diff --git a/ChangeLog b/ChangeLog
index 9d297cae6..288864639 100644
--- a/ChangeLog
+++ b/ChangeLog
@@ -1,3 +1,17 @@
+2010-01-16  Damien Lefortier <dam@lrde.epita.fr>
+
+	Introduce taa_tgba_labelled<label> so that we can build
+	taa_tgba instances labelled by other objects than strings
+	in the same way Alexandre did for tgba_explicit.
+
+	* src/tgba/taatgba.cc, src/tgba/taatgba.hh: Split taa_tgba in two
+	levels: taa_tgba with no label and taa_tgba_labelled templated by
+	the type of the label.  Define taa_tgba_string (with the interface
+	of the former taa_tgba class) and taa_tgba_formula for future use
+	in ltl2taa.cc.
+	* src/tgbaalgos/ltl2taa.cc, src/tgbatest/taatgba.cc: Adjust to use
+	taa_tgba_string.
+
 2010-01-06  Damien Lefortier <dam@lrde.epita.fr>
 
 	Fix a longstanding bug reported by Guillaume Sadegh.
diff --git a/src/tgba/taatgba.cc b/src/tgba/taatgba.cc
index 65b14ba4c..0b5519cfa 100644
--- a/src/tgba/taatgba.cc
+++ b/src/tgba/taatgba.cc
@@ -24,6 +24,7 @@
 #include <iterator>
 #include <iostream>
 #include "tgba/formula2bdd.hh"
+#include "ltlvisit/tostring.hh"
 #include "misc/bddop.hh"
 #include "taatgba.hh"
 
@@ -34,7 +35,7 @@ namespace spot
   `--------*/
 
   taa_tgba::taa_tgba(bdd_dict* dict)
-    : name_state_map_(), state_name_map_(), dict_(dict),
+    : dict_(dict),
       all_acceptance_conditions_(bddfalse),
       all_acceptance_conditions_computed_(false),
       neg_acceptance_conditions_(bddtrue),
@@ -44,56 +45,12 @@ namespace spot
 
   taa_tgba::~taa_tgba()
   {
-    ns_map::iterator i;
-    for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
-    {
-      taa_tgba::state::iterator i2;
-      for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
-	delete *i2;
-      delete i->second;
-    }
     ss_vec::iterator j;
     for (j = state_set_vec_.begin(); j != state_set_vec_.end(); ++j)
       delete *j;
     dict_->unregister_all_my_variables(this);
   }
 
-  void
-  taa_tgba::set_init_state(const std::string& s)
-  {
-    std::vector<std::string> v(1);
-    v[0] = s;
-    set_init_state(v);
-  }
-
-  void
-  taa_tgba::set_init_state(const std::vector<std::string>& s)
-  {
-    init_ = add_state_set(s);
-  }
-
-  taa_tgba::transition*
-  taa_tgba::create_transition(const std::string& s,
-                             const std::vector<std::string>& d)
-  {
-    state* src = add_state(s);
-    state_set* dst = add_state_set(d);
-    transition* t = new transition;
-    t->dst = dst;
-    t->condition = bddtrue;
-    t->acceptance_conditions = bddfalse;
-    src->push_back(t);
-    return t;
-  }
-
-  taa_tgba::transition*
-  taa_tgba::create_transition(const std::string& s, const std::string& d)
-  {
-    std::vector<std::string> vec;
-    vec.push_back(d);
-    return create_transition(s, vec);
-  }
-
   void
   taa_tgba::add_condition(transition* t, const ltl::formula* f)
   {
@@ -101,51 +58,6 @@ namespace spot
     f->destroy();
   }
 
