diff --git a/src/ta/ta.cc b/src/ta/ta.cc
index 8121921e7..e7b506a02 100644
--- a/src/ta/ta.cc
+++ b/src/ta/ta.cc
@@ -24,11 +24,6 @@
 namespace spot
 {
 
-  spot::state*
-  ta::get_artificial_initial_state() const
-  {
-    return 0;
-  }
 
   scc_stack_ta::connected_component::connected_component(int i)
   {
diff --git a/src/ta/ta.hh b/src/ta/ta.hh
index 2561b72da..a589a13a7 100644
--- a/src/ta/ta.hh
+++ b/src/ta/ta.hh
@@ -31,10 +31,51 @@
 
 namespace spot
 {
+
   // Forward declarations.  See below.
   class ta_succ_iterator;
 
-  /// ta representation of a Testing Automata
+  /// \defgroup ta TA (Testing Automata)
+  ///
+  /// This type and its cousins are listed \ref ta_essentials "here".
+  /// This is an abstract interface.  Its implementations are \ref
+  /// ta_representation "concrete representations".  The
+  /// algorithms that work on spot::ta are \ref tgba_algorithms
+  /// "listed separately".
+
+  /// \addtogroup ta_essentials Essential TA types
+  /// \ingroup ta
+
+  /// \brief A Testing Automaton.
+  /// \ingroup ta_essentials
+  ///
+  /// The Testing Automata (TA) were introduced by
+  /// Henri Hansen, Wojciech Penczek and Antti Valmari
+  /// in "Stuttering-insensitive automata for on-the-fly de- tection of livelock
+  /// properties" In Proc. of FMICSÕ02, vol. 66(2) of Electronic Notes in
+  /// Theoretical Computer Science.Elsevier.
+  ///
+  /// While a TGBA automaton observes the value of the atomic propositions, the
+  /// basic idea of TA is to detect the changes in these values; if a valuation
+  ///  does not change between two consecutive valuations of an execution,
+  /// the TA stay in the same state. A TA transition \c (s,k,d) is labeled by a
+  /// "changeset" \c k: i.e. the set of atomic propositions that change between
+  /// states \c s and \c d, if the changeset is empty then the transition is
+  /// called stuttering transition.
+  /// To detect execution that ends by stuttering in the same TA state, a
+  /// new kind of acceptance states is introduced: "livelock-acceptance states"
+  /// (in addition to the standard Buchi-acceptance states).
+  ///
+  /// Browsing such automaton can be achieved using two functions:
+  /// \c get_initial_states_set or \c get_artificial_initial_state, and \c
+  /// succ_iter. The former returns the initial state(s) while the latter lists
+  /// the successor states of any state (filtred by transition "changeset").
+  ///
+  /// Note that although this is a transition-based automata,
+  /// we never represent transitions!  Transition informations are
+  /// obtained by querying the iterator over the successors of
+  /// a state.
+
   class ta
   {
 
@@ -46,52 +87,103 @@ namespace spot
 
     typedef std::set<state*, state_ptr_less_than> states_set_t;
 
+    /// \brief Get the initial states set of the automaton.
     virtual const states_set_t
     get_initial_states_set() const = 0;
 
-    virtual spot::state*
-    get_artificial_initial_state() const = 0;
+    /// \brief Get the artificial initial state set of the automaton.
+    /// Return 0 if this artificial state is not implemented
+    /// (in this case, use \c get_initial_states_set)
+    /// The aim of adding this state is to have an unique initial state. This
+    /// artificial initial state have one transition to each real initial state,
+    /// and this transition is labeled by the corresponding initial condition.
+    /// (For more details, see the paper cited above)
+    spot::state*
+    get_artificial_initial_state() const
+    {
+      return 0;
+    }
 
+    /// \brief Get an iterator over the successors of \a state.
+    ///
+    /// The iterator has been allocated with \c new.  It is the
+    /// responsability of the caller to \c delete it when no
+    /// longer needed.
+    ///
     virtual ta_succ_iterator*
-    succ_iter(const spot::state* s) const = 0;
+    succ_iter(const spot::state* state) const = 0;
 
+    /// \brief Get an iterator over the successors of \a state
+    /// filtred by the changeset labeling the transitions
+    ///
+    /// The iterator has been allocated with \c new.  It is the
+    /// responsability of the caller to \c delete it when no
+    /// longer needed.
+    ///
     virtual ta_succ_iterator*
-    succ_iter(const spot::state* s, bdd condition) const = 0;
+    succ_iter(const spot::state* state, bdd changeset) const = 0;
 
+    /// \brief Get the dictionary associated to the automaton.
+    ///
+    /// State are represented as BDDs.  The dictionary allows
+    /// to map BDD variables back to formulae, and vice versa.
+    /// This is useful when dealing with several automata (which
+    /// may use the same BDD variable for different formula),
+    /// or simply when printing.
     virtual bdd_dict*
     get_dict() const = 0;
 
+    /// \brief Format the state as a string for printing.
+    ///
+    /// This formating is the responsability of the automata
+    /// that owns the state.
     virtual std::string
     format_state(const spot::state* s) const = 0;
 
+    /// \brief Return true if \a s is a Buchi-accepting state, otherwise false
     virtual bool
     is_accepting_state(const spot::state* s) const = 0;
 
+    /// \brief Return true if \a s is a livelock-accepting state
+    /// , otherwise false
     virtual bool
     is_livelock_accepting_state(const spot::state* s) const = 0;
 
+    /// \brief Return true if \a s is an initial state, otherwise false
     virtual bool
     is_initial_state(const spot::state* s) const = 0;
 
+    /// \brief Return a BDD condition that represents the valuation
+    /// of atomic propositions in the state \a s
     virtual bdd
     get_state_condition(const spot::state* s) const = 0;
 
+    /// \brief Release a state \a s
     virtual void
     free_state(const spot::state* s) const = 0;
 
     /// \brief Return the set of all acceptance conditions used
-    /// by this automaton.
+    /// by this automaton
+    /// (for Generalized form: Transition-based Generalized Testing Automata).
     ///
     /// The goal of the emptiness check is to ensure that
     /// a strongly connected component walks through each
     /// of these acceptiong conditions.  I.e., the union
     /// of the acceptiong conditions of all transition in
     /// the SCC should be equal to the result of this function.
-    virtual bdd all_acceptance_conditions() const = 0;
+    virtual bdd
+    all_acceptance_conditions() const = 0;
 
   };
 
