// -*- coding: utf-8 -*-
// Copyright (C) 2013, 2014, 2015 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 <spot/twaalgos/dtwasat.hh>
#include <spot/twaalgos/dtbasat.hh>
#include <map>
#include <utility>
#include <spot/twaalgos/sccinfo.hh>
#include <spot/twa/bddprint.hh>
#include <spot/twaalgos/stats.hh>
#include <spot/tl/defaultenv.hh>
#include <spot/misc/satsolver.hh>
#include <spot/misc/timer.hh>
#include <spot/twaalgos/isweakscc.hh>
#include <spot/twaalgos/isdet.hh>
#include <spot/twaalgos/dot.hh>
#include <spot/twaalgos/complete.hh>
#include <spot/misc/optionmap.hh>
#include <spot/twaalgos/sccfilter.hh>
#include <spot/twaalgos/sbacc.hh>
#include <spot/twaalgos/postproc.hh>

// If you set the SPOT_TMPKEEP environment variable the temporary
// file used to communicate with the sat solver will be left in
// the current directory.
//
// Additionally, if the following DEBUG macro is set to 1, the CNF
// file will be output with a comment before each clause, and an
// additional output file (dtwa-sat.dbg) will be created with a list
// of all positive variables in the result and their meaning.

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

namespace spot
{
  namespace
  {
    static bdd_dict_ptr debug_dict = nullptr;
    static const acc_cond* debug_ref_acc = nullptr;
    static const acc_cond* debug_cand_acc = nullptr;

    struct transition
    {
      unsigned src;
      bdd cond;
      unsigned 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 src_cond
    {
      unsigned src;
      bdd cond;

      src_cond(int src, bdd cond)
	: src(src), cond(cond)
      {
      }

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

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

    struct transition_acc
    {
      unsigned src;
      bdd cond;
      acc_cond::mark_t acc;
      unsigned dst;

      transition_acc(int src, bdd cond, acc_cond::mark_t 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 < other.acc;
      }

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

    struct path
    {
      unsigned src_cand;
      unsigned src_ref;
      unsigned dst_cand;
      unsigned dst_ref;
      acc_cond::mark_t acc_cand;
      acc_cond::mark_t acc_ref;

      path(unsigned src_cand, unsigned src_ref)
	: src_cand(src_cand), src_ref(src_ref),
	  dst_cand(src_cand), dst_ref(src_ref),
	  acc_cand(0U), acc_ref(0U)
      {
      }

      path(unsigned src_cand, unsigned src_ref,
	   unsigned dst_cand, unsigned dst_ref,
	   acc_cond::mark_t acc_cand, acc_cond::mark_t 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 < other.acc_ref)
	  return true;
	if (this->acc_ref > other.acc_ref)
	  return false;
	if (this->acc_cand < other.acc_cand)
	  return true;
	if (this->acc_cand > other.acc_cand)
	  return false;

	return false;
      }

    };

    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) << ','
	 << debug_cand_acc->format(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 << ", "
	 << debug_cand_acc->format(p.acc_cand) << ", "
	 << debug_ref_acc->format(p.acc_ref) << '>';
      return os;
    }

    // If the DNF is
    //  Fin(1)&Fin(2)&Inf(3) | Fin(0)&Inf(3) | Fin(4)&Inf(5)&Inf(6)
    // this returns the following map:
    //  {3} => [{1,2} {0}]
    //  {5} => [{4}]
    //  {6} => [{4}]
    // We use that do detect (and disallow) what we call "silly histories",
    // i.e., transitions or histories labeled by sets such as
    // {3,1,0}, that have no way to be satisfied.  So whenever we see
    // such history in a path, we actually map it to {1,0} instead,
    // which is enough to remember that this history is not satisfiable.
    // We also forbid any transition from being labeled by {3,1,0}.
    typedef std::map<unsigned, std::vector<acc_cond::mark_t>> trimming_map;
    static trimming_map
    split_dnf_acc_by_inf(const acc_cond::acc_code& input_acc)
    {
      trimming_map res;
      auto acc = input_acc.to_dnf();
      auto pos = &acc.back();
      if (pos->op == acc_cond::acc_op::Or)
	--pos;
      acc_cond::mark_t all_fin = 0U;
      auto start = &acc.front();
      while (pos > start)
	{
	  if (pos->op == acc_cond::acc_op::Fin)
	    {
	      // We have only a Fin term, without Inf.
	      // There is nothing to do about it.
	      pos -= pos->size + 1;
	    }
	  else
	    {
	      // We have a conjunction of Fin and Inf sets.
	      auto end = pos - pos->size - 1;
	      acc_cond::mark_t fin = 0U;
	      acc_cond::mark_t inf = 0U;
	      while (pos > end)
		{
		  switch (pos->op)
		    {
		    case acc_cond::acc_op::And:
		      --pos;
		      break;
		    case acc_cond::acc_op::Fin:
		      fin |= pos[-1].mark;
		      assert(pos[-1].mark.count() == 1);
		      pos -= 2;
		      break;
		    case acc_cond::acc_op::Inf:
		      inf |= pos[-1].mark;
		      pos -= 2;
		      break;
		    case acc_cond::acc_op::FinNeg:
		    case acc_cond::acc_op::InfNeg:
		    case acc_cond::acc_op::Or:
		      SPOT_UNREACHABLE();
		      break;
		    }
		}
	      assert(pos == end);