-  void
-  taa_tgba::add_acceptance_condition(transition* t, const ltl::formula* f)
-  {
-    if (dict_->acc_map.find(f) == dict_->acc_map.end())
-    {
-      int v = dict_->register_acceptance_variable(f, this);
-      bdd neg = bdd_nithvar(v);
-      neg_acceptance_conditions_ &= neg;
-
-      // Append neg to all acceptance conditions.
-      ns_map::iterator i;
-      for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
-      {
-	taa_tgba::state::iterator i2;
-	for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
-	  (*i2)->acceptance_conditions &= neg;
-      }
-
-      all_acceptance_conditions_computed_ = false;
-    }
-
-    bdd_dict::fv_map::iterator i = dict_->acc_map.find(f);
-    assert(i != dict_->acc_map.end());
-    f->destroy();
-    bdd v = bdd_ithvar(i->second);
-    t->acceptance_conditions |= v & bdd_exist(neg_acceptance_conditions_, v);
-  }
-
-  void
-  taa_tgba::output(std::ostream& os) const
-  {
-    ns_map::const_iterator i;
-    for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
-    {
-      taa_tgba::state::const_iterator i2;
-      os << "State: " << i->first << std::endl;
-      for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
-      {
-	os << " " << format_state_set((*i2)->dst)
-	   << ", C:" << (*i2)->condition
-	   << ", A:" << (*i2)->acceptance_conditions << std::endl;
-      }
-    }
-  }
-
   state*
   taa_tgba::get_init_state() const
   {
@@ -171,15 +83,6 @@ namespace spot
     return dict_;
   }
 
-  std::string
-  taa_tgba::format_state(const spot::state* s) const
-  {
-    const spot::state_set* se = dynamic_cast<const spot::state_set*>(s);
-    assert(se);
-    const state_set* ss = se->get_state();
-    return format_state_set(ss);
-  }
-
   bdd
   taa_tgba::all_acceptance_conditions() const
   {
@@ -230,58 +133,6 @@ namespace spot
     return res;
   }
 
-  taa_tgba::state*
-  taa_tgba::add_state(const std::string& name)
-  {
-    ns_map::iterator i = name_state_map_.find(name);
-    if (i == name_state_map_.end())
-    {
-      taa_tgba::state* s = new taa_tgba::state;
-      name_state_map_[name] = s;
-      state_name_map_[s] = name;
-      return s;
-    }
-    return i->second;
-  }
-
-  taa_tgba::state_set*
-  taa_tgba::add_state_set(const std::vector<std::string>& names)
-  {
-    state_set* ss = new state_set;
-    for (unsigned i = 0; i < names.size(); ++i)
-      ss->insert(add_state(names[i]));
-    state_set_vec_.push_back(ss);
-    return ss;
-  }
-
-  std::string
-  taa_tgba::format_state_set(const taa_tgba::state_set* ss) const
-  {
-    state_set::const_iterator i1 = ss->begin();
-    sn_map::const_iterator i2;
-    if (ss->empty())
-      return std::string("{}");
-    if (ss->size() == 1)
-    {
-      i2 = state_name_map_.find(*i1);
-      assert(i2 != state_name_map_.end());
-      return "{" + i2->second + "}";
-    }
-    else
-    {
-      std::string res("{");
-      while (i1 != ss->end())
-      {
-	i2 = state_name_map_.find(*i1++);
-	assert(i2 != state_name_map_.end());
-	res += i2->second;
-	res += ",";
-      }
-      res[res.size() - 1] = '}';
-      return res;
-    }
-  }
-
   /*----------.
   | state_set |
   `----------*/
@@ -493,4 +344,24 @@ namespace spot
     return all_acceptance_conditions_ -
       ((*i_)->acceptance_conditions & all_acceptance_conditions_);
   }
+
+  /*----------------.
+  | taa_tgba_string |
+  `----------------*/
+
+  std::string
+  taa_tgba_string::label_to_string(const std::string& label) const
+  {
+    return label;
+  }
+
+  /*-----------------.
+  | taa_tgba_formula |
+  `-----------------*/
+
+  std::string
+  taa_tgba_formula::label_to_string(const ltl::formula* label) const
+  {
+    return ltl::to_string(label);
+  }
 }
diff --git a/src/tgba/taatgba.hh b/src/tgba/taatgba.hh
index 9ec0fd416..b12fddcfa 100644
--- a/src/tgba/taatgba.hh
+++ b/src/tgba/taatgba.hh
@@ -32,7 +32,8 @@
 
