diff --git a/src/tgbaalgos/Makefile.am b/src/tgbaalgos/Makefile.am
index 42e21446e..7905aa803 100644
--- a/src/tgbaalgos/Makefile.am
+++ b/src/tgbaalgos/Makefile.am
@@ -29,13 +29,14 @@ tgbaalgosdir = $(pkgincludedir)/tgbaalgos
 
 tgbaalgos_HEADERS = \
   bfssteps.hh \
+  complete.hh \
   compsusp.hh \
   cutscc.hh \
   cycles.hh \
   dbacomp.hh \
   degen.hh \
-  dotty.hh \
   dottydec.hh \
+  dotty.hh \
   dupexp.hh \
   eltl2tgba_lacim.hh \
   emptiness.hh \
@@ -56,12 +57,13 @@ tgbaalgos_HEADERS = \
   randomgraph.hh \
   reachiter.hh \
   reducerun.hh \
+  reductgba_sim.hh \
   replayrun.hh \
   rundotdec.hh \
   safety.hh \
   save.hh \
-  scc.hh \
   sccfilter.hh \
+  scc.hh \
   se05.hh \
   simulation.hh \
   stats.hh \
@@ -69,12 +71,12 @@ tgbaalgos_HEADERS = \
   tau03.hh \
   tau03opt.hh \
   translate.hh \
-  reductgba_sim.hh \
   word.hh
 
 noinst_LTLIBRARIES = libtgbaalgos.la
 libtgbaalgos_la_SOURCES = \
   bfssteps.cc \
+  complete.cc \
   compsusp.cc \
   cutscc.cc \
   cycles.cc \
@@ -102,6 +104,7 @@ libtgbaalgos_la_SOURCES = \
   randomgraph.cc \
   reachiter.cc \
   reducerun.cc \
+  reductgba_sim.cc \
   replayrun.cc \
   rundotdec.cc \
   safety.cc \
@@ -115,7 +118,6 @@ libtgbaalgos_la_SOURCES = \
   tau03.cc \
   tau03opt.cc \
   translate.cc \
-  reductgba_sim.cc \
   weight.cc \
   weight.hh \
   word.cc
diff --git a/src/tgbaalgos/complete.cc b/src/tgbaalgos/complete.cc
new file mode 100644
index 000000000..8de040498
--- /dev/null
+++ b/src/tgbaalgos/complete.cc
@@ -0,0 +1,118 @@
+// -*- 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 "complete.hh"
+#include "reachiter.hh"
+#include "ltlast/constant.hh"
+
+namespace spot
+{
+
+  namespace
+  {
+    class tgbacomplete_iter:
+      public tgba_reachable_iterator_depth_first_stack
+    {
+      bdd_dict* dict_;
+      tgba_explicit_number* out_;
+      bdd addacc_;
+
+      typedef state_explicit_number::transition trans;
+    public:
+      tgbacomplete_iter(const tgba* a)
+	: tgba_reachable_iterator_depth_first_stack(a),
+	  dict_(a->get_dict()),
+	  out_(new tgba_explicit_number(dict_)),
+	  addacc_(bddfalse)
+      {
+	dict_->register_all_variables_of(a, out_);
+
+	if (a->number_of_acceptance_conditions() == 0)
+	  {
+	    const ltl::formula* t = ltl::constant::true_instance();
+	    int accvar =
+	      dict_->register_acceptance_variable(t, out_);
+	    addacc_ = bdd_ithvar(accvar);
+	    out_->set_acceptance_conditions(addacc_);
+	  }
+	else
+	  {
+	    out_->set_acceptance_conditions(a->all_acceptance_conditions());
+	  }
+      }
+
+      tgba_explicit_number*
+      result()
+      {
+	return out_;
+      }
+
+      void
+      end()
+      {
+	out_->merge_transitions();
+	// create a sink state if needed.
+	if (out_->has_state(0))
+	  {
+	    trans* t = out_->create_transition(0, 0);
+	    t->condition = bddtrue;
+	  }
+      }
+
+      void process_state(const state*, int n,
+			 tgba_succ_iterator* i)
+      {
+	// add a transition to a sink state if the state is not complete.
+	bdd all = bddtrue;
+	for (i->first(); !i->done(); i->next())
+	  all -= i->current_condition();
+	if (all != bddfalse)
+	  {
+	    trans* t = out_->create_transition(n, 0);
+	    t->condition = all;
+	  }
+      }
+
+      void
+      process_link(const state*, int in,
+		   const state*, int out,
+		   const tgba_succ_iterator* si)
+      {
+	assert(in > 0);
+	assert(out > 0);
+	trans* t1 = out_->create_transition(in, out);
+
+	t1->condition = si->current_condition();
+	t1->acceptance_conditions =
+	  si->current_acceptance_conditions() | addacc_;
+      }
+
+    };
+
+  } // anonymous
+
+  tgba_explicit_number* tgba_complete(const tgba* aut)
+  {
+    tgbacomplete_iter ci(aut);
+    ci.run();
+    return ci.result();
+  }
+}
+
+
diff --git a/src/tgbaalgos/complete.hh b/src/tgbaalgos/complete.hh
new file mode 100644
index 000000000..35a173980
--- /dev/null
+++ b/src/tgbaalgos/complete.hh
@@ -0,0 +1,32 @@
+// -*- 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_COMPLETE_HH
+# define SPOT_TGBAALGOS_COMPLETE_HH
+
+#include "tgba/tgbaexplicit.hh"
+
+namespace spot
+{
+  /// Complete a TGBA
+  SPOT_API tgba_explicit_number*
+  tgba_complete(const tgba* aut);
+}
+
+#endif // SPOT_TGBAALGOS_COMPLETE_HH