-  /// Successor iterators used by spot::ta.
+  /// \brief Iterate over the successors of a state.
+  /// \ingroup ta_essentials
+  ///
+  /// This class provides the basic functionalities required to
+  /// iterate over the successors of a state, as well as querying
+  /// transition labels.  Because transitions are never explicitely
+  /// encoded, labels (conditions and acceptance conditions) can only
+  /// be queried while iterating over the successors.
   class ta_succ_iterator : public tgba_succ_iterator
   {
   public:
@@ -109,12 +201,13 @@ namespace spot
 
     virtual state*
     current_state() const = 0;
+
+    /// \brief Get the changeset on the transition leading to current successor.
+    ///
+    /// This is a boolean function of atomic propositions.
     virtual bdd
     current_condition() const = 0;
 
-    virtual bool
-    is_stuttering_transition() const = 0;
-
     bdd
     current_acceptance_conditions() const = 0;
 
@@ -173,6 +266,29 @@ namespace spot
     stack_type s;
   };
 
+/// \addtogroup ta_representation TA representations
+/// \ingroup ta
+
+/// \addtogroup ta_algorithms TA algorithms
+/// \ingroup ta
+
+/// \addtogroup ta_io Input/Output of TA
+/// \ingroup ta_algorithms
+
+/// \addtogroup tgba_ta Transforming TGBA into TA
+/// \ingroup ta_algorithms
+
+
+/// \addtogroup ta_generic Algorithm patterns
+/// \ingroup ta_algorithms
+
+/// \addtogroup ta_reduction TA simplifications
+/// \ingroup ta_algorithms
+
+/// \addtogroup ta_misc Miscellaneous algorithms on TA
+/// \ingroup ta_algorithms
+
+
 }
 
 #endif // SPOT_TA_TA_HH
diff --git a/src/ta/taexplicit.cc b/src/ta/taexplicit.cc
index 9132c4c0a..cd1e24d1b 100644
--- a/src/ta/taexplicit.cc
+++ b/src/ta/taexplicit.cc
@@ -80,9 +80,13 @@ namespace spot
   state*
   ta_explicit_succ_iterator::current_state() const
   {
-    trace << "***ta_explicit_succ_iterator::current_state()  if(done()) =***" << done() << std::endl;
+    trace
+      << "***ta_explicit_succ_iterator::current_state()  if(done()) =***"
+          << done() << std::endl;
     assert(!done());
-    trace << "***ta_explicit_succ_iterator::current_state() (*i_)->condition =***" << (*i_)->condition << std::endl;
+    trace
+      << "***ta_explicit_succ_iterator::current_state() (*i_)->condition =***"
+          << (*i_)->condition << std::endl;
     state_ta_explicit* s = (*i_)->dest;
     return s;
   }
@@ -101,11 +105,6 @@ namespace spot
     return (*i_)->acceptance_conditions;
   }
 
-  bool
-  ta_explicit_succ_iterator::is_stuttering_transition() const
-  {
-    return source_->get_tgba_condition() == ((*i_)->dest)->get_tgba_condition();
-  }
 
   ////////////////////////////////////////
   // state_ta_explicit
@@ -414,7 +413,6 @@ namespace spot
 
   }
 
-
   void
   ta_explicit::create_transition(state_ta_explicit* source, bdd condition,
       bdd acceptance_conditions, state_ta_explicit* dest, bool add_at_beginning)
diff --git a/src/ta/taexplicit.hh b/src/ta/taexplicit.hh
index 93c3a956d..1d81c2247 100644
--- a/src/ta/taexplicit.hh
+++ b/src/ta/taexplicit.hh
@@ -37,7 +37,8 @@ namespace spot
   class ta_explicit_succ_iterator;
   class ta_explicit;
 
-  /// ta_explicit explicit representa_explicittion of a Testing Automata_explicit
+  /// Explicit representation of a spot::ta.
+  /// \ingroup ta_representation
   class ta_explicit : public ta
   {
   public:
@@ -53,7 +54,6 @@ namespace spot
     void
     add_to_initial_states_set(state* s, bdd condition = bddfalse);
 
-
     void
     create_transition(state_ta_explicit* source, bdd condition,
         bdd acceptance_conditions, state_ta_explicit* dest,
@@ -145,11 +145,12 @@ namespace spot
   };
 
   /// states used by spot::ta_explicit.
-  /// \ingroup ta_
+  /// \ingroup ta_representation
   class state_ta_explicit : public spot::state
   {
   public:
 
+    /// Explicit transitions.
     struct transition
     {
       bdd condition;
@@ -176,11 +177,11 @@ namespace spot
     virtual state_ta_explicit*
     clone() const;
 
-    virtual void destroy() const
+    virtual void
+    destroy() const
     {
     }
 
-
     virtual
     ~state_ta_explicit()
     {
@@ -214,9 +215,12 @@ namespace spot
     void
     set_initial_state(bool is_initial_state);
 
+    /// \brief Return true if the state has no successors
     bool
     is_hole_state() const;
 
+    /// \brief Remove stuttering transitions
+    /// and transitions leading to states having no successors
     void
     delete_stuttering_and_hole_successors();
 
@@ -257,9 +261,6 @@ namespace spot
     virtual bdd
     current_acceptance_conditions() const;
 
-    virtual bool
-    is_stuttering_transition() const;
-
   private:
     state_ta_explicit::transitions* transitions_;
     state_ta_explicit::transitions::const_iterator i_;
diff --git a/src/ta/taproduct.cc b/src/ta/taproduct.cc
index cdf79b56c..bca321a60 100644
--- a/src/ta/taproduct.cc
+++ b/src/ta/taproduct.cc
@@ -348,11 +348,6 @@ namespace spot
     return ta_->is_livelock_accepting_state(stp->get_ta_state());
   }
 
-  spot::state*
-  ta_product::get_artificial_initial_state() const
-  {
-    return 0;
-  }
 
   bool
   ta_product::is_initial_state(const spot::state* s) const
diff --git a/src/ta/taproduct.hh b/src/ta/taproduct.hh
index 93cf9d4fc..8a41fd1b3 100644
--- a/src/ta/taproduct.hh
+++ b/src/ta/taproduct.hh
@@ -28,8 +28,9 @@ namespace spot
 {
 
   /// \brief A state for spot::ta_product.
+  /// \ingroup emptiness_check
   ///
-  /// This state is in fact a pair of state: the state from the ta
+  /// This state is in fact a pair of state: the state from the TA
   /// automaton and that of Kripke structure.
   class state_ta_product : public state
   {
@@ -37,7 +38,6 @@ namespace spot
     /// \brief Constructor
     /// \param ta_state The state from the ta automaton.
     /// \param kripke_state_ The state from Kripke structure.
-
     state_ta_product(state* ta_state, state* kripke_state) :
       ta_state_(ta_state), kripke_state_(kripke_state)
     {
@@ -100,6 +100,7 @@ namespace spot
     bdd
     current_acceptance_conditions() const;
 
