diff --git a/spot/taalgos/emptinessta.hh b/spot/taalgos/emptinessta.hh
index 39cc65106..ff3abd6f3 100644
--- a/spot/taalgos/emptinessta.hh
+++ b/spot/taalgos/emptinessta.hh
@@ -1,9 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2008, 2012, 2013, 2014, 2016 Laboratoire de Recherche
+// Copyright (C) 2012-2014, 2016, 2018 Laboratoire de Recherche
 // et Dévelopment de l'Epita (LRDE).
-// Copyright (C) 2003, 2004, 2005, 2006 Laboratoire d'Informatique de
-// Paris 6 (LIP6), département Systèmes Répartis Coopératifs (SRC),
-// Université Pierre et Marie Curie.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -39,7 +36,8 @@ namespace spot
 
   /// \addtogroup ta_emptiness_check Emptiness-checks
   /// \ingroup ta_algorithms
-  ///
+
+  /// \ingroup ta_emptiness_check
   /// \brief Check whether the language of a product (spot::ta_product) between
   ///  a Kripke structure and a TA  is empty. It works also for the product
   /// using Generalized TA (GTA and SGTA).
@@ -156,6 +154,4 @@ namespace spot
 
   /// @}
 
-    /// \addtogroup ta_emptiness_check_algorithms Emptiness-check algorithms
-    /// \ingroup ta_emptiness_check
 }
diff --git a/spot/twa/twa.hh b/spot/twa/twa.hh
index d9699cc67..1438ddb5c 100644
--- a/spot/twa/twa.hh
+++ b/spot/twa/twa.hh
@@ -1690,6 +1690,9 @@ namespace spot
   /// \addtogroup stutter_inv Stutter-invariance checks
   /// \ingroup twa_algorithms
 
+  /// \addtogroup twa_acc_transform Conversion between acceptance conditions
+  /// \ingroup twa_algorithms
+
   /// \addtogroup twa_ltl Translating LTL formulas into TωA
   /// \ingroup twa_algorithms
 
diff --git a/spot/twa/twagraph.cc b/spot/twa/twagraph.cc
index f4330b078..f43b1b48d 100644
--- a/spot/twa/twagraph.cc
+++ b/spot/twa/twagraph.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016, 2017 Laboratoire de Recherche et
-// Développement de l'Epita.
+// Copyright (C) 2014-2018 Laboratoire de Recherche et Développement
+// de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -494,8 +494,8 @@ namespace spot
         // #3 get rid of the unused universal destinations
         // #4 merge identical universal destinations
         //
-        // graph::degrag_states() actually does only #1. It it could
-        // do #2, but that would prevent use from doing #3 and #4.  It
+        // graph::degrag_states() actually does only #1. It could
+        // do #2, but that would prevent us from doing #3 and #4.  It
         // cannot do #3 and #4 because the graph object does not know
         // what an initial state is, and our initial state might be
         // universal.
diff --git a/spot/twa/twagraph.hh b/spot/twa/twagraph.hh
index fa738aefc..46d4d506b 100644
--- a/spot/twa/twagraph.hh
+++ b/spot/twa/twagraph.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement de l'Epita.
+// Copyright (C) 2014-2018 Laboratoire de Recherche et Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -29,6 +29,12 @@
 namespace spot
 {
 
+  /// \ingroup twa_representation
+  /// \brief Graph-based representation of a TωA
+  ///
+  /// In a twa_graph, states are usually denoted by their number.  However
+  /// if the on-the-fly interface is used, it returns pointer to instances
+  /// of the twa_graph_state class.
   struct SPOT_API twa_graph_state: public spot::state
   {
   public:
@@ -69,6 +75,13 @@ namespace spot
     }
   };
 
+  /// \ingroup twa_representation
+  /// \brief Data attached to edges of a twa_graph
+  ///
+  /// Each edge of the graph has to additional data that are \a cond
+  /// (a BDD representing the Boolean formula labeling the edge), and
+  /// \a acc a set of acceptance marks representing the membership of
+  /// the each to each acceptance set.
   struct SPOT_API twa_graph_edge_data
   {
     bdd cond;
@@ -101,6 +114,11 @@ namespace spot
   };
 
 
+
+  /// \ingroup twa_representation
+  /// \brief Iterator used by the on-the-fly interface of twa_graph.
+  ///
+  /// Instances of this class are returned by twa_graph::succ_iter().
   template<class Graph>
   class SPOT_API twa_graph_succ_iterator final:
     public twa_succ_iterator
@@ -165,6 +183,8 @@ namespace spot
 