	      all_fin |= fin;
	      for (unsigned i: inf.sets())
		if (fin)
		  {
		    res[i].emplace_back(fin);
		  }
		else
		  {
		    // Make sure the empty set is always the first one.
		    res[i].clear();
		    res[i].emplace_back(fin);
		  }
	    }
	}
      // Remove entries that are necessarily false because they
      // contain an emptyset, or entries that also appear as Fin
      // somewhere in the acceptance.
      auto i = res.begin();
      while (i != res.end())
	{
	  if (all_fin.has(i->first) || !i->second[0])
	    i = res.erase(i);
	  else
	    ++i;
	}

      return res;
    }

    struct dict
    {
      dict(const const_twa_ptr& a)
	: aut(a)
      {
      }

      const_twa_ptr 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<path, int> pathid;
      int nvars = 0;
      //typedef std::unordered_map<const state*, int,
      //state_ptr_hash, state_ptr_equal> state_map;
      //typedef std::unordered_map<int, const state*> int_map;
      //state_map state_to_int;
      //      int_map int_to_state;
      unsigned cand_size;
      unsigned int cand_nacc;
      acc_cond::acc_code cand_acc;

      std::vector<acc_cond::mark_t> all_cand_acc;
      std::vector<acc_cond::mark_t> all_ref_acc;
      // Markings that make no sense and that we do not want to see in
      // the candidate.  See comment above split_dnf_acc_by_inf().
      std::vector<acc_cond::mark_t> all_silly_cand_acc;

      std::vector<bool> is_weak_scc;
      std::vector<acc_cond::mark_t> scc_marks;

      acc_cond cacc;
      trimming_map ref_inf_trim_map;
      trimming_map cand_inf_trim_map;

      ~dict()
      {
	aut->get_dict()->unregister_all_my_variables(this);
      }

      acc_cond::mark_t
      inf_trim(acc_cond::mark_t m, trimming_map& tm)
      {
	for (auto& s: tm)
	  {
	    unsigned inf = s.first;
	    if (m.has(inf))
	      {
		bool remove = true;
		for (auto fin: s.second)
		  if (!(m & fin))
		    {
		      remove = false;
		      break;
		    }
		if (remove)
		  m.clear(inf);
	      }
	  }
	return m;
      }

      acc_cond::mark_t
      ref_inf_trim(acc_cond::mark_t m)
      {
	return inf_trim(m, ref_inf_trim_map);
      }

      acc_cond::mark_t
      cand_inf_trim(acc_cond::mark_t m)
      {
	return inf_trim(m, cand_inf_trim_map);
      }
    };


    unsigned declare_vars(const const_twa_graph_ptr& aut,
			  dict& d, bdd ap, bool state_based, scc_info& sm)
    {
      d.is_weak_scc = sm.weak_sccs();
      unsigned scccount = sm.scc_count();
      {
	auto tmp = sm.used_acc();
	d.scc_marks.reserve(scccount);
	for (auto& v: tmp)
	  {
	    acc_cond::mark_t m = 0U;
	    for (auto i: v)
	      m |= i;
	    d.scc_marks.emplace_back(m);
	  }
      }

      d.cacc.add_sets(d.cand_nacc);
      d.cacc.set_acceptance(d.cand_acc);