+    /// \brief Return true if the changeset of the current transition is empty
     bool
     is_stuttering_transition() const;
 
@@ -111,6 +112,7 @@ namespace spot
     void
     next_non_stuttering_();
 
+    /// \brief Move to the next successor in the kripke structure
     void
     next_kripke_dest();
 
@@ -131,31 +133,26 @@ namespace spot
 
   };
 
-  /// \brief A lazy product.  (States are computed on the fly.)
+  /// \brief A lazy product between a Testing automaton and a Kripke structure.
+  /// (States are computed on the fly.)
+  /// \ingroup emptiness_check
   class ta_product : public ta
   {
   public:
-    ta_product(const ta* testing_automata, const kripke* kripke_structure);
+    /// \brief Constructor.
+    /// \param testing_automaton The TA component in the product.
+    /// \param kripke_structure The Kripke component in the product.
+    ta_product(const ta* testing_automaton, const kripke* kripke_structure);
 
     virtual
     ~ta_product();
 
-    virtual const states_set_t
+    virtual const std::set<state*, state_ptr_less_than>
     get_initial_states_set() const;
 
     virtual ta_succ_iterator_product*
     succ_iter(const spot::state* s) const;
 
-    virtual ta_succ_iterator_product*
-    succ_iter(const spot::state* s, bdd condition) const
-    {
-
-      if (condition == bddtrue)
-        return succ_iter(s);
-      //TODO
-      return 0;
-    }
-
     virtual bdd_dict*
     get_dict() const;
 
@@ -168,12 +165,11 @@ namespace spot
     virtual bool
     is_livelock_accepting_state(const spot::state* s) const;
 
-    virtual spot::state*
-    get_artificial_initial_state() const;
-
     virtual bool
     is_initial_state(const spot::state* s) const;
 
+    /// \brief Return true if the state \a s has no succeseurs
+    /// in the ta automaton (the TA component of the product automaton)
     virtual bool
     is_hole_state_in_ta_component(const spot::state* s) const;
 
diff --git a/src/ta/tgbtaexplicit.cc b/src/ta/tgbtaexplicit.cc
index 9f55c35a4..8f94317c2 100644
--- a/src/ta/tgbtaexplicit.cc
+++ b/src/ta/tgbtaexplicit.cc
@@ -46,8 +46,8 @@ namespace spot
 
    tgba_succ_iterator*
    tgbta_explicit::succ_iter(const spot::state* state,
-                            const spot::state* global_state,
-                            const tgba* global_automaton) const
+                            const spot::state*,
+                            const tgba*) const
    {
      return ta_explicit::succ_iter(state);
    }
@@ -55,13 +55,13 @@ namespace spot
    bdd
    tgbta_explicit::compute_support_conditions(const spot::state* in) const
    {
-     return get_tgba()->support_conditions(((state_ta_explicit*) in)->get_tgba_state());
+     return get_tgba()->support_conditions(((const state_ta_explicit*) in)->get_tgba_state());
    }
 
    bdd
    tgbta_explicit::compute_support_variables(const spot::state* in) const
    {
-     return get_tgba()->support_variables(((state_ta_explicit*) in)->get_tgba_state());
+     return get_tgba()->support_variables(((const state_ta_explicit*) in)->get_tgba_state());
    }
 
    bdd_dict*
diff --git a/src/ta/tgbtaproduct.cc b/src/ta/tgbtaproduct.cc
index 1ea7c3174..878478504 100644
--- a/src/ta/tgbtaproduct.cc
+++ b/src/ta/tgbtaproduct.cc
@@ -58,16 +58,16 @@ namespace spot
   }
 
   tgba_succ_iterator*
-  tgbta_product::succ_iter(const state* local_state, const state* global_state,
-      const tgba* global_automaton) const
+  tgbta_product::succ_iter(const state* local_state, const state*,
+      const tgba*) const
   {
     const state_product* s = down_cast<const state_product*> (local_state);
     assert(s);
 
     fixed_size_pool* p = const_cast<fixed_size_pool*> (&pool_);
 
-    return new tgbta_succ_iterator_product(s, (kripke*) left_,
-        (tgbta *) right_, p);
+    return new tgbta_succ_iterator_product(s, (const kripke*) left_,
+        (const tgbta *) right_, p);
   }
 
   ////////////////////////////////////////////////////////////
diff --git a/src/taalgos/emptinessta.cc b/src/taalgos/emptinessta.cc
index df3665264..14869af89 100644
--- a/src/taalgos/emptinessta.cc
+++ b/src/taalgos/emptinessta.cc
@@ -43,11 +43,11 @@ namespace spot
 
   ta_check::~ta_check()
   {
-
   }
 
   bool
-  ta_check::check(bool disable_second_pass)
+  ta_check::check(bool disable_second_pass,
+      disable_heuristic_for_livelock_detection)
   {
 
     // We use five main data in this algorithm:
@@ -67,14 +67,12 @@ namespace spot
     int num = 1;
 
     // * todo: the depth-first search stack.  This holds pairs of the
-    //   form (STATE, ITERATOR) where ITERATOR is a ta_succ_iterator
+    //   form (STATE, ITERATOR) where ITERATOR is a ta_succ_iterator_product
     //   over the successors of STATE.  In our use, ITERATOR should
     //   always be freed when TODO is popped, but STATE should not because
     //   it is also used as a key in H.
     std::stack<pair_state_iter> todo;
 
-
-
     Sgi::hash_map<const state*, std::string, state_ptr_hash, state_ptr_equal>
         colour;
 
@@ -88,7 +86,8 @@ namespace spot
 
     bool livelock_acceptance_states_not_found = true;
 
-    bool activate_heuristic = (is_full_2_pass_ == disable_second_pass);
+    bool activate_heuristic = !disable_heuristic_for_livelock_detection
+        && (is_full_2_pass_ == disable_second_pass);
 
     // Setup depth-first search from initial states.
     const ta* ta_ = a_->get_ta();
@@ -117,7 +116,7 @@ namespace spot
         scc.push(num);
         arc.push(bddfalse);
 
-        ta_succ_iterator* iter = a_->succ_iter(init);
+        ta_succ_iterator_product* iter = a_->succ_iter(init);
         iter->first();
         todo.push(pair_state_iter(init, iter));
 
