	for (unsigned n = 0; n < d.cand_nacc; ++n)
	  {
	    std::ostringstream s;
	    s << n;
	    const ltl::formula* af = env.require(s.str());
	    int v = bd->register_acceptance_variable(af, &d);
	    af->destroy();
	    d.cand_acc[n] = bdd_ithvar(v);
	    allneg &= bdd_nithvar(v);
	  }
	for (unsigned n = 0; n < d.cand_nacc; ++n)
	  {
	    bdd c = bdd_exist(allneg, d.cand_acc[n]) & d.cand_acc[n];
	    d.cand_acc[n] = c;

	    size_t s = d.all_cand_acc.size();
	    for (size_t i = 0; i < s; ++i)
	      d.all_cand_acc.push_back(d.all_cand_acc[i] | c);
	  }
	d.cand_all_acc = bdd_support(allneg);
	d.ref_all_acc = bdd_support(aut->all_acceptance_conditions());

	bdd refall = d.ref_all_acc;
	bdd refnegall = aut->neg_acceptance_conditions();

	d.all_ref_acc.push_back(bddfalse);
	while (refall != bddtrue)
	  {
	    bdd v = bdd_ithvar(bdd_var(refall));
	    bdd c = bdd_exist(refnegall, v) & v;

	    size_t s = d.all_ref_acc.size();
	    for (size_t i = 0; i < s; ++i)
	      d.all_ref_acc.push_back(d.all_ref_acc[i] | c);

	    refall = bdd_high(refall);
	  }
      }

      int size()
      {
	return size_;
      }

      void end()
      {
	size_ = seen.size();

	if (d.cand_size == -1)
	  d.cand_size = size_ - 1;

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	for (dict::state_map::const_iterator i2 = seen.begin();
	     i2 != seen.end(); ++i2)
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	  {
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	    int i = i2->second;
	    d.int_to_state[i] = i2->first;
	    unsigned i_scc = sm_.scc_of_state(i2->first);
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	    for (int j = 1; j <= d.cand_size; ++j)
	      {
		d.prodid[state_pair(j, i)] = ++d.nvars;

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		for (dict::state_map::const_iterator k2 = seen.begin();
		     k2 != seen.end(); ++k2)
		  {
		    int k = k2->second;
		    if (sm_.scc_of_state(k2->first) != i_scc)
		      continue;
		    for (int l = 1; l <= d.cand_size; ++l)
		      {
			size_t sf = d.all_cand_acc.size();
			for (size_t f = 0; f < sf; ++f)
			  {
			    size_t sfp = d.all_ref_acc.size();
			    for (size_t fp = 0; fp < sfp; ++fp)
			      {
				path p(j, i, l, k,
				       d.all_cand_acc[f],
				       d.all_ref_acc[fp]);
				d.pathid[p] = ++d.nvars;
			      }

			  }
		      }
		  }
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	      }
	  }

	std::swap(d.state_to_int, seen);

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	if (!state_based_)
	  {
	    for (int i = 1; i <= d.cand_size; ++i)
	      for (int j = 1; j <= d.cand_size; ++j)
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		{
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		  bdd all = bddtrue;
		  while (all != bddfalse)
		    {
		      bdd one = bdd_satoneset(all, ap_, bddfalse);
		      all -= one;

		      transition t(i, one, j);
		      d.transid[t] = ++d.nvars;
		      d.revtransid.insert(dict::rev_map::
					  value_type(d.nvars, t));

