diff --git a/src/tgbaalgos/Makefile.am b/src/tgbaalgos/Makefile.am
index 7905aa803..3e55350f1 100644
--- a/src/tgbaalgos/Makefile.am
+++ b/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 \
diff --git a/src/tgbaalgos/dtbasat.cc b/src/tgbaalgos/dtbasat.cc
new file mode 100644
index 000000000..e2bc00c7f
--- /dev/null
+++ b/src/tgbaalgos/dtbasat.cc
@@ -0,0 +1,764 @@
+// -*- 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
+
+      dout << "--- transition variables ---\n";
+      for (;;)
+	{
+	  int v;
+	  sol >> v;
+	  if (!sol)
+	    break;
+
+	  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 << "δ\n";
+	    }
+	  else
+	    {
+	      t = satdict.revtransacc.find(v);
+	      // This assumes that the sat solvers output variables in
+	      // increasing order.
+	      if (t != satdict.revtransacc.end())
+		{
+		  dout << v << "\t" << t->second << "F\n";
+
+		  if (last_sat_trans && t->second == *last_sat_trans)
+		    last_aut_trans->acceptance_conditions = acc;
+		}
+	    }
+	}
+#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*
+  dba_sat_minimize(const tgba* a, int target_state_number)
+  {
+    int ref_states =
+      target_state_number == -1
+      ? stats_reachable(a).states - 1
+      : target_state_number;
+
+    std::string current_solution;
+    std::string last_solution;
+    dict* last = 0;
+    dict* current = 0;
+    temporary_file* cnf = 0;
+    temporary_file* out = 0;
+
+    do
+      {
+	if (DEBUG && current)
+	  {
+	    xrename(out->name(), "dtba-sat.out");
+	    xrename(cnf->name(), "dtba-sat.cnf");
+	  }
+	delete out;
+	delete cnf;
+	std::swap(current_solution, last_solution);
+	delete last;
+	last = current;
+	current = new dict;
+	current->cand_size = ref_states--;
+
+	cnf = create_tmpfile("dtba-sat-", ".cnf");
+
+	// FIXME: we should use proper temporary names
+	std::fstream cnfs(cnf->name(),
+			  std::ios_base::trunc | std::ios_base::out);
+	dtba_to_sat(cnfs, a, *current);
+	cnfs.close();
+
+	out = create_tmpfile("dtba-sat-", ".out");
+
+	const char* satsolver = getenv("SATSOLVER");
+	if (!satsolver)
+	  satsolver = "glucose";
+
+	std::string s(satsolver);
+	s += " ";
+	s += cnf->name();
+	s += " > ";
+	s += out->name();
+	system(s.c_str());
+
+	current_solution = get_solution(out->name());
+      }
+    while (target_state_number == -1 && !current_solution.empty());
+
+    if (target_state_number != -1)
+      {
+	std::swap(current_solution, last_solution);
+	last = current;
+      }
+    else
+      {
+	delete current;
+      }
+
+    tgba_explicit_number* res;
+    if (last == 0)
+      {
+	res = 0;
+	if (DEBUG)
+	  {
+	    xrename(out->name(), "dtba-sat.out");
+	    xrename(cnf->name(), "dtba-sat.cnf");
+	  }
+      }
+    else
+      {
+	res = sat_build(last_solution, *last, a);
+	delete last;
+      }
+
+    delete out;
+    delete cnf;
+    return res;
+  }
+
+}
diff --git a/src/tgbaalgos/dtbasat.hh b/src/tgbaalgos/dtbasat.hh
new file mode 100644
index 000000000..5cd820fb2
--- /dev/null
+++ b/src/tgbaalgos/dtbasat.hh
@@ -0,0 +1,46 @@
+// -*- 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/>.
+
+#ifndef SPOT_TGBAALGOS_DTBASAT_HH
+# define SPOT_TGBAALGOS_DTBASAT_HH
+
+#include <iosfwd>
+#include "tgba/tgba.hh"
+#include "tgba/tgbaexplicit.hh"
+
+namespace spot
+{
+  /// \brief Attempt to reduce a deterministic TBA with a SAT solver.
+  ///
+  /// \param a the TGBA to reduce.  It should have only one acceptance
+  ///  set and be deterministic.  I.e., it should be a deterministic TBA.
+  ///
+  /// \param target_state_number the expected number of states wanted
+  /// in the resulting automaton.  If \a target_state_number is left
+  /// to its default value of -1, this function will attempt to build
+  /// the smallest possible deterministic TBA is can produce.
+  ///
+  /// If no automaton with \a target_state_number states is found, or
+  /// (in case <code>target_state_number == -1</code>) if no smaller
+  /// automaton is found, then a null pointer is returned.
+  SPOT_API tgba_explicit_number*
+  dba_sat_minimize(const tgba* a, int target_state_number = -1);
+}
+
+#endif // SPOT_TGBAALGOS_DTBASAT_HH
diff --git a/src/tgbatest/ltl2tgba.cc b/src/tgbatest/ltl2tgba.cc
index 301786329..b0bf6b254 100644
--- a/src/tgbatest/ltl2tgba.cc
+++ b/src/tgbatest/ltl2tgba.cc
@@ -71,6 +71,8 @@
 #include "tgbaalgos/compsusp.hh"
 #include "tgbaalgos/powerset.hh"
 #include "tgbaalgos/dbacomp.hh"
+#include "tgbaalgos/complete.hh"
+#include "tgbaalgos/dtbasat.hh"
 