@@ -133,7 +132,7 @@ namespace spot
             state* curr = todo.top().first;
 
             // We are looking at the next successor in SUCC.
-            ta_succ_iterator* succ = todo.top().second;
+            ta_succ_iterator_product* succ = todo.top().second;
 
             // If there is no more successor, backtrack.
             if (succ->done())
@@ -147,7 +146,8 @@ namespace spot
                 trace
                   << "PASS 1 : backtrack" << std::endl;
 
-                if (a_->is_livelock_accepting_state(curr))
+                if (a_->is_livelock_accepting_state(curr)
+                    && !a_->is_accepting_state(curr))
                   {
                     livelock_acceptance_states_not_found = false;
                     trace
@@ -241,7 +241,7 @@ namespace spot
                 scc.push(num);
                 arc.push(acc_cond);
 
-                ta_succ_iterator* iter = a_->succ_iter(dest);
+                ta_succ_iterator_product* iter = a_->succ_iter(dest);
                 iter->first();
                 todo.push(pair_state_iter(dest, iter));
                 //colour[dest] = GREY;
@@ -315,10 +315,11 @@ namespace spot
                       a_->get_dict(), scc.top().condition) << std::endl;
                 trace
                   << "PASS 1: a_->all_acceptance_conditions() : "
-                      << ( a_->all_acceptance_conditions()) << std::endl;
+                      << (a_->all_acceptance_conditions()) << std::endl;
                 trace
-                                  << "PASS 1 CYCLE and (scc.top().condition == a_->all_acceptance_conditions()) : "
-                                      << (scc.top().condition == a_->all_acceptance_conditions()) << std::endl;
+                      << "PASS 1 CYCLE and (scc.top().condition == a_->all_acceptance_conditions()) : "
+                      << (scc.top().condition
+                          == a_->all_acceptance_conditions()) << std::endl;
 
                 trace
                   << "PASS 1: bddtrue : " << (a_->all_acceptance_conditions()
@@ -407,7 +408,7 @@ namespace spot
   }
 
   bool
-  ta_check::livelock_detection(const ta* t)
+  ta_check::livelock_detection(const ta_product* t)
   {
     // We use five main data in this algorithm:
 
@@ -460,7 +461,7 @@ namespace spot
             h->insert(init, ++num);
             sscc.push(num);
             sscc.top().is_accepting = t->is_livelock_accepting_state(init);
-            ta_succ_iterator* iter = t->succ_iter(init);
+            ta_succ_iterator_product* iter = t->succ_iter(init);
             iter->first();
             todo.push(pair_state_iter(init, iter));
             inc_depth();
@@ -473,7 +474,7 @@ namespace spot
             state* curr = todo.top().first;
 
             // We are looking at the next successor in SUCC.
-            ta_succ_iterator* succ = todo.top().second;
+            ta_succ_iterator_product* succ = todo.top().second;
 
             // If there is no more successor, backtrack.
             if (succ->done())
@@ -554,7 +555,7 @@ namespace spot
                 sscc.push(num);
                 sscc.top().is_accepting = t->is_livelock_accepting_state(dest);
 
-                ta_succ_iterator* iter = t->succ_iter(dest);
+                ta_succ_iterator_product* iter = t->succ_iter(dest);
                 iter->first();
                 todo.push(pair_state_iter(dest, iter));
                 inc_depth();
@@ -651,26 +652,24 @@ namespace spot
     delete h;
   }
 
-
   void
-   ta_check::clear(numbered_state_heap* h, std::stack<pair_state_iter> todo,
-       spot::ta_succ_iterator* init_states_it)
-   {
+  ta_check::clear(numbered_state_heap* h, std::stack<pair_state_iter> todo,
+      spot::ta_succ_iterator* init_states_it)
+  {
 
-     set_states(states() + h->size());
+    set_states(states() + h->size());
 
     delete init_states_it;
 
-     // Release all iterators in TODO.
-     while (!todo.empty())
-       {
-         delete todo.top().second;
-         todo.pop();
-         dec_depth();
-       }
-     delete h;
-   }
-
+    // Release all iterators in TODO.
+    while (!todo.empty())
+      {
+        delete todo.top().second;
+        todo.pop();
+        dec_depth();
+      }
+    delete h;
+  }
 
   std::ostream&
   ta_check::print_stats(std::ostream& os) const
diff --git a/src/taalgos/emptinessta.hh b/src/taalgos/emptinessta.hh
index 60a8d4421..8055ce735 100644
--- a/src/taalgos/emptinessta.hh
+++ b/src/taalgos/emptinessta.hh
@@ -36,11 +36,54 @@ namespace spot
 
   namespace
   {
-    typedef std::pair<spot::state*, ta_succ_iterator*> pair_state_iter;
+    typedef std::pair<spot::state*, ta_succ_iterator_product*> pair_state_iter;
   }
-  /// \brief An implementation of the ta emptiness-check algorithm.
+
+  /// \addtogroup emptiness_check Emptiness-checks
+  /// \ingroup ta_algorithms
   ///
-  /// See the documentation for spot::ta.
+  /// \brief Check whether the language of a product between a Kripke structure
+  ///  and a TA is empty. It works for both standard and generalized form of TA.
+  ///
+  /// you should call \c check to check the product automaton.
+  /// If \c check() returns false, then the product automaton
+  /// was found empty.  Otherwise the automaton accepts some run.
+  ///
+  /// This is based on the following paper.
+  /// \verbatim
+  ///  @InProceedings{        geldenhuys.06.spin,
+  ///  author        = {Jaco Geldenhuys and Henri Hansen},
+  ///  title         = {Larger Automata and Less Work for {LTL} Model Checking},
+  ///  booktitle     = {Proceedings of the 13th International SPIN Workshop
+  ///                  (SPIN'06)},
+  ///  year          = {2006},
+  ///  pages         = {53--70},
+  ///  series        = {Lecture Notes in Computer Science},
+  ///  volume        = {3925},
+  ///  publisher     = {Springer}
+  /// }
+  /// \endverbatim
+  ///
+  /// the implementation of \c check is inspired from the two-pass algorithm
+  /// of the paper above:
+  /// - the fist-pass detect all Buchi-accepting cycles and includes
+  //  the heuristic proposed in the paper to detect some
+  /// livelock-accepting cycles.
+  /// - the second-pass detect all livelock-accepting cycles.
+  /// In addition, we add some optimizations to the fist pass:
+  /// 1- Detection of all (livelock-accepting) cycles containing a least
+  /// one state that is both livelock and accepting states
+  /// 2- Detection of all livelock-accepting cycles containing a least
+  /// one state (k,t) such as its "TA component" t is a livelock-accepting
+  /// state that has no successors in the TA automaton.
+  ///
+  /// The implementation of each pass is a SCC-based algorithm inspired
+  /// from spot::gtec.hh.
+
+  /// \brief An implementation of the emptiness-check algorithm for a product
+  /// between a TA and a Kripke structure
+  ///
+  /// See the paper cited above.
   class ta_check : public ec_statistics
   {
   public:
@@ -48,26 +91,38 @@ namespace spot
     virtual
     ~ta_check();
 
