diff --git a/ChangeLog b/ChangeLog
index 288864639..78c942e17 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,12 @@
+2010-01-16  Damien Lefortier <dam@lrde.epita.fr>
+
+	Use taa_tgba_formula instead of taa_tgba_string in ltl_to_taa to
+	speed up a little the translation.
+
+	* src/tgbaalgos/ltl2taa.cc: Adjust.  Also fix a bug with
+	acceptance conditions in all_n_tuples.
+	* src/tgba/taatgba.cc, src/tgba/taatgba.hh: Adjust.
+
 2010-01-16  Damien Lefortier <dam@lrde.epita.fr>
 
 	Introduce taa_tgba_labelled<label> so that we can build
diff --git a/src/tgba/taatgba.cc b/src/tgba/taatgba.cc
index 0b5519cfa..d085c14ff 100644
--- a/src/tgba/taatgba.cc
+++ b/src/tgba/taatgba.cc
@@ -350,7 +350,7 @@ namespace spot
   `----------------*/
 
   std::string
-  taa_tgba_string::label_to_string(const std::string& label) const
+  taa_tgba_string::label_to_string(const std::string label) const
   {
     return label;
   }
diff --git a/src/tgba/taatgba.hh b/src/tgba/taatgba.hh
index b12fddcfa..8ca8088e6 100644
--- a/src/tgba/taatgba.hh
+++ b/src/tgba/taatgba.hh
@@ -338,7 +338,7 @@ namespace spot
     taa_tgba_string(bdd_dict* dict) :
       taa_tgba_labelled<std::string, string_hash>(dict) {};
   protected:
-    std::string label_to_string(const std::string& label) const;
+    virtual std::string label_to_string(const std::string label) const;
   };
 
   class taa_tgba_formula :
@@ -348,7 +348,7 @@ namespace spot
     taa_tgba_formula(bdd_dict* dict):
       taa_tgba_labelled<const ltl::formula*, ltl::formula_ptr_hash>(dict) {};
   protected:
-    std::string label_to_string(const ltl::formula* label) const;
+    virtual std::string label_to_string(const ltl::formula* label) const;
   };
 }
 
diff --git a/src/tgbaalgos/ltl2taa.cc b/src/tgbaalgos/ltl2taa.cc
index 708a2276d..65efa8a10 100644
--- a/src/tgbaalgos/ltl2taa.cc
+++ b/src/tgbaalgos/ltl2taa.cc
@@ -39,7 +39,7 @@ namespace spot
     class ltl2taa_visitor : public const_visitor
     {
     public:
-      ltl2taa_visitor(taa_tgba_string* res, language_containment_checker* lcc,
+      ltl2taa_visitor(taa_tgba_formula* res, language_containment_checker* lcc,
 		      bool refined = false, bool negated = false)
 	: res_(res), refined_(refined), negated_(negated),
 	  lcc_(lcc), init_(), succ_(), to_free_()
@@ -51,7 +51,7 @@ namespace spot
       {
       }
 
-      taa_tgba_string*
+      taa_tgba_formula*
       result()
       {
 	for (unsigned i = 0; i < to_free_.size(); ++i)
@@ -69,28 +69,35 @@ namespace spot
 	  f = unop::instance(unop::Not, node->clone());
 	  to_free_.push_back(f);
 	}
-	init_ = to_string(f);
-	std::vector<std::string> dst;
+	init_ = f;
+	std::vector<const formula*> dst;
+	std::vector<const formula*> a;
 
-	dst.push_back(std::string("sink"));
+	// A little hack to define a sink
+	dst.push_back(unop::instance(unop::Finish, constant::true_instance()));
+	to_free_.push_back(dst[0]);
 	taa_tgba::transition* t = res_->create_transition(init_, dst);
 	res_->add_condition(t, f->clone());
-	succ_state ss = { dst, f, constant::true_instance() };
+	succ_state ss = { dst, f, a };
 	succ_.push_back(ss);
       }
 