		      // Create the variable for the accepting transition
		      // immediately afterwards.  It helps parsing the
		      // result.
		      for (unsigned n = 0; n < d.cand_nacc; ++n)
			{
			  transition_acc ta(i, one, d.cand_acc[n], j);
			  d.transaccid[ta] = ++d.nvars;
			  d.revtransaccid.insert(dict::rev_acc_map::
						 value_type(d.nvars, ta));
			}
		    }
		}
	  }
	else // state based
	  {
	    for (int i = 1; i <= d.cand_size; ++i)
	      for (unsigned n = 0; n < d.cand_nacc; ++n)
		{
		  ++d.nvars;
		  for (int j = 1; j <= d.cand_size; ++j)
		    {
		      bdd all = bddtrue;
		      while (all != bddfalse)
			{
			  bdd one = bdd_satoneset(all, ap_, bddfalse);
			  all -= one;
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			  transition_acc ta(i, one, d.cand_acc[n], j);
			  d.transaccid[ta] = d.nvars;
			  d.revtransaccid.insert(dict::rev_acc_map::
						 value_type(d.nvars, ta));
			}
		    }
		}
	    for (int i = 1; i <= d.cand_size; ++i)
	      for (int j = 1; j <= d.cand_size; ++j)
		{
		  bdd all = bddtrue;
		  while (all != bddfalse)
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		    {
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		      bdd one = bdd_satoneset(all, ap_, bddfalse);
		      all -= one;

		      transition t(i, one, j);
		      d.transid[t] = ++d.nvars;
		      d.revtransid.insert(dict::rev_map::
					  value_type(d.nvars, t));
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		    }
		}
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	  }
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      }
    };

    static
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    void dtgba_to_sat(std::ostream& out, const tgba* ref, dict& d,
		      bool state_based)
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    {
      int nclauses = 0;
      int ref_size = 0;

      scc_map sm(ref);
      sm.build_map();
      bdd ap = sm.aprec_set_of(sm.initial());

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      // Count the number of atomic propositions
      int nap = 0;
      {
	bdd cur = ap;
	while (cur != bddtrue)
	  {
	    ++nap;
	    cur = bdd_high(cur);
	  }
	nap = 1 << nap;
      }
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      // Number all the SAT variable we may need.
      {
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	filler_dfs f(ref, d, ap, state_based, sm);
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	f.run();
	ref_size = f.size();
      }

      // empty automaton is impossible
      if (d.cand_size == 0)
	{
	  out << "p cnf 1 2\n-1 0\n1 0\n";
	  return;
	}

      // An empty line for the header
      out << "                                                 \n";

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#if DEBUG
      debug_dict = ref->get_dict();
      dout << "ref_size: " << ref_size << "\n";
      dout << "cand_size: " << d.cand_size << "\n";
#endif

      dout << "symmetry-breaking clauses\n";
      int j = 0;
      bdd all = bddtrue;
      while (all != bddfalse)
 	{
 	  bdd s = bdd_satoneset(all, ap, bddfalse);
 	  all -= s;
 	  for (int i = 1; i < d.cand_size; ++i)
 	    for (int k = (i - 1) * nap + j + 3; k <= d.cand_size; ++k)
	      {
		transition t(i, s, k);
		int ti = d.transid[t];
		dout << "¬" << t << "\n";
		out << -ti << " 0\n";
		++nclauses;
	      }
 	  ++j;
 	}
      if (!nclauses)
 	dout << "(none)\n";

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      dout << "(8) the candidate automaton is complete\n";
      for (int q1 = 1; q1 <= d.cand_size; ++q1)
	{
	  bdd all = bddtrue;
	  while (all != bddfalse)
	    {
	      bdd s = bdd_satoneset(all, ap, bddfalse);
	      all -= s;

#if DEBUG
	      dout;
	      for (int q2 = 1; q2 <= d.cand_size; q2++)
		{
		  transition t(q1, s, q2);
		  out << t << "δ";
		  if (q2 != d.cand_size)
		    out << " ∨ ";
		}
	      out << "\n";
#endif

	      for (int q2 = 1; q2 <= d.cand_size; q2++)
		{
		  transition t(q1, s, q2);
		  int ti = d.transid[t];

		  out << ti << " ";
		}
	      out << "0\n";
	      ++nclauses;
	    }
	}

      dout << "(9) the initial state is reachable\n";
      dout << state_pair(1, 1) << "\n";
      out << d.prodid[state_pair(1, 1)] << " 0\n";
      ++nclauses;