-    /// Check whether the automaton's language is empty.
+    /// \brief Check whether the TA product automaton contains an accepting run:
+    /// it detects the two kinds of accepting runs: Buchi-accepting runs
+    /// and livelock-accepting runs. This emptiness check algorithm can also
+    /// check a product using the generalized form of TA.
+    ///
+    /// Return false if the product automaton accepts no run, otherwise true
+    ///
+    /// \param disable_second_pass: is used to disable the second pass when
+    /// when it is not necessary, for example when all the livelock-accepting
+    /// states of the TA automaton have no successors, we call this kind of
+    /// TA as STA (Single-pass Testing Automata)
+    /// (see spot::tgba2ta::add_artificial_livelock_accepting_state() for an
+    /// automatic transformation of any TA automaton into STA automaton
+    ///
+    /// \param disable_heuristic_for_livelock_detection: disable the heuristic
+    /// used in the first pass to detect livelock-accepting runs,
+    /// this heuristic is described in the paper cited above
     virtual bool
-    check(bool disable_second_pass = false);
+    check(bool disable_second_pass = false,
+        bool disable_heuristic_for_livelock_detection = false);
 
+    /// \brief Check whether the product automaton contains
+    /// a livelock-accepting run
+    /// Return false if the product automaton accepts no livelock-accepting run,
+    /// otherwise true
     virtual bool
-    livelock_detection(const ta* t);
+    livelock_detection(const ta_product* t);
 
+    /// Print statistics, if any.
     virtual std::ostream&
     print_stats(std::ostream& os) const;
 
-    /// \brief Return the status of the emptiness-check.
-    ///
-    /// When check() succeed, the status should be passed along
-    /// to spot::counter_example.
-    ///
-    /// This status should not be deleted, it is a pointer
-    /// to a member of this class that will be deleted when
-    /// the ta object is deleted.
-    //  const tgba_check_status* result() const;
-
   protected:
     void
     clear(numbered_state_heap* h, std::stack<pair_state_iter> todo, std::queue<
@@ -77,19 +132,23 @@ namespace spot
     clear(numbered_state_heap* h, std::stack<pair_state_iter> todo,
         spot::ta_succ_iterator* init_states_it);
 
+    /// the heuristic for livelock-accepting runs detection, it's described
+    /// in the paper cited above
     bool
     heuristic_livelock_detection(const state * stuttering_succ,
         numbered_state_heap* h, int h_livelock_root, std::set<const state*,
             state_ptr_less_than> liveset_curr);
+
     const ta_product* a_; ///< The automaton.
     option_map o_; ///< The options
 
+    // Force the second pass
     bool is_full_2_pass_;
 
-    // * scc: a stack of strongly connected components (SCC)
+    // scc: a stack of strongly connected components (SCC)
     scc_stack_ta scc;
 
-    // * sscc: a stack of strongly stuttering-connected components (SSCC)
+    // sscc: a stack of strongly stuttering-connected components (SSCC)
     scc_stack_ta sscc;
 
   };
diff --git a/src/taalgos/tgba2ta.cc b/src/taalgos/tgba2ta.cc
index ec1c0beb0..30782d923 100644
--- a/src/taalgos/tgba2ta.cc
+++ b/src/taalgos/tgba2ta.cc
@@ -48,7 +48,6 @@ namespace spot
 
   ta_explicit*
   build_ta(ta_explicit* ta, bdd atomic_propositions_set_,
-      bool artificial_initial_state_mode,
       bool artificial_livelock_accepting_state_mode, bool degeneralized)
   {
 
@@ -70,7 +69,8 @@ namespace spot
           {
             init_state = new state_ta_explicit(tgba_init_state->clone(),
                 satone_tgba_condition, true,
-                ((tgba_sba_proxy*) tgba_)->state_is_accepting(tgba_init_state));
+                ((const tgba_sba_proxy*) tgba_)->state_is_accepting(
+                    tgba_init_state));
           }
         else
           {
@@ -117,10 +117,13 @@ namespace spot
                       if (degeneralized)
                         {
 
-                          new_dest = new state_ta_explicit(tgba_state->clone(),
-                              dest_condition, false,
-                              ((tgba_sba_proxy*) tgba_)->state_is_accepting(
-                                  tgba_state));
+                          new_dest
+                              = new state_ta_explicit(
+                                  tgba_state->clone(),
+                                  dest_condition,
+                                  false,
+                            ((const tgba_sba_proxy*) tgba_)->state_is_accepting(
+                                      tgba_state));
 
                         }
                       else
@@ -133,7 +136,7 @@ namespace spot
 
                       if (dest != new_dest)
                         {
-                          // the state dest already exists in the testing automata
+                       // the state dest already exists in the testing automata
                           new_dest->get_tgba_state()->destroy();
                           delete new_dest;
                         }
@@ -158,22 +161,21 @@ namespace spot
 
     state_ta_explicit* artificial_livelock_accepting_state = 0;
 
-    trace << "*** build_ta: artificial_livelock_accepting_state_mode = ***"
-        << artificial_livelock_accepting_state_mode << std::endl;
+    trace
+      << "*** build_ta: artificial_livelock_accepting_state_mode = ***"
+          << artificial_livelock_accepting_state_mode << std::endl;
 
     if (artificial_livelock_accepting_state_mode)
       {
 
-        artificial_livelock_accepting_state =
-            new state_ta_explicit(ta->get_tgba()->get_init_state(), bddtrue,
-                false, false, true, 0);
-        trace << "*** build_ta: artificial_livelock_accepting_state = ***"
-                << artificial_livelock_accepting_state << std::endl;
+        artificial_livelock_accepting_state = new state_ta_explicit(
+            ta->get_tgba()->get_init_state(), bddtrue, false, false, true, 0);
+        trace
+          << "*** build_ta: artificial_livelock_accepting_state = ***"
+              << artificial_livelock_accepting_state << std::endl;
 