      // If the acceptance conditions use both Fin and Inf primitives,
      // we may have some silly history configurations to ignore.
      if (aut->acc().uses_fin_acceptance())
	d.ref_inf_trim_map = split_dnf_acc_by_inf(aut->get_acceptance());
      if (d.cacc.uses_fin_acceptance())
	d.cand_inf_trim_map = split_dnf_acc_by_inf(d.cand_acc);

      bdd_dict_ptr bd = aut->get_dict();
      d.all_cand_acc.push_back(0U);
      for (unsigned n = 0; n < d.cand_nacc; ++n)
	{
	  auto c = d.cacc.mark(n);

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

	  size_t s = d.all_cand_acc.size();
	  for (size_t i = 0; i < s; ++i)
	    {
	      acc_cond::mark_t m = d.all_cand_acc[i] | c;
	      if (d.cand_inf_trim(m) == m)
		d.all_cand_acc.push_back(m);
	      else
		d.all_silly_cand_acc.push_back(m);
	    }
	}

      d.all_ref_acc.push_back(0U);
      unsigned ref_nacc = aut->num_sets();
      for (unsigned n = 0; n < ref_nacc; ++n)
	{
	  auto c = aut->acc().mark(n);
	  size_t s = d.all_ref_acc.size();
	  for (size_t i = 0; i < s; ++i)
	    {
	      acc_cond::mark_t m = d.all_ref_acc[i] | c;
	      if (d.ref_inf_trim(m) != m)
		continue;
	      d.all_ref_acc.push_back(m);
	    }
	}

      unsigned ref_size = aut->num_states();

      if (d.cand_size == -1U)
	for (unsigned i = 0; i < ref_size; ++i)
	  if (sm.reachable_state(i))
	    ++d.cand_size;      // Note that we start from -1U the
				// cand_size is one less than the
				// number of reachable states.

      for (unsigned i = 0; i < ref_size; ++i)
	{
	  if (!sm.reachable_state(i))
	    continue;
	  unsigned i_scc = sm.scc_of(i);
	  bool is_weak = d.is_weak_scc[i_scc];

	  for (unsigned j = 0; j < d.cand_size; ++j)
	    {
	      for (unsigned k = 0; k < ref_size; ++k)
		{
		  if (!sm.reachable_state(k))
		    continue;
		  if (sm.scc_of(k) != i_scc)
		    continue;
		  for (unsigned l = 0; l < d.cand_size; ++l)
		    {
		      size_t sfp = is_weak ? 1 : d.all_ref_acc.size();
		      acc_cond::mark_t sccmarks = d.scc_marks[i_scc];
		      for (size_t fp = 0; fp < sfp; ++fp)
			{
			  auto refhist = d.all_ref_acc[fp];
			  // refhist cannot have more sets than used in the SCC
			  if (!is_weak && (sccmarks & refhist) != refhist)
			    continue;

			  size_t sf = d.all_cand_acc.size();
			  for (size_t f = 0; f < sf; ++f)
			    {
			      path p(j, i, l, k,
				     d.all_cand_acc[f], refhist);
			      d.pathid[p] = ++d.nvars;
			    }

			}
		    }
		}
	    }
	}

      if (!state_based)
	{
	  for (unsigned i = 0; i < d.cand_size; ++i)
	    for (unsigned j = 0; 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.emplace(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.cacc.mark(n), j);
			d.transaccid[ta] = ++d.nvars;
			d.revtransaccid.emplace(d.nvars, ta);
		      }
		  }
	      }
	}
      else // state based
	{
	  for (unsigned i = 0; i < d.cand_size; ++i)
	    for (unsigned n = 0; n < d.cand_nacc; ++n)
	      {
		++d.nvars;
		for (unsigned j = 0; j < d.cand_size; ++j)
		  {
		    bdd all = bddtrue;
		    while (all != bddfalse)
		      {
			bdd one = bdd_satoneset(all, ap, bddfalse);
			all -= one;

			transition_acc ta(i, one, d.cacc.mark(n), j);
			d.transaccid[ta] = d.nvars;
			d.revtransaccid.emplace(d.nvars, ta);
		      }
		  }
	      }
	  for (unsigned i = 0; i < d.cand_size; ++i)
	    for (unsigned j = 0; 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.emplace(d.nvars, t);
		  }
	      }
	}
      return ref_size;
    }

    typedef std::pair<int, int> sat_stats;

    static
    sat_stats dtwa_to_sat(std::ostream& out, const_twa_graph_ptr ref,
			   dict& d, bool state_based, bool colored)
    {
#if DEBUG
      debug_dict = ref->get_dict();
#endif
      clause_counter nclauses;