 #include "taalgos/tgba2ta.hh"
 #include "taalgos/dotty.hh"
@@ -402,7 +404,7 @@ main(int argc, char** argv)
   bool spin_comments = false;
   spot::ltl::environment& env(spot::ltl::default_environment::instance());
   spot::ltl::atomic_prop_set* unobservables = 0;
-  spot::tgba* system = 0;
+  spot::tgba* system_aut = 0;
   const spot::tgba* product_to_free = 0;
   spot::bdd_dict* dict = new spot::bdd_dict();
   spot::timer_map tm;
@@ -428,6 +430,8 @@ main(int argc, char** argv)
   bool cs_nosimul = true;
   bool cs_early_start = false;
   bool cs_oblig = false;
+  bool opt_complete = false;
+  int opt_dtbasat = -1;
 
   for (;;)
     {
@@ -596,8 +600,8 @@ main(int argc, char** argv)
 	  tm.start("reading -KP's argument");
 
 	  spot::kripke_parse_error_list pel;
-	  system = spot::kripke_parse(argv[formula_index] + 3,
-				      pel, dict, env, debug_opt);
+	  system_aut = spot::kripke_parse(argv[formula_index] + 3,
+					  pel, dict, env, debug_opt);
 	  if (spot::format_kripke_parse_errors(std::cerr,
 					       argv[formula_index] + 2, pel))
 	    return 2;
@@ -678,7 +682,7 @@ main(int argc, char** argv)
 	    return 2;
 	  s->merge_transitions();
 	  tm.stop("reading -P's argument");
-	  system = s;
+	  system_aut = s;
 	}
       else if (!strcmp(argv[formula_index], "-r"))
 	{
@@ -764,6 +768,10 @@ main(int argc, char** argv)
 	{
 	  simpcache_stats = true;
 	}
+      else if (!strcmp(argv[formula_index], "-RC"))
+	{
+	  opt_complete = true;
+	}
       else if (!strcmp(argv[formula_index], "-RDS"))
         {
           reduction_dir_sim = true;
@@ -805,6 +813,14 @@ main(int argc, char** argv)
 	  if (argv[formula_index][3] != 0)
 	    opt_determinize_threshold = to_int(argv[formula_index] + 3);
         }
+      else if (!strncmp(argv[formula_index], "-RS", 3))
+        {
+	  if (argv[formula_index][3] != 0)
+	    opt_dtbasat = to_int(argv[formula_index] + 3);
+	  else
+	    opt_dtbasat = -1;
+          //output = -1;
+        }
       else if (!strcmp(argv[formula_index], "-RT"))
         {
           opt_bisim_ta = true;
@@ -1435,6 +1451,17 @@ main(int argc, char** argv)
 	    }
 	}
 