       }
 
-
-
     compute_livelock_acceptance_states(ta, artificial_livelock_accepting_state);
 
     return ta;
@@ -203,7 +205,7 @@ namespace spot
     tgba_init_state->destroy();
 
     // build ta automata:
-    build_ta(ta, atomic_propositions_set_, artificial_initial_state_mode,
+    build_ta(ta, atomic_propositions_set_,
         artificial_livelock_accepting_state_mode, degeneralized);
     return ta;
   }
@@ -221,9 +223,11 @@ namespace spot
         == artificial_livelock_accepting_state);
 
     trace
-        << "*** add_artificial_livelock_accepting_state: assert(artificial_livelock_accepting_state_added == artificial_livelock_accepting_state) = ***"
-        << (artificial_livelock_accepting_state_added
-            == artificial_livelock_accepting_state) << std::endl;
+          << "*** add_artificial_livelock_accepting_state: "
+          <<  "assert(artificial_livelock_accepting_state_added == "
+          <<  "artificial_livelock_accepting_state) = ***"
+          << (artificial_livelock_accepting_state_added
+              == artificial_livelock_accepting_state) << std::endl;
 
     ta::states_set_t states_set = testing_automata->get_states_set();
     ta::states_set_t::iterator it;
@@ -250,7 +254,7 @@ namespace spot
                   (dest)->get_transitions();
               bool dest_trans_empty = dest_trans == 0 || dest_trans->empty();
 
-              //TODO TA++
+              //TA++
               if (dest->is_livelock_accepting_state()
                   && (!dest->is_accepting_state() || dest_trans_empty))
                 {
@@ -260,7 +264,6 @@ namespace spot
                 }
 
               //remove hole successors states
-
               if (dest_trans_empty)
                 {
                   source->get_transitions((*it_trans)->condition)->remove(
@@ -325,7 +328,8 @@ namespace spot
     // * h: a hash of all visited nodes, with their order,
     //   (it is called "Hash" in Couvreur's paper)
     numbered_state_heap* h =
-        numbered_state_heap_hash_map_factory::instance()->build(); ///< Heap of visited states.
+        numbered_state_heap_hash_map_factory::instance()->build();
+    ///< Heap of visited states.
 
     // * num: the number of visited nodes.  Used to set the order of each
     //   visited node,
@@ -424,14 +428,17 @@ namespace spot
                         assert(*spi.second != -1);
                         *spi.second = -1;
                         if (is_livelock_accepting_sscc)
-                          {//if it is an accepting sscc
-                            //add the state to G (=the livelock-accepting states set)
+                          {//if it is an accepting sscc add the state to
+                            //G (=the livelock-accepting states set)
 
                             state_ta_explicit * livelock_accepting_state =
                                 down_cast<state_ta_explicit*> (*i);
 
-                            livelock_accepting_state->set_livelock_accepting_state(
+                         livelock_accepting_state->set_livelock_accepting_state(
                                 true);
+
+                         //case STA (Single-pass Testing Automata) or case
+            //STGTA (Single-pass Transition-based Generalised Testing Automata)
                             if (artificial_livelock_accepting_state != 0)
                               livelock_accepting_state->set_accepting_state(
                                   true);
@@ -498,8 +505,8 @@ namespace spot
             if (*spi.second == -1)
               continue;
 
-            trace << "***compute_livelock_acceptance_states: CYCLE***"
-                << std::endl;
+            trace
+              << "***compute_livelock_acceptance_states: CYCLE***" << std::endl;
 
             if (!curr->compare(dest))
               {
@@ -512,13 +519,14 @@ namespace spot
                         == testing_automata->all_acceptance_conditions()))
                   {
                     self_loop_state->set_livelock_accepting_state(true);
-                    if (artificial_livelock_accepting_state != 0) self_loop_state->set_accepting_state(true);
+                    if (artificial_livelock_accepting_state != 0)
+                      self_loop_state->set_accepting_state(true);
 
                   }
 
                 trace
-                    << "***compute_livelock_acceptance_states: CYCLE: self_loop_state***"
-                    << std::endl;
+                      << "***compute_livelock_acceptance_states: CYCLE: self_loop_state***"
+                      << std::endl;
 
               }
 
@@ -566,16 +574,16 @@ namespace spot
     delete h;
 
     trace
-        << "*** compute_livelock_acceptance_states: PRE call add_artificial_livelock_accepting_state() method ... (artificial_livelock_accepting_state != 0) :***"
-        << (artificial_livelock_accepting_state != 0) << std::endl;
+          << "*** compute_livelock_acceptance_states: PRE call add_artificial_livelock_accepting_state() method ... (artificial_livelock_accepting_state != 0) :***"
+          << (artificial_livelock_accepting_state != 0) << std::endl;
 
     if (artificial_livelock_accepting_state != 0)
       add_artificial_livelock_accepting_state(testing_automata,
           artificial_livelock_accepting_state);
 
     trace
-        << "*** compute_livelock_acceptance_states: POST call add_artificial_livelock_accepting_state() method ***"
-        << std::endl;
+          << "*** compute_livelock_acceptance_states: POST call add_artificial_livelock_accepting_state() method ***"
+          << std::endl;
   }
 
   tgbta_explicit*
@@ -591,9 +599,10 @@ namespace spot
         tgba_->all_acceptance_conditions(), ta_init_state);
 
     // build ta automata:
-    build_ta(tgbta, atomic_propositions_set_, true, true, false);
+    build_ta(tgbta, atomic_propositions_set_, true, false);
 
-    trace << "***tgba_to_tgbta: POST build_ta***" << std::endl;
+    trace
+      << "***tgba_to_tgbta: POST build_ta***" << std::endl;
 
     // adapt a ta automata to build tgbta automata :
     ta::states_set_t states_set = tgbta->get_states_set();
@@ -622,13 +631,13 @@ namespace spot
             if (trans_empty || state->is_accepting_state())
               {
                 trace
-                    << "***tgba_to_tgbta: PRE if (state->is_livelock_accepting_state()) ... create_transition ***"
-                    << std::endl;
+                      << "***tgba_to_tgbta: PRE if (state->is_livelock_accepting_state()) ... create_transition ***"
+                      << std::endl;
                 tgbta->create_transition(state, bdd_stutering_transition,
                     tgbta->all_acceptance_conditions(), state);
                 trace
-                    << "***tgba_to_tgbta: POST if (state->is_livelock_accepting_state()) ... create_transition ***"
-                    << std::endl;
+                      << "***tgba_to_tgbta: POST if (state->is_livelock_accepting_state()) ... create_transition ***"
+                      << std::endl;
 