      // Compute the AP used in the hard way.
      bdd ap = bddtrue;
      for (auto& t: ref->edges())
	ap &= bdd_support(t.cond);

      // Count the number of atomic propositions
      int nap = 0;
      {
	bdd cur = ap;
	while (cur != bddtrue)
	  {
	    ++nap;
	    cur = bdd_high(cur);
	  }
	nap = 1 << nap;
      }

      scc_info sm(ref);
      sm.determine_unknown_acceptance();

      // Number all the SAT variables we may need.
      unsigned ref_size = declare_vars(ref, d, ap, state_based, sm);

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

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

#if DEBUG
      debug_ref_acc = &ref->acc();
      debug_cand_acc = &d.cacc;
      dout << "ref_size: " << ref_size << '\n';
      dout << "cand_size: " << d.cand_size << '\n';
#endif
      auto& racc = ref->acc();

      dout << "symmetry-breaking clauses\n";
      int j = 0;
      bdd all = bddtrue;
      while (all != bddfalse)
 	{
 	  bdd s = bdd_satoneset(all, ap, bddfalse);
 	  all -= s;
 	  for (unsigned i = 0; i < d.cand_size - 1; ++i)
 	    for (unsigned k = i * nap + j + 2; 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.nb_clauses())
 	dout << "(none)\n";

      dout << "(8) the candidate automaton is complete\n";
      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
	{
	  bdd all = bddtrue;
	  while (all != bddfalse)
	    {
	      bdd s = bdd_satoneset(all, ap, bddfalse);
	      all -= s;

#if DEBUG
	      dout;
	      for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
		{
		  transition t(q1, s, q2);
		  out << t << "δ";
		  if (q2 != d.cand_size)
		    out << " ∨ ";
		}
	      out << '\n';
#endif

	      for (unsigned q2 = 0; 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";
      {
	unsigned init = ref->get_init_state_number();
	dout << path(0, init) << '\n';
	out << d.pathid[path(0, init)] << " 0\n";
	++nclauses;
      }

      if (colored)
	{
	  unsigned nacc = d.cand_nacc;
	  dout << "transitions belong to exactly one of the "
	       << nacc << " acceptance set\n";
	  bdd all = bddtrue;
	  while (all != bddfalse)
	    {
	      bdd l = bdd_satoneset(all, ap, bddfalse);
	      all -= l;
	      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
		for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
		  {
		    for (unsigned i = 0; i < nacc; ++i)
		      {
			transition_acc ti(q1, l, {i}, q2);
			int tai = d.transaccid[ti];

			for (unsigned j = 0; j < nacc; ++j)
			  if (i != j)
			    {
			      transition_acc tj(q1, l, {j}, q2);
			      int taj = d.transaccid[tj];
			      out << -tai << ' ' << -taj << " 0\n";
			      ++nclauses;
			    }
		      }
		    for (unsigned i = 0; i < nacc; ++i)
		      {
			transition_acc ti(q1, l, {i}, q2);
			int tai = d.transaccid[ti];
			out << tai << ' ';
		      }
		    out << "0\n";
		    ++nclauses;
		  }
	    }
	}

      if (!d.all_silly_cand_acc.empty())
	{
	  dout << "no transition with silly acceptance\n";
	  bdd all = bddtrue;
	  while (all != bddfalse)
	    {
	      bdd l = bdd_satoneset(all, ap, bddfalse);
	      all -= l;
	      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
		for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
		  for (auto& s: d.all_silly_cand_acc)
		    {
		      dout << "no (" << q1 << ','
			   << bdd_format_formula(debug_dict, l)
			   << ',' << s << ',' << q2 << ")\n";
		      for (unsigned v: s.sets())
			{
			  transition_acc ta(q1, l, d.cacc.mark(v), q2);
			  int tai = d.transaccid[ta];
			  assert(tai != 0);
			  out << ' ' << -tai;
			}
		      for (unsigned v: d.cacc.comp(s).sets())
			{
			  transition_acc ta(q1, l, d.cacc.mark(v), q2);
			  int tai = d.transaccid[ta];
			  assert(tai != 0);
			  out << ' ' << tai;
			}
		      out << " 0\n";
		      ++nclauses;
		    }
	    }
	}