 namespace spot
 {
-  /// \brief A Transition-based Alternating Automaton (TAA).
+  /// \brief A self-loop Transition-based Alternating Automaton (TAA)
+  /// which is seen as a TGBA (abstract class, see below).
   class taa_tgba : public tgba
   {
   public:
@@ -50,20 +51,7 @@ namespace spot
       const state_set* dst;
     };
 
-    void set_init_state(const std::string& state);
-    void set_init_state(const std::vector<std::string>& state);
-
-    transition*
-    create_transition(const std::string& src,
-		      const std::vector<std::string>& dst);
-    transition*
-    create_transition(const std::string& src, const std::string& dst);
-
     void add_condition(transition* t, const ltl::formula* f);
-    void add_acceptance_condition(transition* t, const ltl::formula* f);
-
-    /// \brief Output a TAA.
-    void output(std::ostream& os) const;
 
     /// TGBA interface.
     virtual ~taa_tgba();
@@ -73,17 +61,7 @@ namespace spot
 	      const spot::state* global_state = 0,
 	      const tgba* global_automaton = 0) const;
     virtual bdd_dict* get_dict() const;
-
-    /// \brief Format the state as a string for printing.
-    ///
-    /// If state is a spot::state_set of only one element, then the
-    /// string corresponding to state->get_state() is returned.
-    ///
-    /// Otherwise a string composed of each string corresponding to
-    /// each state->get_state() in the spot::state_set is returned,
-    /// e.g. like {string_1,...,string_n}.
-    virtual std::string format_state(const spot::state* state) const;
-
+    virtual std::string format_state(const spot::state* state) const = 0;
     virtual bdd all_acceptance_conditions() const;
     virtual bdd neg_acceptance_conditions() const;
 
@@ -91,18 +69,8 @@ namespace spot
     virtual bdd compute_support_conditions(const spot::state* state) const;
     virtual bdd compute_support_variables(const spot::state* state) const;
 
-    typedef Sgi::hash_map<
-      const std::string, taa_tgba::state*, string_hash
-      > ns_map;
-
-    typedef Sgi::hash_map<
-      const taa_tgba::state*, std::string, ptr_hash<taa_tgba::state>
-      > sn_map;
-
     typedef std::vector<taa_tgba::state_set*> ss_vec;
 
-    ns_map name_state_map_;
-    sn_map state_name_map_;
     bdd_dict* dict_;
     mutable bdd all_acceptance_conditions_;
     mutable bool all_acceptance_conditions_computed_;
@@ -114,17 +82,6 @@ namespace spot
     // Disallow copy.
     taa_tgba(const taa_tgba& other);
     taa_tgba& operator=(const taa_tgba& other);
-
-    /// \brief Return the taa_tgba::state for \a name, creating it if it
-    /// does not exist.  The first state added is the initial state
-    /// which can be overridden with set_init_state.
-    taa_tgba::state* add_state(const std::string& name);
-
-    /// \brief Return the taa::state_set for \a names.
-    taa_tgba::state_set* add_state_set(const std::vector<std::string>& names);
-
-    /// \brief Format a taa::state_set as a string for printing.
-    std::string format_state_set(const taa_tgba::state_set* ss) const;
   };
 