      for (std::map<state_pair, int>::const_iterator pit = d.prodid.begin();
	   pit != d.prodid.end(); ++pit)
	{
	  int q1 = pit->first.a;
	  int q1p = pit->first.b;

	  dout << "(9) states Cand[" << q1 << "] and Ref[" << q1p
	       << "] are 0-length paths\n";
	  path p(q1, q1p, q1, q1p, bddfalse, bddfalse);
	  dout << pit->first << " → " << p << "\n";
	  out << -pit->second << " " << d.pathid[p] <<" 0\n";
	  ++nclauses;

	  dout << "(10) augmenting paths based on Cand[" << q1
	       << "] and Ref[" << q1p << "]\n";
	  tgba_succ_iterator* it = ref->succ_iter(d.int_to_state[q1p]);
	  for (it->first(); !it->done(); it->next())
	    {
	      const state* dps = it->current_state();
	      int dp = d.state_to_int[dps];
	      dps->destroy();

	      bdd all = it->current_condition();
	      while (all != bddfalse)
		{
		  bdd s = bdd_satoneset(all, ap, bddfalse);
		  all -= s;

		  for (int q2 = 1; q2 <= d.cand_size; q2++)
		    {
		      transition t(q1, s, q2);
		      int ti = d.transid[t];

		      state_pair p2(q2, dp);
		      int succ = d.prodid[p2];

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617
618
		      if (pit->second == succ)
			continue;

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631
		      dout << pit->first << " ∧ " << t << "δ → " << p2 << "\n";
		      out << -pit->second << " " << -ti << " "
			  << succ << " 0\n";
		      ++nclauses;
		    }
		}
	    }
	  delete it;
	}

      bdd all_acc = ref->all_acceptance_conditions();

      // construction of constraints (11,12,13)
632
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      for (int q1p = 1; q1p <= ref_size; ++q1p)
	{
	  unsigned q1p_scc = sm.scc_of_state(d.int_to_state[q1p]);
	  for (int q2p = 1; q2p <= ref_size; ++q2p)
	    {
	      // We are only interested in transition that can form a
	      // cycle, so they must belong to the same SCC.
	      if (sm.scc_of_state(d.int_to_state[q2p]) != q1p_scc)
		continue;
	      for (int q1 = 1; q1 <= d.cand_size; ++q1)
		for (int q2 = 1; q2 <= d.cand_size; ++q2)
		  {
		    size_t sf = d.all_cand_acc.size();
		    size_t sfp = d.all_ref_acc.size();
		    for (size_t f = 0; f < sf; ++f)
		      for (size_t fp = 0; fp < sfp; ++fp)
			{
			  path p(q1, q1p, q2, q2p,
				 d.all_cand_acc[f], d.all_ref_acc[fp]);
651

652
			  dout << "(11&12&13) paths from " << p << "\n";
653

654
			  int pid = d.pathid[p];
655

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657
			  tgba_succ_iterator* it =
			    ref->succ_iter(d.int_to_state[q2p]);
658

659
			  for (it->first(); !it->done(); it->next())
660
			    {
661
662
663
			      const state* dps = it->current_state();
			      // Skip destinations not in the SCC.
			      if (sm.scc_of_state(dps) != q1p_scc)
664
				{
665
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669
				  dps->destroy();
				  continue;
				}
			      int dp = d.state_to_int[dps];
			      dps->destroy();
670

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675
			      for (int q3 = 1; q3 <= d.cand_size; ++q3)
				{
				  bdd all = it->current_condition();
				  bdd curacc =
				    it->current_acceptance_conditions();
676

677
				  while (all != bddfalse)
678
				    {
679
680
				      bdd l = bdd_satoneset(all, ap, bddfalse);
				      all -= l;
681