   };
 
+  /// \ingroup twa_representation
+  /// \brief Graph-based representation of a TωA
   class SPOT_API twa_graph final: public twa
   {
   public:
@@ -505,11 +525,25 @@ namespace spot
       SPOT_RETURN(g_.is_dead_edge(t));
 #endif
 
-    /// Iterate over all edges, and merge those with compatible
-    /// extremities and acceptance.
+    /// \brief Merge edges that can be merged.
+    ///
+    /// This makes two passes over the automaton to reduce the number
+    /// of edges with an identical pair of source and destination.
+    ///
+    /// In the first pass, edges that share their source, destination,
+    /// and acceptance marks are merged into a single edge whose condition
+    /// is the conjunction of the conditions of the original edges.
+    ///
+    /// In the second pass, which is performed only on automata with
+    /// Fin-less acceptance, edges with the same source, destination,
+    /// and conditions are merged into a single edge whose set of
+    /// acceptance marks is the intersection of the sets of the edges.
+    ///
+    /// If the automaton uses some universal edges, the method
+    /// merge_univ_dests() is also called.
     void merge_edges();
 
-    /// \brief marge common universal destination
+    /// \brief Merge common universal destinations.
     ///
     /// This is already called by merge_edges().
     void merge_univ_dests();
@@ -559,6 +593,8 @@ namespace spot
     /// assumed.
     void copy_state_names_from(const const_twa_graph_ptr& other);
 
+    /// \brief Return the marks associated to a state if the
+    /// acceptance is state-based.
     acc_cond::mark_t state_acc_sets(unsigned s) const
     {
       if (SPOT_UNLIKELY(!(bool)prop_state_acc()))
@@ -572,6 +608,12 @@ namespace spot
       return 0U;
     }
 
+    /// \brief Tell if a state is acceptince.
+    ///
+    /// This makes only sense for automata using state-based
+    /// acceptance, and a simple acceptance condition like Büchi or
+    /// co-Büchi.
+    ///@{
     bool state_is_accepting(unsigned s) const
     {
       if (SPOT_UNLIKELY(!(bool)prop_state_acc()))
@@ -589,6 +631,7 @@ namespace spot
     {
       return state_is_accepting(state_number(s));
     }
+    ///@}
 
     bool operator==(const twa_graph& aut) const
     {
@@ -608,17 +651,26 @@ namespace spot
                         dests2.begin());
     }
 
+    /// \brief Renumber all states, and drop some.
+    ///
+    /// This semi-internal function is a wrapper around
+    /// digraph::defrag_state() that additionally deals with universal
+    /// branching.
+    ///
+    /// \param newst A vector indicating how each state should be renumbered.
+    /// Use -1U to erase a state.
+    /// \param used_states the number of states used (after renumbering)
     void defrag_states(std::vector<unsigned>&& newst, unsigned used_states);
   };
 
-  /// \ingroup twa
+  /// \ingroup twa_representation
   /// \brief Build an explicit automaton from all states of \a aut,
   inline twa_graph_ptr make_twa_graph(const bdd_dict_ptr& dict)
   {
     return std::make_shared<twa_graph>(dict);
   }
 
-  /// \ingroup twa
+  /// \ingroup twa_representation
   /// \brief Build an explicit automaton from all states of \a aut,
   inline twa_graph_ptr make_twa_graph(const twa_graph_ptr& aut,
                                       twa::prop_set p)
@@ -626,7 +678,7 @@ namespace spot
     return std::make_shared<twa_graph>(aut, p);
   }
 
-  /// \ingroup twa
+  /// \ingroup twa_representation
   /// \brief Build an explicit automaton from all states of \a aut,
   inline twa_graph_ptr make_twa_graph(const const_twa_graph_ptr& aut,
                                       twa::prop_set p)
@@ -634,7 +686,7 @@ namespace spot
     return std::make_shared<twa_graph>(aut, p);
   }
 