      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
	for (unsigned q1p = 0; q1p < ref_size; ++q1p)
	  {
	    if (!sm.reachable_state(q1p))
	      continue;
	    dout << "(10) augmenting paths based on Cand[" << q1
		 << "] and Ref[" << q1p << "]\n";
	    path p1(q1, q1p);
	    int p1id = d.pathid[p1];

	    for (auto& tr: ref->out(q1p))
	      {
		unsigned dp = tr.dst;
		bdd all = tr.cond;
		while (all != bddfalse)
		  {
		    bdd s = bdd_satoneset(all, ap, bddfalse);
		    all -= s;

		    for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
		      {
			transition t(q1, s, q2);
			int ti = d.transid[t];

			path p2(q2, dp);
			int succ = d.pathid[p2];

			if (p1id == succ)
			  continue;

			dout << p1 << " ∧ " << t << "δ → " << p2 << '\n';
			out << -p1id << ' ' << -ti << ' ' << succ << " 0\n";
			++nclauses;
		      }
		  }
	      }
	  }

      // construction of constraints (11,12,13)
      for (unsigned q1p = 0; q1p < ref_size; ++q1p)
	{
	  if (!sm.reachable_state(q1p))
	    continue;
	  unsigned q1p_scc = sm.scc_of(q1p);
	  for (unsigned q2p = 0; q2p < ref_size; ++q2p)
	    {
	      if (!sm.reachable_state(q2p))
		continue;
	      // We are only interested in transition that can form a
	      // cycle, so they must belong to the same SCC.
	      if (sm.scc_of(q2p) != q1p_scc)
		continue;
	      bool is_weak = d.is_weak_scc[q1p_scc];
	      bool is_rej = sm.is_rejecting_scc(q1p_scc);

	      for (unsigned q1 = 0; q1 < d.cand_size; ++q1)
		for (unsigned q2 = 0; q2 < d.cand_size; ++q2)
		  {
		    size_t sf = d.all_cand_acc.size();
		    size_t sfp = is_weak ? 1 : d.all_ref_acc.size();
		    acc_cond::mark_t sccmarks = d.scc_marks[q1p_scc];

		    for (size_t f = 0; f < sf; ++f)
		      for (size_t fp = 0; fp < sfp; ++fp)
			{
			  auto refhist = d.all_ref_acc[fp];
			  // refhist cannot have more sets than used in the SCC
			  if (!is_weak && (sccmarks & refhist) != refhist)
			    continue;

			  path p(q1, q1p, q2, q2p,
				 d.all_cand_acc[f], refhist);

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

			  int pid = d.pathid[p];

			  for (auto& tr: ref->out(q2p))
			    {
			      unsigned dp = tr.dst;
			      // Skip destinations not in the SCC.
			      if (sm.scc_of(dp) != q1p_scc)
				continue;

			      for (unsigned q3 = 0; q3 < d.cand_size; ++q3)
				{
				  bdd all = tr.cond;
				  acc_cond::mark_t curacc = tr.acc;
				  while (all != bddfalse)
				    {
				      bdd l = bdd_satoneset(all, ap, bddfalse);
				      all -= l;

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

				      if (dp == q1p && q3 == q1) // (11,12) loop
					{
					  bool rejloop =
					    (is_rej ||
					     !racc.accepting
					     (curacc | d.all_ref_acc[fp]));

					  auto missing =
					    d.cand_acc.
					    missing(d.all_cand_acc[f],
						    !rejloop);

					  for (auto& v: missing)
					    {
#if DEBUG
					      dout << (rejloop ?
						       "(11) " : "(12) ")
						   << p << " ∧ "
						   << t << "δ → (";
					      const char* orsep = "";
					      for (int s: v)
						{
						  if (s < 0)
						    {
						      transition_acc
							ta(q2, l,
							   d.cacc.mark(-s - 1),
							   q1);
						      out << orsep << "¬" << ta;
						    }
						  else
						    {
						      transition_acc
							ta(q2, l,
							   d.cacc.mark(s), q1);
						      out << orsep << ta;
						    }
						  out << "FC";
						  orsep = " ∨ ";
						}
					      out << ")\n";
#endif // DEBUG
					      out << -pid << ' ' << -ti;
					      for (int s: v)
						if (s < 0)
						  {
						    transition_acc
						      ta(q2, l,
							 d.cacc.mark(-s - 1),
							 q1);
						    int tai = d.transaccid[ta];
						    assert(tai != 0);
						    out << ' ' << -tai;
						  }
						else
						  {
						    transition_acc
						      ta(q2, l,
							 d.cacc.mark(s), q1);
						    int tai = d.transaccid[ta];
						    assert(tai != 0);
						    out << ' ' << tai;
						  }
					      out << " 0\n";
					      ++nclauses;
					    }
					}
				      // (13) augmenting paths (always).
				      {
					size_t sf = d.all_cand_acc.size();
					for (size_t f = 0; f < sf; ++f)
					  {
					    acc_cond::mark_t f2 =
					      d.cand_inf_trim
					      (p.acc_cand |
					       d.all_cand_acc[f]);
					    acc_cond::mark_t f2p = 0U;
					    if (!is_weak)
					      f2p = d.ref_inf_trim(p.acc_ref |
								   curacc);