       void
       visit(const constant* node)
       {
-	init_ = to_string(node);
-	std::vector<std::string> dst;
+	init_ = node;
 	switch (node->val())
 	{
 	  case constant::True:
 	  {
-	    dst.push_back(std::string("sink"));
+	    std::vector<const formula*> dst;
+	    std::vector<const formula*> a;
+	    // A little hack to define a sink
+	    dst.push_back(unop::instance(unop::Finish,
+					 constant::true_instance()));
+	    to_free_.push_back(dst[0]);
 	    res_->create_transition(init_, dst);
-	    succ_state ss = { dst, node, constant::true_instance() };
+	    succ_state ss = { dst, node, a };
 	    succ_.push_back(ss);
 	    return;
 	  }
@@ -107,18 +114,19 @@ namespace spot
 	negated_ = node->op() == unop::Not;
 	ltl2taa_visitor v = recurse(node->child());
 
-	init_ = to_string(node);
-	std::vector<std::string> dst;
+	init_ = node;
 	switch (node->op())
 	{
 	  case unop::X:
 	  {
+	    std::vector<const formula*> dst;
+	    std::vector<const formula*> a;
 	    if (v.succ_.empty()) // Handle X(0)
 	      return;
 	    dst.push_back(v.init_);
 	    res_->create_transition(init_, dst);
 	    succ_state ss =
-	      { dst, constant::true_instance(), constant::true_instance() };
+	      { dst, constant::true_instance(), a };
 	    succ_.push_back(ss);
 	    return;
 	  }
@@ -143,7 +151,7 @@ namespace spot
 	ltl2taa_visitor v1 = recurse(node->first());
 	ltl2taa_visitor v2 = recurse(node->second());
 
-	init_ = to_string(node);
+	init_ = node;
 	std::vector<succ_state>::iterator i1;
 	std::vector<succ_state>::iterator i2;
 	taa_tgba::transition* t = 0;
@@ -161,10 +169,10 @@ namespace spot
 		  (remove(i1->Q.begin(), i1->Q.end(), v1.init_), i1->Q.end());
 
 	      i1->Q.push_back(init_); // Add the initial state
-	      i1->acc = node;
+	      i1->acc.push_back(node);
 	      t = res_->create_transition(init_, i1->Q);
 	      res_->add_condition(t, i1->condition->clone());
-	      res_->add_acceptance_condition(t, node->clone());
+	      res_->add_acceptance_condition(t, node->second()->clone());
 	      succ_.push_back(*i1);
 	    }
 	    for (i2 = v2.succ_.begin(); i2 != v2.succ_.end(); ++i2)
@@ -181,19 +189,20 @@ namespace spot
 	    {
 	      for (i1 = v1.succ_.begin(); i1 != v1.succ_.end(); ++i1)
 	      {
-		std::vector<std::string> u; // Union
-		std::copy(i1->Q.begin(), i1->Q.end(), ii(u, u.begin()));
+		std::vector<const formula*> u; // Union
+		std::vector<const formula*> a; // Acceptance conditions
+		std::copy(i1->Q.begin(), i1->Q.end(), ii(u, u.end()));
 		formula* f = i1->condition->clone(); // Refined rule
 		if (!refined_ || !contained)
 		{
-		  std::copy(i2->Q.begin(), i2->Q.end(), ii(u, u.begin()));
+		  std::copy(i2->Q.begin(), i2->Q.end(), ii(u, u.end()));
 		  f = multop::instance(multop::And, f, i2->condition->clone());
 		}
 		to_free_.push_back(f);
 
 		t = res_->create_transition(init_, u);
 		res_->add_condition(t, f->clone());
-		succ_state ss = { u, f, constant::true_instance() };
+		succ_state ss = { u, f, a };
 		succ_.push_back(ss);
 	      }
 
@@ -204,8 +213,9 @@ namespace spot
 	      i2->Q.push_back(init_); // Add the initial state
 	      t = res_->create_transition(init_, i2->Q);
 	      res_->add_condition(t, i2->condition->clone());
-	      if (refined_ && i2->acc != constant::true_instance())
-		res_->add_acceptance_condition(t, i2->acc->clone());
+	      if (refined_)
+		for (unsigned i = 0; i < i2->acc.size(); ++i)
+		  res_->add_acceptance_condition(t, i2->acc[i]->clone());
 	      succ_.push_back(*i2);
 	    }
 	    return;
@@ -230,7 +240,7 @@ namespace spot
 	    ok = false;
 	}
 