-  /// \ingroup twa
+  /// \ingroup twa_representation
   /// \brief Build an explicit automaton from all states of \a aut,
   ///
   /// This overload works using the abstract interface for automata.
diff --git a/spot/twaalgos/bfssteps.hh b/spot/twaalgos/bfssteps.hh
index 32fa9ed15..015a41328 100644
--- a/spot/twaalgos/bfssteps.hh
+++ b/spot/twaalgos/bfssteps.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2013, 2014 Laboratoire de Recherche et Developpement de
-// l'Epita (LRDE).
+// Copyright (C) 2011, 2013, 2014, 2018 Laboratoire de Recherche et
+// Developpement de l'Epita (LRDE).
 // Copyright (C) 2004, 2005  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
@@ -27,7 +27,7 @@
 
 namespace spot
 {
-  /// \ingroup twa_misc
+  /// \ingroup twa_generic
   /// \brief Make a BFS in a spot::tgba to compute a twa_run::steps.
   ///
   /// This class should be used to compute the shortest path
diff --git a/spot/twaalgos/cleanacc.hh b/spot/twaalgos/cleanacc.hh
index 461dad9d3..600653466 100644
--- a/spot/twaalgos/cleanacc.hh
+++ b/spot/twaalgos/cleanacc.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2017 Laboratoire de Recherche et Développement
-// de l'Epita.
+// Copyright (C) 2015, 2017, 2018 Laboratoire de Recherche et
+// Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -23,7 +23,7 @@
 
 namespace spot
 {
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Remove useless acceptance sets
   ///
   /// This removes from the automaton the acceptance marks that are
@@ -37,7 +37,7 @@ namespace spot
   SPOT_API twa_graph_ptr
   cleanup_acceptance_here(twa_graph_ptr aut, bool strip = true);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Remove useless acceptance sets
   ///
   /// This removes from the automaton the acceptance marks that are
@@ -49,7 +49,7 @@ namespace spot
   cleanup_acceptance(const_twa_graph_ptr aut);
 
   /// @{
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Simplify an acceptance condition
   ///
   /// Does evereything cleanup_acceptance() does, but additionally:
diff --git a/spot/twaalgos/degen.hh b/spot/twaalgos/degen.hh
index 665ff838f..6063bf4b7 100644
--- a/spot/twaalgos/degen.hh
+++ b/spot/twaalgos/degen.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014 2015, 2017, Laboratoire de Recherche et
-// Développement de l'Epita.
+// Copyright (C) 2012-2015, 2017, 2018 Laboratoire de
+// Recherche et Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -23,7 +23,7 @@
 
 namespace spot
 {
-  /// \ingroup twa_misc
+  /// \ingroup twa_acc_transform
   /// \brief Degeneralize a spot::tgba into an equivalent sba with
   /// only one acceptance condition.
   ///
diff --git a/spot/twaalgos/dualize.hh b/spot/twaalgos/dualize.hh
index 100b2107f..f5f5cb7af 100644
--- a/spot/twaalgos/dualize.hh
+++ b/spot/twaalgos/dualize.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2017 Laboratoire de Recherche et Développement de
-// l'Epita (LRDE).
+// Copyright (C) 2017, 2018 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -24,6 +24,7 @@
 
 namespace spot
 {
+  /// \ingroup twa_misc
   /// \brief Complement an automaton by dualizing it.
   ///
   /// Given an automaton \a aut of any type, produces the dual as output. The
diff --git a/spot/twaalgos/parity.hh b/spot/twaalgos/parity.hh
index f1765df0e..672bb5754 100644
--- a/spot/twaalgos/parity.hh
+++ b/spot/twaalgos/parity.hh
@@ -25,7 +25,7 @@
 namespace spot
 {
   /// \addtogroup parity_algorithms Algorithms for parity acceptance
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
 
   /// \ingroup parity_algorithms
   /// @{
diff --git a/spot/twaalgos/rabin2parity.hh b/spot/twaalgos/rabin2parity.hh
index 64b74b414..56fd78142 100644
--- a/spot/twaalgos/rabin2parity.hh
+++ b/spot/twaalgos/rabin2parity.hh
@@ -22,6 +22,7 @@
 
 namespace spot
 {
+  /// \ingroup twa_acc_transform
   /// \brief Turn a Rabin-like automaton into a parity automaton based on the
   /// index appearence record (IAR)
   ///
@@ -34,12 +35,18 @@ namespace spot
   /// acceptance condition.
   /// Details on the algorithm can be found in:
   ///   https://arxiv.org/pdf/1701.05738.pdf (published at TACAS 2017)
+  ///
+  /// Throws an std::runtime_error if the input is not Rabin-like.
   SPOT_API
   twa_graph_ptr
   iar(const const_twa_graph_ptr& aut);
 