					    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 ";

					    auto biga_ = d.all_cand_acc[f];
					    for (unsigned m = 0;
						 m < d.cand_nacc; ++m)
					      {
						transition_acc
						  ta(q2, l,
						     d.cacc.mark(m), q3);
						const char* not_ = "¬";
						if (d.cacc.has(biga_, m))
						  not_ = "";
						out <<  " ∧ " << not_
						    << ta << "FC";
					      }
					    out << " → " << p2 << '\n';
#endif
					    out << -pid << ' ' << -ti << ' ';
					    auto biga = d.all_cand_acc[f];
					    for (unsigned m = 0;
						 m < d.cand_nacc; ++m)
					      {
						transition_acc
						  ta(q2, l,
						     d.cacc.mark(m), q3);
						int tai = d.transaccid[ta];
						if (biga.has(m))
						  tai = -tai;
						out << tai << ' ';
					      }

					    out << p2id << " 0\n";
					    ++nclauses;
					  }
				      }
				    }
				}
			    }
			}
		  }
	    }
	}
      out.seekp(0);
      out << "p cnf " << d.nvars << ' ' << nclauses.nb_clauses();
      return std::make_pair(d.nvars, nclauses.nb_clauses());
    }

    static twa_graph_ptr
    sat_build(const satsolver::solution& solution, dict& satdict,
	      const_twa_graph_ptr aut, bool state_based)
    {
      auto autdict = aut->get_dict();
      auto a = make_twa_graph(autdict);
      a->copy_ap_of(aut);
      if (state_based)
	a->prop_state_acc(true);
      a->prop_deterministic(true);
      a->set_acceptance(satdict.cand_nacc, satdict.cand_acc);
      a->new_states(satdict.cand_size);

      // Last transition set in the automaton.
      unsigned last_aut_trans = -1U;
      // Last transition read from the SAT result.
      const transition* last_sat_trans = nullptr;

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

      dout << "--- transition variables ---\n";
      std::map<int, acc_cond::mark_t> state_acc;
      std::set<src_cond> seen_trans;
      for (int v: solution)
	{
	  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())
	    {
	      // Skip (s,l,d2) if we have already seen some (s,l,d1).
	      if (seen_trans.insert(src_cond(t->second.src,
					     t->second.cond)).second)
		{
		  acc_cond::mark_t acc = 0U;
		  if (state_based)
		    {
		      auto i = state_acc.find(t->second.src);
		      if (i != state_acc.end())
			acc = i->second;
		    }

		  last_aut_trans = a->new_edge(t->second.src,
					       t->second.dst,
					       t->second.cond, acc);
		  last_sat_trans = &t->second;

		  dout << v << '\t' << t->second << "δ\n";
		}
	    }
	  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)
		    {
		      assert(!state_based);
		      auto& v = a->edge_data(last_aut_trans).acc;
		      v |= ta->second.acc;
		    }
		  else if (state_based)
		    {
		      auto& v = state_acc[ta->second.src];
		      v |= ta->second.acc;
		    }
		}
	    }
	}
#if DEBUG
      dout << "--- pathid variables ---\n";
      for (auto pit: satdict.pathid)
	if (positive.find(pit.second) != positive.end())
	  dout << pit.second << '\t' << pit.first << "C\n";
#endif