-	init_ = to_string(node);
+	init_ = node;
 	std::vector<succ_state>::iterator i;
 	taa_tgba::transition* t = 0;
 	switch (node->op())
@@ -242,7 +252,7 @@ namespace spot
 	    {
 	      if (refined_)
 	      {
-		std::vector<std::string> v; // All sub initial states.
+		std::vector<const formula*> v; // All sub initial states.
 		sort(p[n].Q.begin(), p[n].Q.end());
 		for (unsigned m = 0; m < node->size(); ++m)
 		{
@@ -253,7 +263,7 @@ namespace spot
 
 		if (v.size() == node->size())
 		{
-		  std::vector<std::string> Q;
+		  std::vector<const formula*> Q;
 		  sort(v.begin(), v.end());
 		  for (unsigned m = 0; m < p[n].Q.size(); ++m)
 		    if (!binary_search(v.begin(), v.end(), p[n].Q[m]))
@@ -261,8 +271,8 @@ namespace spot
 		  Q.push_back(init_);
 		  t = res_->create_transition(init_, Q);
 		  res_->add_condition(t, p[n].condition->clone());
-		  if (p[n].acc != constant::true_instance())
-		    res_->add_acceptance_condition(t, p[n].acc->clone());
+		  for (unsigned i = 0; i < p[n].acc.size(); ++i)
+		    res_->add_acceptance_condition(t, p[n].acc[i]->clone());
 		  succ_.push_back(p[n]);
 		  return;
 		}
@@ -305,23 +315,23 @@ namespace spot
       }
 
     private:
-      taa_tgba_string* res_;
+      taa_tgba_formula* res_;
       bool refined_;
       bool negated_;
       language_containment_checker* lcc_;
 
       typedef std::insert_iterator<
-	std::vector<std::string>
+	std::vector<const formula*>
       > ii;
 
       struct succ_state
       {
-	std::vector<std::string> Q; // States
+	std::vector<const formula*> Q; // States
 	const formula* condition;
-	const formula* acc;
+	std::vector<const formula*> acc;
       };
 
-      std::string init_;
+      const formula* init_;
       std::vector<succ_state> succ_;
 
       std::vector<const formula*> to_free_;
@@ -338,20 +348,25 @@ namespace spot
 
 	while (pos[0] != 0)
 	{
-	  std::vector<std::string> u; // Union
+	  std::vector<const formula*> u; // Union
+	  std::vector<const formula*> a; // Acceptance conditions
 	  formula* f = constant::true_instance();
-	  formula* a = constant::true_instance();
+	  formula* g = 0;
 	  for (unsigned i = 0; i < vs.size(); ++i)
 	  {
 	    if (vs[i].succ_.empty())
 	      continue;
 	    const succ_state& ss(vs[i].succ_[pos[i] - 1]);
-	    std::copy(ss.Q.begin(), ss.Q.end(), ii(u, u.begin()));
+	    std::copy(ss.Q.begin(), ss.Q.end(), ii(u, u.end()));
 	    f = multop::instance(multop::And, ss.condition->clone(), f);
-	    a = multop::instance(multop::And, ss.acc->clone(), a);
+	    for (unsigned i = 0; i < ss.acc.size(); ++i)
+	    {
+	      g = ss.acc[i]->clone();
+	      a.push_back(g);
+	      to_free_.push_back(g);
+	    }
 	  }
 	  to_free_.push_back(f);
-	  to_free_.push_back(a);
 	  succ_state ss = { u, f, a };
 	  product.push_back(ss);
 
@@ -381,7 +396,7 @@ namespace spot
     const ltl::formula* f2 = ltl::negative_normal_form(f1);
     f1->destroy();
 
-    spot::taa_tgba_string* res = new spot::taa_tgba_string(dict);
+    spot::taa_tgba_formula* res = new spot::taa_tgba_formula(dict);
     bdd_dict b;
     language_containment_checker* lcc =
       new language_containment_checker(&b, false, false, false, false);