               }
 
@@ -640,7 +649,8 @@ namespace spot
 
         state->set_livelock_accepting_state(false);
         state->set_accepting_state(false);
-        trace << "***tgba_to_tgbta: POST create_transition ***" << std::endl;
+        trace
+          << "***tgba_to_tgbta: POST create_transition ***" << std::endl;
 
       }
 
diff --git a/src/taalgos/tgba2ta.hh b/src/taalgos/tgba2ta.hh
index a035fde66..c0cf96ebf 100644
--- a/src/taalgos/tgba2ta.hh
+++ b/src/taalgos/tgba2ta.hh
@@ -34,22 +34,73 @@
 
 namespace spot
 {
+  /// \brief Build a spot::tgba_explicit* from an LTL formula.
+  /// \ingroup tgba_ta
+  ///
+  /// This is based on the following paper.
+  /// \verbatim
+  ///  @InProceedings{        geldenhuys.06.spin,
+  ///  author        = {Jaco Geldenhuys and Henri Hansen},
+  ///  title         = {Larger Automata and Less Work for {LTL} Model Checking},
+  ///  booktitle     = {Proceedings of the 13th International SPIN Workshop
+  ///                  (SPIN'06)},
+  ///  year          = {2006},
+  ///  pages         = {53--70},
+  ///  series        = {Lecture Notes in Computer Science},
+  ///  volume        = {3925},
+  ///  publisher     = {Springer}
+  /// }
+  /// \endverbatim
+  ///
+  /// \param tgba_to_convert The TGBA automaton to convert into a TA automaton
+  ///
+  /// \param atomic_propositions_set The set of atomic propositions used in the
+  /// input TGBA \a tgba_to_convert
+  ///
+  /// \param artificial_initial_state_mode When set, the algorithm will build
+  /// a TA automaton with an unique initial state.  This
+  /// artificial initial state have one transition to each real initial state,
+  /// and this transition is labeled by the corresponding initial condition.
+  /// (see spot::ta::get_artificial_initial_state())
+  ///
+  /// \param STA_mode When set, the returned TA
+  /// automaton is a STA (Single-pass Testing Automata): a STA automaton is a TA
+  /// where: for every livelock-accepting state s, if s is not also a
+  /// Buchi-accepting state, then s has no successors. A STA product requires
+  /// only one-pass emptiness check algorithm (see spot::ta_check::check)
+  ///
+  /// \param degeneralized When false, the returned automaton is a generalized
+  /// form of TA, called TGTA (Transition-based Generalized Testing Automaton).
+  /// Like TGBA, TGTA use Generalized Büchi acceptance
+  /// conditions intead of Büchi-accepting states: there are several acceptance
+  /// sets (of transitions), and a path is accepted if it traverses
+  /// at least one transition of each set infinitely often or if it contains a
+  /// livelock-accepting cycle.
+  ///
+  /// \return A spot::ta_explicit that recognizes the same language as the
+  /// TGBA \a tgba_to_convert.
   ta_explicit*
   tgba_to_ta(const tgba* tgba_to_convert, bdd atomic_propositions_set,
-      bool artificial_initial_state_mode = true,
-      bool artificial_livelock_accepting_state_mode = false,
+      bool artificial_initial_state_mode = true, bool STA_mode = false,
       bool degeneralized = true);
 
-  //artificial_livelock_accepting_state is used in the case of TA+ automata
-  void
-  compute_livelock_acceptance_states(ta_explicit* testing_automata, state_ta_explicit* artificial_livelock_accepting_state = 0);
+  stgta_explicit*
+  tgba_to_stgta(const tgba* tgba_to_convert, bdd atomic_propositions_set);
 
-  void
-  add_artificial_livelock_accepting_state(ta_explicit* testing_automata,
-      state_ta_explicit* artificial_livelock_accepting_state);
 
-  tgbta_explicit*
-  tgba_to_tgbta(const tgba* tgba_to_convert, bdd atomic_propositions_set);
+  //artificial_livelock_accepting_state is used in the case of
+    //STA (Single-pass Testing Automata) or in the case
+    //STGTA (Single-pass Transition-based Generalised Testing Automata)
+    void
+    compute_livelock_acceptance_states(ta_explicit* testing_automata,
+        state_ta_explicit* artificial_livelock_accepting_state = 0);
+
+    //artificial_livelock_accepting_state is added to transform TA into
+    //STA (Single-pass Testing Automata) or to transform TGTA into
+    //STGTA (Single-pass Transition-based Generalised Testing Automata)
+    void
+    add_artificial_livelock_accepting_state(ta_explicit* testing_automata,
+        state_ta_explicit* artificial_livelock_accepting_state);
 
 }
 
diff --git a/src/tgbatest/ltl2ta.test b/src/tgbatest/ltl2ta.test
index f4182146f..26a604ecc 100755
--- a/src/tgbatest/ltl2ta.test
+++ b/src/tgbatest/ltl2ta.test
@@ -62,7 +62,7 @@ done
 
 
 for opt in -TM; do
-  ../ltl2tgba -ks $opt -in 'a U (b U c)' > stdout
+  ../ltl2tgba -ks $opt -in -DS 'a U (b U c)' > stdout
   grep 'transitions: 69$' stdout
   grep 'states: 10$' stdout
 done
@@ -70,7 +70,7 @@ done
 
 
 for opt in  -TM; do
-  ../ltl2tgba -ks $opt '!(Ga U b)' > stdout
+  ../ltl2tgba -ks $opt -DS '!(Ga U b)' > stdout
   grep 'transitions: 15$' stdout
   grep 'states: 5$' stdout
 done
@@ -78,7 +78,7 @@ done
 # Make sure 'Ga U b' has 6 states and 12 transitions,
 # before and after degeneralization.
 for opt in -TM; do
-  ../ltl2tgba -ks $opt 'Ga U b' > stdout
+  ../ltl2tgba -ks $opt -DS 'Ga U b' > stdout
   grep 'transitions: 13$' stdout
   grep 'states: 6$' stdout
 done
@@ -88,13 +88,13 @@ done
 # has 21 states and 96 transitions, before minimization.
 f='(G (p -> F q)) && ((X (p) U q) || ! X (p U (p && q)))'
 
-../ltl2tgba -ks -TA "$f" > stdout
+../ltl2tgba -ks -TA  -DS "$f" > stdout
 grep 'transitions: 96$' stdout
 grep 'states: 21$' stdout
 
 # Note:  after minimization with -TM.
 # has 20 states and 89 transitions, after minimization.
-../ltl2tgba -ks -TM "$f" > stdout
+../ltl2tgba -ks -TM  -DS "$f" > stdout
 grep 'transitions: 89$' stdout
 grep 'states: 20$' stdout
 