682
683
				      transition t(q2, l, q3);
				      int ti = d.transid[t];
684

685
				      if (dp == q1p && q3 == q1) // (11,12) loop
686
					{
687
688
					  bdd unio = curacc | d.all_ref_acc[fp];
					  if (unio != all_acc)
689
					    {
690
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709
710
#if DEBUG
					      dout << "(11) " << p << " ∧ "
						   << t << "δ → ¬(";

					      bdd all_ = d.all_cand_acc.back();
					      all_ -= d.all_cand_acc[f];
					      bool notfirst = false;
					      while (all_ != bddfalse)
						{
						  bdd one = bdd_satone(all_);
						  all_ -= one;

						  transition_acc ta(q2, l,
								    one, q1);
						  if (notfirst)
						    out << " ∧ ";
						  else
						    notfirst = true;
						  out << ta << "FC";
						}
					      out << ")\n";
711
#endif // DEBUG
712
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727
728
					      out << -pid << " " << -ti;

					      // 11
					      bdd all_f = d.all_cand_acc.back();
					      all_f -= d.all_cand_acc[f];
					      while (all_f != bddfalse)
						{
						  bdd one = bdd_satone(all_f);
						  all_f -= one;

						  transition_acc ta(q2, l,
								    one, q1);
						  int tai = d.transaccid[ta];
						  assert(tai != 0);
						  out << " " << -tai;
						}
					      out << " 0\n";
729
730
					      ++nclauses;
					    }
731
732
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771
772
					  else
					    {
#if DEBUG
					      dout << "(12) " << p << " ∧ "
						   << t << "δ → (";

					      bdd all_ = d.all_cand_acc.back();
					      all_ -= d.all_cand_acc[f];
					      bool notfirst = false;
					      while (all_ != bddfalse)
						{
						  bdd one = bdd_satone(all_);
						  all_ -= one;

						  transition_acc ta(q2, l,
								    one, q1);
						  if (notfirst)
						    out << " ∧ ";
						  else
						    notfirst = true;
						  out << ta << "FC";
						}
					      out << ")\n";
#endif // DEBUG
					      // 12
					      bdd all_f = d.all_cand_acc.back();
					      all_f -= d.all_cand_acc[f];
					      while (all_f != bddfalse)
						{
						  bdd one = bdd_satone(all_f);
						  all_f -= one;

						  transition_acc ta(q2, l,
								    one, q1);
						  int tai = d.transaccid[ta];
						  assert(tai != 0);

						  out << -pid << " " << -ti
						      << " " << tai << " 0\n";
						  ++nclauses;
						}
					    }
773
					}
774
				      // (13) augmenting paths (always).
775
				      {
776
777
					size_t sf = d.all_cand_acc.size();
					for (size_t f = 0; f < sf; ++f)
778
779
					  {

780
781
782
					    bdd f2 = p.acc_cand |
					      d.all_cand_acc[f];
					    bdd f2p = p.acc_ref | curacc;
783

784
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811
812
					    path p2(p.src_cand, p.src_ref,
						    q3, dp, f2, f2p);
					    int p2id = d.pathid[p2];
					    if (pid == p2id)
					      continue;
#if DEBUG
					    dout << "(13) " << p << " ∧ "
						 << t << "δ ";

					    bdd biga_ = d.all_cand_acc[f];
					    while (biga_ != bddfalse)
					      {
						bdd a = bdd_satone(biga_);
						biga_ -= a;

						transition_acc ta(q2, l, a, q3);
						out <<  " ∧ " << ta << "FC";
					      }
					    biga_ = d.all_cand_acc.back()
					      - d.all_cand_acc[f];
					    while (biga_ != bddfalse)
					      {
						bdd a = bdd_satone(biga_);
						biga_ -= a;

						transition_acc ta(q2, l, a, q3);
						out << " ∧ ¬" << ta << "FC";
					      }
					    out << " → " << p2 << "\n";
813
#endif
814
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					    out << -pid << " " << -ti << " ";
					    bdd biga = d.all_cand_acc[f];
					    while (biga != bddfalse)
					      {
						bdd a = bdd_satone(biga);
						biga -= a;