      a->merge_edges();
      return a;
    }
  }

  twa_graph_ptr
  dtwa_sat_synthetize(const const_twa_graph_ptr& a,
		      unsigned target_acc_number,
		      const acc_cond::acc_code& target_acc,
		      int target_state_number,
		      bool state_based, bool colored)
  {
    if (target_state_number == 0)
      return nullptr;
    trace << "dtwa_sat_synthetize(..., nacc = " << target_acc_number
	  << ", acc = \"" << target_acc
	  << "\", states = " << target_state_number
	  << ", state_based = " << state_based << ")\n";

    dict d(a);
    d.cand_size = target_state_number;
    d.cand_nacc = target_acc_number;
    d.cand_acc = target_acc;

    satsolver solver;
    satsolver::solution_pair solution;

    timer_map t;
    t.start("encode");
    sat_stats s = dtwa_to_sat(solver(), a, d, state_based, colored);
    t.stop("encode");
    t.start("solve");
    solution = solver.get_solution();
    t.stop("solve");

    twa_graph_ptr res = nullptr;
    if (!solution.second.empty())
      res = sat_build(solution.second, d, a, state_based);

    // Always copy the environment variable into a static string,
    // so that we (1) look it up once, but (2) won't crash if the
    // environment is changed.
    static std::string log = []()
      {
	auto s = getenv("SPOT_SATLOG");
	return s ? s : "";
      }();
    if (!log.empty())
      {
	std::fstream out(log,
			 std::ios_base::app | std::ios_base::out);
	out.exceptions(std::ifstream::failbit | std::ifstream::badbit);
	const timer& te = t.timer("encode");
	const timer& ts = t.timer("solve");
	out << target_state_number << ',';
	if (res)
	  {
	    twa_sub_statistics st = sub_stats_reachable(res);
	    out << st.states << ',' << st.edges << ',' << st.transitions;
	  }
	else
	  {
	    out << ",,";
	  }
	out << ','
	    << s.first << ',' << s.second << ','
	    << te.utime() << ',' << te.stime() << ','
	    << ts.utime() << ',' << ts.stime() << '\n';
      }
    static bool show = getenv("SPOT_SATSHOW");
    if (show && res)
      print_dot(std::cout, res);

    trace << "dtwa_sat_synthetize(...) = " << res << '\n';
    return res;
  }


  namespace
  {
    // Chose a good reference automaton given two automata.
    //
    // The right automaton only is allowed to be null.  In that
    // case the left automaton is returned.
    //
    // The selection relies on the fact that the SAT encoding is
    // quadratic in the number of input states, and exponential in the
    // number of input sets.
    static const_twa_graph_ptr
    best_aut(const const_twa_graph_ptr& left,
	     const const_twa_graph_ptr& right)
    {
      if (right == nullptr)
	return left;
      auto lstates = left->num_states();
      auto lsets = left->num_sets();
      auto rstates = right->num_states();
      auto rsets = right->num_sets();
      if (lstates <= rstates && lsets <= rsets)
	return left;
      if (lstates >= rstates && lsets >= rsets)
	return right;

      long long unsigned lw = (1ULL << lsets) * lstates * lstates;
      long long unsigned rw = (1ULL << rsets) * rstates * rstates;

      return lw <= rw ? left : right;
    }
  }

  twa_graph_ptr
  dtwa_sat_minimize(const const_twa_graph_ptr& a,
		    unsigned target_acc_number,
		    const acc_cond::acc_code& target_acc,
		    bool state_based, int max_states,
		    bool colored)
  {
    int n_states = (max_states < 0) ?
      stats_reachable(a).states : max_states + 1;

    twa_graph_ptr prev = nullptr;
    for (;;)
      {
	auto src = best_aut(a, prev);
	auto next = dtwa_sat_synthetize(src, target_acc_number,
					target_acc, --n_states,
					state_based, colored);
	if (!next)
	  return prev;
	else
	  n_states = stats_reachable(next).states;
	prev = next;
      }
    SPOT_UNREACHABLE();
  }

  twa_graph_ptr
  dtwa_sat_minimize_dichotomy(const const_twa_graph_ptr& a,
			      unsigned target_acc_number,
			      const acc_cond::acc_code& target_acc,
			      bool state_based, int max_states,
			      bool colored)
  {
    if (max_states < 1)
      max_states = stats_reachable(a).states - 1;
    int min_states = 1;

