dtbasat.cc 20 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 "dtbasat.hh"
#include "reachiter.hh"
#include <map>
#include <utility>
#include "scc.hh"
#include "tgba/bddprint.hh"
#include "ltlast/constant.hh"
#include "stats.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 dtba-sat.cnf and dtba-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 (dtba-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 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;

      path(int src_cand, int src_ref,
	   int dst_cand, int dst_ref)
	: src_cand(src_cand), src_ref(src_ref),
	  dst_cand(dst_cand), dst_ref(dst_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;
	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 path& p)
    {
      os << "<"
	 << p.src_cand << ","
	 << p.src_ref << ","
	 << p.dst_cand << ","
	 << p.dst_ref << ">";
      return os;
    }

    struct dict
    {
      typedef std::map<transition, int> trans_map;
      trans_map transid;
      trans_map transacc;
      typedef std::map<int, transition> rev_map;
      rev_map revtransid;
      rev_map revtransacc;

      std::map<state_pair, int> prodid;
      std::map<path, int> pathid_ref;
      std::map<path, int> pathid_cand;
      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;

      ~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();
      }
    };


    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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    public:
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      filler_dfs(const tgba* aut, dict& d, bdd ap, bool state_based)
	: tgba_reachable_iterator_depth_first(aut), d(d), ap_(ap),
	  state_based_(state_based)
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      {
	d.nvars = 0;
      }

      int size()
      {
	return size_;
      }

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

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

	int seen_size = seen.size();
	for (int i = 1; i <= seen_size; ++i)
	  {
	    for (int j = 1; j <= d.cand_size; ++j)
	      {
		d.prodid[state_pair(j, i)] = ++d.nvars;

		for (int k = 1; k <= seen_size; ++k)
		  for (int l = 1; l <= d.cand_size; ++l)
		    {
		      path p(j, i, l, k);
		      d.pathid_ref[p] = ++d.nvars;
		      d.pathid_cand[p] = ++d.nvars;
		    }
	      }
	  }

	for (dict::state_map::const_iterator i = seen.begin();
	     i != seen.end(); ++i)
	  {
	    d.int_to_state[i->second] = i->first;
	  }

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

	for (int i = 1; i <= d.cand_size; ++i)
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	  {
	    int transacc = -1;
	    if (state_based_)
	      // All outgoing transitions use the same acceptance variable.
	      transacc = ++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;

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

    static
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    void dtba_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());

      // Number all the SAT variable we may need.
      {
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	filler_dfs f(ref, d, ap, state_based);
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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";

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

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      // dout << "symmetry-breaking clauses\n";
      // int k = 1;
      // bdd all = bddtrue;
      // while (all != bddfalse)
      // 	{
      // 	  bdd s = bdd_satoneset(all, ap, bddfalse);
      // 	  all -= s;
      // 	  for (int q1 = 1; q1 < d.cand_size; ++q1)
      // 	    for (int q2 = q1 + 2; q2 <= d.cand_size; ++q2)
      // 	      if ((q1 - 1) * d.cand_size + q2 + 2 <= k)
      // 		{
      // 		  transition t(q1, s, q2);
      // 		  int ti = d.transid[t];
      // 		  dout << "¬" << t << "\n";
      // 		  out << -ti << " 0\n";
      // 		  ++nclauses;
      // 		}
      // 	  ++k;
      // 	}
      // if (!nclauses)
      // 	dout << "(none)\n";

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      dout << "(1) 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 << "(2) 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 << "(2) states Cand[" << q1 << "] and Ref[" << q1p
	       << "] are 0-length paths\n";
	  path p(q1, q1p, q1, q1p);
	  dout << pit->first << " → (" << p << "R ∧ " << p << "C)\n";
	  out << -pit->second << " " << d.pathid_ref[p] <<" 0\n";
	  out << -pit->second << " " << d.pathid_cand[p] <<" 0\n";
	  nclauses += 2;

	  dout << "(3) 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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		      if (pit->second == succ)
			continue;