						transition_acc ta(q2, l, a, q3);
						int tai = d.transaccid[ta];
						out << -tai << " ";
					      }
					    biga = d.all_cand_acc.back()
					      - d.all_cand_acc[f];
					    while (biga != bddfalse)
					      {
						bdd a = bdd_satone(biga);
						biga -= a;

						transition_acc ta(q2, l, a, q3);
						int tai = d.transaccid[ta];
						out << tai << " ";
					      }

					    out << p2id << " 0\n";
					    ++nclauses;
839
840
					  }
				      }
841
				    }
842
843
				}
			    }
844
			  delete it;
845
			}
846
847
848
		  }
	    }
	}
849
850
851
852
853
      out.seekp(0);
      out << "p cnf " << d.nvars << " " << nclauses;
    }

    static tgba_explicit_number*
854
    sat_build(const sat_solution& solution, dict& satdict, const tgba* aut,
855
	      bool state_based)
856
857
858
859
860
861
862
863
864
865
866
867
868
869
870
871
872
873
874
875
    {
      bdd_dict* autdict = aut->get_dict();
      tgba_explicit_number* a = new tgba_explicit_number(autdict);
      autdict->register_all_variables_of(aut, a);
      autdict->unregister_all_typed_variables(bdd_dict::acc, aut);
      a->set_acceptance_conditions(satdict.all_cand_acc.back());

      for (int s = 1; s < satdict.cand_size; ++s)
	a->add_state(s);

      state_explicit_number::transition* last_aut_trans = 0;
      const transition* last_sat_trans = 0;

#if DEBUG
      std::fstream out("dtgba-sat.dbg",
		       std::ios_base::trunc | std::ios_base::out);
      std::set<int> positive;
#endif

      dout << "--- transition variables ---\n";
876
      std::map<int, bdd> state_acc;
877
878
      for (sat_solution::const_iterator i = solution.begin();
	   i != solution.end(); ++i)
879
	{
880
	  int v = *i;
881
882
883
884
885
886
887
888
889
890
891
892
893
894
895
896
897
898

	  if (v < 0)  // FIXME: maybe we can have (v < NNN)?
	    continue;

#if DEBUG
	  positive.insert(v);
#endif

	  dict::rev_map::const_iterator t = satdict.revtransid.find(v);

	  if (t != satdict.revtransid.end())
	    {
	      last_aut_trans = a->create_transition(t->second.src,
						    t->second.dst);
	      last_aut_trans->condition = t->second.cond;
	      last_sat_trans = &t->second;

	      dout << v << "\t" << t->second << \n";
899
900
901
902
903
904
905
906

	      if (state_based)
		{
		  std::map<int, bdd>::const_iterator i =
		    state_acc.find(t->second.src);
		  if (i != state_acc.end())
		    last_aut_trans->acceptance_conditions = i->second;
		}
907
908
909
910
911
912
913
914
915
916
917
918
919
920
921
	    }
	  else
	    {
	      dict::rev_acc_map::const_iterator ta;
	      ta = satdict.revtransaccid.find(v);
	      // This assumes that the sat solvers output variables in
	      // increasing order.
	      if (ta != satdict.revtransaccid.end())
		{
		  dout << v << "\t" << ta->second << "F\n";

		  if (last_sat_trans &&
		      ta->second.src == last_sat_trans->src &&
		      ta->second.cond == last_sat_trans->cond &&
		      ta->second.dst == last_sat_trans->dst)
922
923
924
925
926
927
928
929
		    {
		      assert(!state_based);
		      last_aut_trans->acceptance_conditions |= ta->second.acc;
		    }
		  else if (state_based)
		    {
		      state_acc[ta->second.src] |= ta->second.acc;
		    }
930
931
932
933
934
935
936
937
938
939
940
941
942
943
944
945
946
947
948
949
950
951
952
953
954
955
956
957
958
959
960
961
962
963
964
965
		}
	    }
	}
#if DEBUG
      dout << "--- state_pair variables ---\n";
      for (std::map<state_pair, int>::const_iterator pit =
	     satdict.prodid.begin(); pit != satdict.prodid.end(); ++pit)
	if (positive.find(pit->second) != positive.end())
	  dout << pit->second << "\t" << pit->first << "\n";