+      spot::tgba* determinized = 0;
+      if (opt_determinize && a->number_of_acceptance_conditions() <= 1
+	  && (!f || f->is_syntactic_recurrence()))
+	{
+	  tm.start("determinization 2");
+	  determinized = tba_determinize(a, 0, opt_determinize_threshold);
+	  tm.stop("determinization 2");
+	  if (determinized)
+	    a = determinized;
+	}
+
       const spot::tgba* monitor = 0;
       if (opt_monitor)
 	{
@@ -1446,15 +1473,55 @@ main(int argc, char** argv)
 				// pointless.
 	}
 
-      spot::tgba* determinized = 0;
-      if (opt_determinize && a->number_of_acceptance_conditions() <= 1
-	  && (!f || f->is_syntactic_recurrence()))
+      if (degeneralized || determinized)
+	{
+	  if (reduction_dir_sim && !reduction_iterated_sim)
+	    {
+	      tm.start("direct simulation 2");
+	      spot::tgba* tmp = spot::simulation(a);
+	      delete temp_dir_sim;
+	      a = temp_dir_sim = tmp;
+	      tm.stop("direct simulation 2");
+	      assume_sba = false;
+	    }
+
+	  if (reduction_rev_sim && !reduction_iterated_sim)
+	    {
+	      tm.start("reverse simulation 2");
+	      spot::tgba* tmp = spot::cosimulation(a);
+	      delete temp_rev_sim;
+	      a = temp_rev_sim = tmp;
+	      tm.stop("reverse simulation 2");
+	      assume_sba = false;
+	    }
+
+	  if (reduction_iterated_sim)
+	    {
+	      tm.start("Reduction w/ iterated simulations");
+	      spot::tgba* tmp = spot::iterated_simulations(a);
+	      delete temp_iterated_sim;
+	      a = temp_iterated_sim = tmp;
+	      tm.stop("Reduction w/ iterated simulations");
+	      assume_sba = false;
+	    }
+	}
+
+      spot::tgba* completed = 0;
+      if (opt_complete)
 	{
 	  tm.start("determinization");
-	  determinized = tba_determinize(a, 0, opt_determinize_threshold);
+	  a = completed = tgba_complete(a);
 	  tm.stop("determinization");
-	  if (determinized)
-	    a = determinized;
+	}
+
+      spot::tgba* satminimized = 0;
+      if (opt_dtbasat >= 0)
+	{
+	  tm.start("dtbasat");
+	  satminimized = dba_sat_minimize(a, opt_dtbasat);
+	  tm.stop("dtbasat");
+	  if (satminimized)
+	    a = satminimized;
 	}
 
       spot::tgba* complemented = 0;
@@ -1465,6 +1532,29 @@ main(int argc, char** argv)
 	  tm.stop("DBA complement");
 	}
 
+      if (complemented || satminimized || determinized)
+	{
+	  if (scc_filter && (reduction_dir_sim || reduction_rev_sim))
+	    {
+	      tm.start("SCC-filter post-sim");
+	      delete aut_scc;
+	      // Do not filter_all for SBA
+	      aut_scc = a = spot::scc_filter(a, assume_sba ?
+					     false : scc_filter_all);
+	      tm.stop("SCC-filter post-sim");
+	    }
+	}
+
+      if (opt_monitor)
+	{
+	  tm.start("Monitor minimization");
+	  minimized = a = minimize_monitor(a);
+	  tm.stop("Monitor minimization");
+	  assume_sba = false; 	// All states are accepting, so double
+				// circles in the dot output are
+				// pointless.
+	}
+
       const spot::tgba* expl = 0;
       switch (dupexp)
 	{
@@ -1569,9 +1659,9 @@ main(int argc, char** argv)
 
       spot::tgba* product_degeneralized = 0;
 
-      if (system)
+      if (system_aut)
         {
-	  product_to_free = a = new spot::tgba_product(system, a);
+	  product_to_free = a = new spot::tgba_product(system_aut, a);
 
 	  assume_sba = false;
 
@@ -1921,12 +2011,14 @@ main(int argc, char** argv)
         f->destroy();
       delete product_degeneralized;
       delete product_to_free;
-      delete system;
+      delete system_aut;
       delete expl;
       delete monitor;
       delete minimized;
+      delete satminimized;
       delete degeneralized;
       delete determinized;
+      delete completed;
       delete complemented;
       delete aut_scc;
       delete to_free;