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		      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 contraints (4,5) : all loops in the product
      // where no accepting run is detected in the ref. automaton,
      // must also be marked as not accepting in the cand. automaton
      for (int q1 = 1; q1 <= d.cand_size; ++q1)
	for (int q1p = 1; q1p <= ref_size; ++q1p)
	  {
	    for (int q2 = 1; q2 <= d.cand_size; ++q2)
	      for (int q2p = 1; q2p <= ref_size; ++q2p)
		{
		  path p1(q1, q1p, q2, q2p);

		  dout << "(4&5) matching paths from reference based on "
		       << p1 << "\n";

		  int pid1 = d.pathid_ref[p1];

		  tgba_succ_iterator* it = ref->succ_iter(d.int_to_state[q2p]);
		  for (it->first(); !it->done(); it->next())
		    {
		      const state* dps = it->current_state();
		      int dp = d.state_to_int[dps];
		      dps->destroy();
		      if (it->current_acceptance_conditions() == all_acc)
			continue;
		      for (int q3 = 1; q3 <= d.cand_size; ++q3)
			{
			  if (dp == q1p && q3 == q1) // (4) looping
			    {
			      bdd all = it->current_condition();
			      while (all != bddfalse)
				{
				  bdd s = bdd_satoneset(all, ap, bddfalse);
				  all -= s;

				  transition t(q2, s, q1);
				  int ti = d.transid[t];
				  int ta = d.transacc[t];

				  dout << p1 << "R ∧ " << t << "δ → ¬" << t
				       << "F\n";
				  out << -pid1 << " " << -ti << " "
				      << -ta << " 0\n";
				  ++nclauses;
				}


			    }
			  else // (5) not looping
			    {
			      path p2 = path(q1, q1p, q3, dp);
			      int pid2 = d.pathid_ref[p2];

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			      if (pid1 == pid2)
				continue;

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

				  transition t(q2, s, q3);
				  int ti = d.transid[t];

				  dout << p1 << "R ∧ " << t << "δ → " << p2
				       << "R\n";
				  out << -pid1 << " " << -ti << " "
				      << pid2 << " 0\n";
				  ++nclauses;
				}
			    }
			}
		    }
		  delete it;
		}
	  }

      // construction of contraints (6,7): all loops in the product
      // where accepting run is detected in the ref. automaton, must
      // also be marked as accepting in the candidate.
      for (int q1 = 1; q1 <= d.cand_size; ++q1)
	for (int q1p = 1; q1p <= ref_size; ++q1p)
	  {
	    for (int q2 = 1; q2 <= d.cand_size; ++q2)
	      for (int q2p = 1; q2p <= ref_size; ++q2p)
		{
		  path p1(q1, q1p, q2, q2p);
		  dout << "(6&7) matching paths from candidate based on "
		       << p1 << "\n";
		  int pid1 = d.pathid_cand[p1];

		  tgba_succ_iterator* it = ref->succ_iter(d.int_to_state[q2p]);
		  for (it->first(); !it->done(); it->next())
		    {
		      const state* dps = it->current_state();
		      int dp = d.state_to_int[dps];
		      dps->destroy();
		      for (int q3 = 1; q3 <= d.cand_size; q3++)
			{
			  if (dp == q1p && q3 == q1) // (6) looping
			    {
			      // We only care about the looping case if
			      // it is accepting in the reference.
			      if (it->current_acceptance_conditions()
				  != all_acc)
				continue;
			      bdd all = it->current_condition();
			      while (all != bddfalse)
				{
				  bdd s = bdd_satoneset(all, ap, bddfalse);
				  all -= s;

				  transition t(q2, s, q1);
				  int ti = d.transid[t];
				  int ta = d.transacc[t];

				  dout << p1 << "C ∧ " << t << "δ → " << t
				       << "F\n";
				  out << -pid1 << " " << -ti << " " << ta
				      << " 0\n";
				  ++nclauses;
				}
			    }
			  else // (7) no loop
			    {
			      path p2 = path(q1, q1p, q3, dp);
			      int pid2 = d.pathid_cand[p2];

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			      if (pid1 == pid2)
				continue;