      dout << "--- pathit variables ---\n";
      for (std::map<path, int>::const_iterator pit =
	     satdict.pathid.begin();
	   pit != satdict.pathid.end(); ++pit)
	if (positive.find(pit->second) != positive.end())
	  dout << pit->second << "\t" << pit->first << "C\n";
#endif

      a->merge_transitions();

      return a;
    }

    static bool
    xrename(const char* from, const char* to)
    {
      if (!rename(from, to))
	return false;
      std::ostringstream msg;
      msg << "cannot rename " << from << " to " << to;
      perror(msg.str().c_str());
      return true;
    }
  }

  tgba_explicit_number*
966
967
  dtgba_sat_synthetize(const tgba* a, unsigned target_acc_number,
		       int target_state_number, bool state_based)
968
  {
969
970
971
    trace << "dtgba_sat_synthetize(..., acc = " << target_acc_number
	  << ", states = " << target_state_number
	  << ", state_based = " << state_based << ")\n";
972
973
974
975
    dict* current = 0;
    temporary_file* cnf = 0;
    temporary_file* out = 0;

976
977
978
979
980
981
982
983
984
985
986
987
988
    current = new dict(a);
    current->cand_size = target_state_number;
    current->cand_nacc = target_acc_number;

    cnf = create_tmpfile("dtgba-sat-", ".cnf");
    std::fstream cnfs(cnf->name(),
		      std::ios_base::trunc | std::ios_base::out);
    dtgba_to_sat(cnfs, a, *current, state_based);
    cnfs.close();

    out = create_tmpfile("dtgba-sat-", ".out");
    satsolver(cnf, out);

989
    sat_solution solution = satsolver_get_solution(out->name());
990
991
992
993
994
995

    tgba_explicit_number* res = 0;
    if (!solution.empty())
      res = sat_build(solution, *current, a, state_based);

    delete current;
996

997
    if (DEBUG)
998
      {
999
1000
	xrename(out->name(), "dtgba-sat.out");
	xrename(cnf->name(), "dtgba-sat.cnf");
1001
      }
1002
1003
1004
1005
1006
1007
1008
1009
1010
1011
1012
1013
1014
1015
1016

    delete out;
    delete cnf;
    trace << "dtgba_sat_synthetize(...) = " << res << "\n";
    return res;
  }

  tgba_explicit_number*
  dtgba_sat_minimize(const tgba* a, unsigned target_acc_number,
		     bool state_based)
  {
    int n_states = stats_reachable(a).states;

    tgba_explicit_number* prev = 0;
    for (;;)
1017
      {
1018
1019
1020
1021
1022
1023
1024
	tgba_explicit_number* next =
	  dtgba_sat_synthetize(prev ? prev : a, target_acc_number,
			       --n_states, state_based);
	if (next == 0)
	  break;
	delete prev;
	prev = next;
1025
      }
1026
1027
1028
1029
1030
1031
1032
1033
1034
    return prev;
  }

  tgba_explicit_number*
  dtgba_sat_minimize_dichotomy(const tgba* a, unsigned target_acc_number,
			       bool state_based)
  {
    int max_states = stats_reachable(a).states - 1;
    int min_states = 1;
1035

1036
1037
    tgba_explicit_number* prev = 0;
    while (min_states <= max_states)
1038
      {
1039
1040
1041
1042
1043
	int target = (max_states + min_states) / 2;
	tgba_explicit_number* next =
	  dtgba_sat_synthetize(prev ? prev : a, target_acc_number, target,
			       state_based);
	if (next == 0)
1044
	  {
1045
1046
1047
1048
1049
1050
1051
	    min_states = target + 1;
	  }
	else
	  {
	    delete prev;
	    prev = next;
	    max_states = target - 1;
1052
1053
	  }
      }
1054
    return prev;
1055
1056
1057
  }

}