   /// Set of states deriving from spot::state.
@@ -193,6 +150,206 @@ namespace spot
     bdd all_acceptance_conditions_;
     seen_map seen_;
   };
+
+  /// A taa_tgba instance with states labeled by a given type.
+  /// Still an abstract class, see below.
+  template<typename label, typename label_hash>
+  class taa_tgba_labelled : public taa_tgba
+  {
+  public:
+    taa_tgba_labelled(bdd_dict* dict) : taa_tgba(dict) {};
+
+    virtual ~taa_tgba_labelled()
+    {
+      typename ns_map::iterator i;
+      for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
+      {
+	taa_tgba::state::iterator i2;
+	for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
+	  delete *i2;
+	delete i->second;
+      }
+    }
+
+    void set_init_state(const label& s)
+    {
+      std::vector<label> v(1);
+      v[0] = s;
+      set_init_state(v);
+    }
+    void set_init_state(const std::vector<label>& s)
+    {
+      init_ = add_state_set(s);
+    }
+
+    transition*
+    create_transition(const label& s,
+		      const std::vector<label>& d)
+    {
+      state* src = add_state(s);
+      state_set* dst = add_state_set(d);
+      transition* t = new transition;
+      t->dst = dst;
+      t->condition = bddtrue;
+      t->acceptance_conditions = bddfalse;
+      src->push_back(t);
+      return t;
+    }
+    transition*
+    create_transition(const label& s, const label& d)
+    {
+      std::vector<std::string> vec;
+      vec.push_back(d);
+      return create_transition(s, vec);
+    }
+
+    void add_acceptance_condition(transition* t, const ltl::formula* f)
+    {
+      if (dict_->acc_map.find(f) == dict_->acc_map.end())
+      {
+	int v = dict_->register_acceptance_variable(f, this);
+	bdd neg = bdd_nithvar(v);
+	neg_acceptance_conditions_ &= neg;
+
+	// Append neg to all acceptance conditions.
+	typename ns_map::iterator i;
+	for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
+	{
+	  taa_tgba::state::iterator i2;
+	  for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
+	    (*i2)->acceptance_conditions &= neg;
+	}
+
+	all_acceptance_conditions_computed_ = false;
+      }
+
+      bdd_dict::fv_map::iterator i = dict_->acc_map.find(f);
+      assert(i != dict_->acc_map.end());
+      f->destroy();
+      bdd v = bdd_ithvar(i->second);
+      t->acceptance_conditions |= v & bdd_exist(neg_acceptance_conditions_, v);
+    }
+
+    /// \brief Format the state as a string for printing.
+    ///
+    /// If state is a spot::state_set of only one element, then the
+    /// string corresponding to state->get_state() is returned.
+    ///
+    /// Otherwise a string composed of each string corresponding to
+    /// each state->get_state() in the spot::state_set is returned,
+    /// e.g. like {string_1,...,string_n}.
+    virtual std::string format_state(const spot::state* s) const
+    {
+      const spot::state_set* se = dynamic_cast<const spot::state_set*>(s);
+      assert(se);
+      const state_set* ss = se->get_state();
+      return format_state_set(ss);
+    }
+
+    /// \brief Output a TAA in a stream.
+    void output(std::ostream& os) const
+    {
+      typename ns_map::const_iterator i;
+      for (i = name_state_map_.begin(); i != name_state_map_.end(); ++i)
+      {
+	taa_tgba::state::const_iterator i2;
+	os << "State: " << label_to_string(i->first) << std::endl;
+	for (i2 = i->second->begin(); i2 != i->second->end(); ++i2)
+	{
+	  os << " " << format_state_set((*i2)->dst)
+	     << ", C:" << (*i2)->condition
+	     << ", A:" << (*i2)->acceptance_conditions << std::endl;
+	}
+      }
+    }
+
+  protected:
+    typedef Sgi::hash_map<
+      const label, taa_tgba::state*, label_hash
+    > ns_map;
+    typedef Sgi::hash_map<
+      const taa_tgba::state*, label, ptr_hash<taa_tgba::state>
+    > sn_map;
+
+    ns_map name_state_map_;
+    sn_map state_name_map_;
+
+    /// \brief Return a label as a string.
+    virtual std::string label_to_string(const label lbl) const = 0;
+
+  private:
+    /// \brief Return the taa_tgba::state for \a name, creating it
+    /// when it does not exist already.
+    taa_tgba::state* add_state(const label& name)
+    {
+      typename ns_map::iterator i = name_state_map_.find(name);
+      if (i == name_state_map_.end())
+      {
+	taa_tgba::state* s = new taa_tgba::state;
+	name_state_map_[name] = s;
+	state_name_map_[s] = name;
+	return s;
+      }
+      return i->second;
+    }
+
+    /// \brief Return the taa::state_set for \a names.
+    taa_tgba::state_set* add_state_set(const std::vector<label>& names)
+    {
+      state_set* ss = new state_set;
+      for (unsigned i = 0; i < names.size(); ++i)
+	ss->insert(add_state(names[i]));
+      state_set_vec_.push_back(ss);
+      return ss;
+    }
+
+    std::string format_state_set(const taa_tgba::state_set* ss) const
+    {
+      state_set::const_iterator i1 = ss->begin();
+      typename sn_map::const_iterator i2;
+      if (ss->empty())
+	return std::string("{}");
+      if (ss->size() == 1)
+      {
+	i2 = state_name_map_.find(*i1);
+	assert(i2 != state_name_map_.end());
+	return "{" + label_to_string(i2->second) + "}";
+      }
+      else
+      {
+	std::string res("{");
+	while (i1 != ss->end())
+	{
+	  i2 = state_name_map_.find(*i1++);
+	  assert(i2 != state_name_map_.end());
+	  res += label_to_string(i2->second);
+	  res += ",";
+	}
+	res[res.size() - 1] = '}';
+	return res;
+      }
+    }
+  };
+
+  class taa_tgba_string :
+    public taa_tgba_labelled<std::string, string_hash>
+  {
+  public:
+    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;
+  };
+
+  class taa_tgba_formula :
+    public taa_tgba_labelled<const ltl::formula*, ltl::formula_ptr_hash>
+  {
+  public:
+    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;
+  };
 }
 