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

				  transition t(q2, s, q3);
				  int ti = d.transid[t];
				  int ta = d.transacc[t];

				  dout << p1 << "C ∧ " << t << "δ ∧ ¬"
				       << t << "F → " << p2 << "C\n";

				  out << -pid1 << " " << -ti << " "
				      << ta << " " << pid2 << " 0\n";
				  ++nclauses;
				}
			    }
			}
		    }
		  delete it;
		}
	  }

      out.seekp(0);
      out << "p cnf " << d.nvars << " " << nclauses;
    }

    static tgba_explicit_number*
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    sat_build(const sat_solution& solution, dict& satdict, const tgba* aut,
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	      bool state_based)
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    {
      bdd_dict* autdict = aut->get_dict();
      tgba_explicit_number* a = new tgba_explicit_number(autdict);
      autdict->register_all_variables_of(aut, a);

      const ltl::formula* t = ltl::constant::true_instance();
      bdd acc = bdd_ithvar(autdict->register_acceptance_variable(t, a));
      a->set_acceptance_conditions(acc);

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

      dout << "--- transition variables ---\n";
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      std::set<int> acc_states;
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      for (sat_solution::const_iterator i = solution.begin();
	   i != solution.end(); ++i)
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	{
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	  int v = *i;
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	  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";
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	      // Mark the transition as accepting if the source is.
	      if (state_based
		  && acc_states.find(t->second.src) != acc_states.end())
		last_aut_trans->acceptance_conditions = acc;
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	    }
	  else
	    {
	      t = satdict.revtransacc.find(v);
	      if (t != satdict.revtransacc.end())
		{
		  dout << v << "\t" << t->second << "F\n";
		  if (last_sat_trans && t->second == *last_sat_trans)
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		    {
		      assert(!state_based);
		      // This assumes that the SAT solvers output
		      // variables in increasing order.
		      last_aut_trans->acceptance_conditions = acc;
		    }
		  else if (state_based)
		    {
		      // Accepting translations actually correspond to
		      // states and are announced before listing
		      // outgoing transitions.  Again, this assumes
		      // that the SAT solvers output variables in
		      // increasing order.
		      acc_states.insert(t->second.src);
		    }
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		}
	    }
	}
#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 << "--- pathid_cand variables ---\n";
      for (std::map<path, int>::const_iterator pit =
	     satdict.pathid_cand.begin();
	   pit != satdict.pathid_cand.end(); ++pit)
	if (positive.find(pit->second) != positive.end())
	  dout << pit->second << "\t" << pit->first << "C\n";

      dout << "--- pathid_ref variables ---\n";
      for (std::map<path, int>::const_iterator pit =
	     satdict.pathid_ref.begin();
	   pit != satdict.pathid_ref.end(); ++pit)
	if (positive.find(pit->second) != positive.end())
	  dout << pit->second << "\t" << pit->first << "R\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*
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  dtba_sat_synthetize(const tgba* a, int target_state_number,
		      bool state_based)
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  {
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    trace << "dtba_sat_synthetize(..., states = " << target_state_number
	  << ", state_based = " << state_based << ")\n";
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    dict* current = 0;
    temporary_file* cnf = 0;
    temporary_file* out = 0;

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    current = new dict;
    current->cand_size = target_state_number;

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

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

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    sat_solution solution = satsolver_get_solution(out->name());
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    tgba_explicit_number* res = 0;
    if (!solution.empty())
      res = sat_build(solution, *current, a, state_based);

    delete current;
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    if (DEBUG)
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      {
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	xrename(out->name(), "dtba-sat.out");
	xrename(cnf->name(), "dtba-sat.cnf");
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      }
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    delete out;
    delete cnf;
    trace << "dtba_sat_synthetize(...) = " << res << "\n";
    return res;
  }

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

    tgba_explicit_number* prev = 0;
    for (;;)
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      {
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	tgba_explicit_number* next =
	  dtba_sat_synthetize(prev ? prev : a, --n_states, state_based);
	if (next == 0)
	  break;
	delete prev;
	prev = next;
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      }
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    return prev;
  }
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  tgba_explicit_number*
  dtba_sat_minimize_dichotomy(const tgba* a, bool state_based)
  {
    int max_states = stats_reachable(a).states - 1;
    int min_states = 1;

    tgba_explicit_number* prev = 0;
    while (min_states <= max_states)
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      {
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	int target = (max_states + min_states) / 2;
	tgba_explicit_number* next =
	  dtba_sat_synthetize(prev ? prev : a, target, state_based);
	if (next == 0)
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	  {
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	    min_states = target + 1;
	  }
	else
	  {
	    delete prev;
	    prev = next;
	    max_states = target - 1;
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	  }
      }
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    return prev;
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  }
}