    twa_graph_ptr prev = nullptr;
    while (min_states <= max_states)
      {
	int target = (max_states + min_states) / 2;
	auto src = best_aut(a, prev);
	auto next = dtwa_sat_synthetize(src, target_acc_number,
					target_acc, target, state_based,
					colored);
	if (!next)
	  {
	    min_states = target + 1;
	  }
	else
	  {
	    prev = next;
	    max_states = stats_reachable(next).states - 1;
	  }
      }
    return prev;
  }

  twa_graph_ptr
  sat_minimize(twa_graph_ptr a, const char* opt, bool state_based)
  {
    option_map om;
    auto err = om.parse_options(opt);
    if (err)
      {
	std::string e = "failed to parse option near ";
	e += err;
	throw std::runtime_error(e);
      }

    if (!is_deterministic(a))
      throw std::runtime_error
	("SAT-based minimization only work with deterministic automata");

    bool dicho = om.get("dichotomy", 0);
    int states = om.get("states", -1);
    int max_states = om.get("max-states", -1);
    auto accstr = om.get_str("acc");
    bool colored = om.get("colored", 0);

    // Assume we are going to use the input automaton acceptance...
    bool user_supplied_acc = false;
    acc_cond::acc_code target_acc = a->get_acceptance();
    int nacc = a->num_sets();

    if (accstr == "same")
      accstr.clear();
    // ... unless the user specified otherwise
    if (!accstr.empty())
      {
	user_supplied_acc = true;
	target_acc = acc_cond::acc_code(accstr.c_str());
	// Just in case we were given something like
	//  Fin(1) | Inf(3)
	// Rewrite it as
	//  Fin(0) | Inf(1)
	// without holes in the set numbers
	acc_cond::mark_t used = target_acc.used_sets();
	acc_cond a(used.max_set());
	target_acc = target_acc.strip(a.comp(used), true);
	nacc = used.count();
      }

    bool target_is_buchi = false;
    {
      acc_cond acccond(nacc);
      acccond.set_acceptance(target_acc);
      target_is_buchi = acccond.is_buchi();
    }

    if (int preproc = om.get("preproc", 3))
      {
	postprocessor post;
	auto sba = (state_based && a->prop_state_acc()) ?
	  postprocessor::SBAcc : postprocessor::Any;
	post.set_pref(postprocessor::Deterministic
		      | postprocessor::Complete
		      | sba);
	post.set_type(postprocessor::Generic);
	postprocessor::optimization_level level;
	switch (preproc)
	  {
	  case 1:
	    level = postprocessor::Low;
	    break;
	  case 2:
	    level = postprocessor::Medium;
	    break;
	  case 3:
	    level = postprocessor::High;
	    break;
	  default:
	    throw
	      std::runtime_error("preproc should be a value between 0 and 3.");
	  }
	post.set_level(level);
	a = post.run(a, nullptr);
	// If we have WDBA, it is necessarily minimal because
	// postprocessor always run WDBA minimization in Deterministic
	// mode.  If the desired output is a Büchi automaton, or not
	// desired acceptance was specified, stop here.  There is not
	// point in minimizing a minimal automaton.
	if (a->prop_inherently_weak() && a->prop_deterministic()
	    && (target_is_buchi || !user_supplied_acc))
	  return a;
      }
    else
      {
	complete_here(a);
      }

    if (states == -1 && max_states == -1)
      {
	if (state_based)
	  max_states = sbacc(a)->num_states();
	else
	  max_states = a->num_states();
	// If we have not user-supplied acceptance, the input
	// automaton is a valid one, so we start the search with one
	// less state.
	max_states -= !user_supplied_acc;
      }


    if (states == -1)
      {
	auto orig = a;
	if (!target_is_buchi || !a->acc().is_buchi() || colored)
	  a = (dicho ? dtwa_sat_minimize_dichotomy : dtwa_sat_minimize)
	    (a, nacc, target_acc, state_based, max_states, colored);
	else
	  a = (dicho ? dtba_sat_minimize_dichotomy : dtba_sat_minimize)
	    (a, state_based, max_states);

	if (!a && !user_supplied_acc)
	  a = orig;
      }
    else
      {
	if (!target_is_buchi || !a->acc().is_buchi() || colored)
	  a = dtwa_sat_synthetize(a, nacc, target_acc, states,
				  state_based, colored);
	else
	  a = dtba_sat_synthetize(a, states, state_based);
      }

    if (a)
      {
	if (state_based)
	  a = scc_filter_states(a);
	else
	  a = scc_filter(a);
      }
    return a;
  }

}