 #endif // SPOT_TGBA_TAATGBA_HH
diff --git a/src/tgbaalgos/ltl2taa.cc b/src/tgbaalgos/ltl2taa.cc
index 65c0083f6..708a2276d 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* res, language_containment_checker* lcc,
+      ltl2taa_visitor(taa_tgba_string* 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*
+      taa_tgba_string*
       result()
       {
 	for (unsigned i = 0; i < to_free_.size(); ++i)
@@ -305,7 +305,7 @@ namespace spot
       }
 
     private:
-      taa_tgba* res_;
+      taa_tgba_string* res_;
       bool refined_;
       bool negated_;
       language_containment_checker* lcc_;
@@ -381,7 +381,7 @@ namespace spot
     const ltl::formula* f2 = ltl::negative_normal_form(f1);
     f1->destroy();
 
-    spot::taa_tgba* res = new spot::taa_tgba(dict);
+    spot::taa_tgba_string* res = new spot::taa_tgba_string(dict);
     bdd_dict b;
     language_containment_checker* lcc =
       new language_containment_checker(&b, false, false, false, false);
diff --git a/src/tgbatest/taatgba.cc b/src/tgbatest/taatgba.cc
index 48be22c6b..e28704c1b 100644
--- a/src/tgbatest/taatgba.cc
+++ b/src/tgbatest/taatgba.cc
@@ -34,7 +34,7 @@ main()
 
   spot::ltl::default_environment& e =
     spot::ltl::default_environment::instance();
-  spot::taa_tgba* a = new spot::taa_tgba(dict);
+  spot::taa_tgba_string* a = new spot::taa_tgba_string(dict);
 
   typedef spot::taa_tgba::transition trans;
   typedef spot::taa_tgba::state state;