@@ -102,7 +102,7 @@ grep 'states: 20$' stdout
 # Make sure 'GFa & GFb & GFc & GFd & GFe & GFf'
 # has 448 states and 28224 transitions.
 f='GFa & GFb & GFc & GFd & GFe & GFg'
-../ltl2tgba -ks -TA -x "$f" > stdout
+../ltl2tgba -ks -TA  -DS -x "$f" > stdout
 grep 'transitions: 28351$' stdout
 grep 'states: 449$' stdout
 
@@ -111,71 +111,71 @@ grep 'states: 449$' stdout
 # has 290 states and 18527 transitions with artificial livelock state.
 
 f='GFa & GFb & GFc & GFd & GFe & GFg'
-../ltl2tgba -ks -TM -x -lv "$f" > stdout
-grep 'transitions: 18527$' stdout
+../ltl2tgba -ks -TM -x -lv  -DS "$f" > stdout
+grep 'transitions: 18496$' stdout
 grep 'states: 290$' stdout
 
 
 #tests with artificial livelock state:
-run 0 ../ltl2tgba -ks -TA -lv "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
-grep 'transitions: 920$' stdout
+run 0 ../ltl2tgba -ks -TA -lv  -DS "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
+grep 'transitions: 882$' stdout
 grep 'states: 78$' stdout
 
-run 0 ../ltl2tgba -TM -ks -lv "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
-grep 'transitions: 458$' stdout
+run 0 ../ltl2tgba -TM -ks -lv -DS  "Gq|Gr|(G(q|FGp)&G(r|FG!p))" >stdout
+grep 'transitions: 440$' stdout
 grep 'states: 28$' stdout
 
 
 
-run 0 ../ltl2tgba -TM -ks -in -R3f -x  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+run 0 ../ltl2tgba -TM -ks -in -R3f -x  -DS  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
 grep 'transitions: 521$' stdout
 grep 'states: 43$' stdout
 
 
-run 0 ../ltl2tgba -TM -ks -lv -R3f -x  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 645$' stdout
+run 0 ../ltl2tgba -TM -ks -lv -R3f -x  -DS  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+grep 'transitions: 636$' stdout
 grep 'states: 45$' stdout
 
 
-run 0 ../ltl2tgba -TM -ks "G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))" >stdout
+run 0 ../ltl2tgba -TM -ks  -DS "G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))" >stdout
 grep 'transitions: 2779$' stdout
 grep 'states: 127$' stdout
 
 
-run 0 ../ltl2tgba -TM -ks -lv "G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))" >stdout
-grep 'transitions: 3105$' stdout
+run 0 ../ltl2tgba -TM -ks -lv  -DS "G(F(GWaitLeft7 U Idle4) U (WaitLeft2 M IsEating2))" >stdout
+grep 'transitions: 2831$' stdout
 grep 'states: 128$' stdout
 
 
 
 run 0 ../ltl2tgba -TM -ks "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 536$' stdout
-grep 'states: 37$' stdout
+grep 'transitions: 498$' stdout
+grep 'states: 34$' stdout
 
 
 run 0 ../ltl2tgba -TM -ks  -lv -in "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 612$' stdout
-grep 'states: 37$' stdout
+grep 'transitions: 566$' stdout
+grep 'states: 35$' stdout
 
 
-run 0 ../ltl2tgba -TM -ks -in -R3 -x  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+run 0 ../ltl2tgba -TM -ks -in -R3 -x  -DS  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
 grep 'transitions: 464$' stdout
 grep 'states: 36$' stdout
 
-run 0 ../ltl2tgba -TM -ks -lv -R3 -x  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 575$' stdout
+run 0 ../ltl2tgba -TM -ks -lv -R3 -x   -DS "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+grep 'transitions: 565$' stdout
 grep 'states: 38$' stdout
 
 
-run 0 ../ltl2tgba -TA -ks -lv  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 876$' stdout
+run 0 ../ltl2tgba -TA -ks -lv   -DS "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+grep 'transitions: 831$' stdout
 grep 'states: 56$' stdout
 
 
-run 0 ../ltl2tgba -TM -ks -lv  "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
-grep 'transitions: 631$' stdout
-grep 'states: 38$' stdout
+run 0 ../ltl2tgba -TM -ks -lv "FG((WaitRight4 M (HasRight1 W GWaitLeft0)) M HasLeft4)" >stdout
+grep 'transitions: 585$' stdout
+grep 'states: 36$' stdout
 
 
 
-echo '.................. OK'
+echo '.................. TESTs: OK'
diff --git a/src/tgbatest/ltl2tgba.cc b/src/tgbatest/ltl2tgba.cc
index c6543d344..061c530a4 100644
--- a/src/tgbatest/ltl2tgba.cc
+++ b/src/tgbatest/ltl2tgba.cc
@@ -288,13 +288,13 @@ syntax(char* prog)
             << "  -TM    Translate an LTL formula into a minimal Testing automata"
             << std::endl
             << std::endl
-            << "  -lv    Translate an LTL formula into a Testing automata with an artificial livelock accepting state"
+            << "  -lv    Translate an LTL formula into a Testing automata with an artificial livelock accepting state (Single-pass Testing Automata)"
             << std::endl
             << std::endl
             << "  -in    Translate an LTL formula into a Testing automata without artificial initial state"
             << std::endl
             << std::endl
-            << "  -TGBTA    Translate an LTL formula into a TGBTA"
+            << "  -STGTA    Translate an LTL formula into a STGTA (Single-pass Transition-based Generalised Testing Automata)"
             << std::endl;
 
 
@@ -697,7 +697,7 @@ main(int argc, char** argv)
           ta_opt = true;
           opt_minimize = true;
         }
-      else if (!strcmp(argv[formula_index], "-TGBTA"))
+      else if (!strcmp(argv[formula_index], "-STGTA"))
         {
           tgbta_opt = true;
         }
@@ -1154,12 +1154,15 @@ main(int argc, char** argv)
               tm.stop("producing output");
             }
 
-          delete testing_automata_nm;
-          //delete testing_automata;
+
+         delete testing_automata_nm;
+         delete testing_automata;
           a = 0;
           degeneralized = 0;
-          output = -1;
+          if (degeneralize_opt != DegenSBA) to_free = 0;
 
+          aut_red  = 0;
+          output = -1;
         } else if (tgbta_opt)
         {
           a = tgba_to_tgbta(a, atomic_props_set_bdd);