dtbasat: implement dba_sat_minimize()

* src/tgbaalgos/dtbasat.cc, src/tgbaalgos/dtbasat.hh: New files.
* src/tgbaalgos/Makefile.am: Add them.
* src/tgbatest/ltl2tgba.cc: Add option -RS.

src/tgbaalgos/Makefile.am

@@ -37,6 +37,7 @@ tgbaalgos_HEADERS = \
   degen.hh \
   dottydec.hh \
   dotty.hh \
+  dtbasat.hh \
   dupexp.hh \
   eltl2tgba_lacim.hh \
   emptiness.hh \
@@ -84,6 +85,7 @@ libtgbaalgos_la_SOURCES = \
   degen.cc \
   dotty.cc \
   dottydec.cc \
+  dtbasat.cc \
   dupexp.cc \
   eltl2tgba_lacim.cc \
   emptiness.cc \

src/tgbaalgos/dtbasat.cc

+// -*- 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"
+
+// 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 "
+#else
+#define dout while (0) out
+#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_;
+    public:
+      filler_dfs(const tgba* aut, dict& d, bdd ap)
+	:tgba_reachable_iterator_depth_first(aut), d(d), ap_(ap)
+      {
+	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)
+	  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));
+		  d.transacc[t] = ++d.nvars;
+		  d.revtransacc.insert(dict::rev_map::value_type(d.nvars, t));
+		}
+	    }
+      }
+    };
+
+    static
+    void dtba_to_sat(std::ostream& out, const tgba* ref, dict& d)
+    {
+      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.
+      {
+	filler_dfs f(ref, d, ap);
+	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();
+#endif
+
+      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];
+
+		      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];
+
+			      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];
+
+			      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 std::string
+    get_solution(const char* filename)
+    {
+      std::fstream in(filename, std::ios_base::in);
+      std::string line;
+      while (std::getline(in, line))
+	{
+	  if (line.empty() || line[0] == 'c')
+	    continue;
+	  if (line[0] == 'v')
+	    break;
+	}
+      if (line[0] == 'v')
+	return line.c_str() + 1;
+      return "";
+    }
+
+
+    static tgba_explicit_number*
+    sat_build(const std::string& solution, dict& satdict, const tgba* aut)
+    {
+      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);
+
+      std::stringstream sol(solution);
+      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;
+#else
+      // "out" is not used, but it has to exist for the dout() macro to
+      // compile.
+      std::ostream& out(std::cout);
+#endif
+