-  /// Return nullptr if the input automaton is not Rabin-like, and calls iar()
-  /// otherwise.
+  /// \ingroup twa_acc_transform
+  /// \brief Turn a Rabin-like automaton into a parity automaton based on the
+  /// index appearence record (IAR)
+  ///
+  /// Return nullptr if the input automaton is not Rabin-like, and
+  /// calls spot::iar() otherwise.
   SPOT_API
   twa_graph_ptr
   iar_maybe(const const_twa_graph_ptr& aut);
diff --git a/spot/twaalgos/remfin.hh b/spot/twaalgos/remfin.hh
index f53dee551..6444eba46 100644
--- a/spot/twaalgos/remfin.hh
+++ b/spot/twaalgos/remfin.hh
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2017 Laboratoire de Recherche et Développement
-// de l'Epita.
+// Copyright (C) 2015, 2017, 2018 Laboratoire de Recherche et
+// Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
 //
@@ -23,7 +23,7 @@
 
 namespace spot
 {
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Convert a Rabin automaton to Büchi automaton, preserving
   /// determinism when possible.
   ///
@@ -40,7 +40,7 @@ namespace spot
   SPOT_API twa_graph_ptr
   rabin_to_buchi_maybe(const const_twa_graph_ptr& aut);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Rewrite an automaton without Fin acceptance.
   ///
   /// This algorithm dispatches between many strategies.  It has
diff --git a/spot/twaalgos/sccinfo.hh b/spot/twaalgos/sccinfo.hh
index 7acd009c6..684a6e9c8 100644
--- a/spot/twaalgos/sccinfo.hh
+++ b/spot/twaalgos/sccinfo.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
+// Copyright (C) 2014-2018 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -211,7 +211,8 @@ namespace spot
   }
 
 
-  /// Storage for SCC related information.
+  /// \ingroup twa_misc
+  /// \brief Storage for SCC related information.
   class SPOT_API scc_info_node
   {
   public:
@@ -298,7 +299,8 @@ namespace spot
     }
   };
 
-  /// Options to alter the behavior of scc_info
+  /// \ingroup twa_misc
+  /// \brief Options to alter the behavior of scc_info
   enum class scc_info_options
   {
     /// Stop exploring when an accepting SCC is found, and do not track
@@ -347,6 +349,7 @@ namespace spot
                                          | static_cast<ut>(right));
   }
 
+  /// \ingroup twa_misc
   /// \brief Compute an SCC map and gather assorted information.
   ///
   /// This takes twa_graph as input and compute its SCCs.  This
diff --git a/spot/twaalgos/sepsets.hh b/spot/twaalgos/sepsets.hh
index 5d7d39270..5fd7c895e 100644
--- a/spot/twaalgos/sepsets.hh
+++ b/spot/twaalgos/sepsets.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015 Laboratoire de Recherche et Développement
+// Copyright (C) 2015, 2018 Laboratoire de Recherche et Développement
 // de l'Epita.
 //
 // This file is part of Spot, a model checking library.
@@ -23,10 +23,12 @@
 
 namespace spot
 {
+  /// \ingroup twa_acc_transform
   /// \brief Whether the Inf and Fin numbers are disjoints
   SPOT_API bool
   has_separate_sets(const const_twa_graph_ptr& aut);
 
+  /// \ingroup twa_acc_transform
   /// \brief Separate the Fin and Inf sets used by an automaton
   ///
   /// This makes sure that the numbers used a Fin and Inf are
diff --git a/spot/twaalgos/split.hh b/spot/twaalgos/split.hh
index 8f9fae443..9247c4aab 100644
--- a/spot/twaalgos/split.hh
+++ b/spot/twaalgos/split.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2017 Laboratoire de Recherche et Développement
+// Copyright (C) 2017, 2018 Laboratoire de Recherche et Développement
 // de l'Epita.
 //
 // This file is part of Spot, a model checking library.
@@ -23,6 +23,7 @@
 
 namespace spot
 {
+  /// \ingroup twa_misc
   /// \brief transform edges into transitions
   ///
   /// Create a new version of the automaton where all edges are split
diff --git a/spot/twaalgos/totgba.hh b/spot/twaalgos/totgba.hh
index f43f52fa2..5e75d703f 100644
--- a/spot/twaalgos/totgba.hh
+++ b/spot/twaalgos/totgba.hh
@@ -25,7 +25,7 @@
 
 namespace spot
 {
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Take an automaton with any acceptance condition and return
   /// an equivalent Generalized Büchi automaton.
   ///
@@ -37,13 +37,13 @@ namespace spot
   SPOT_API twa_graph_ptr
   to_generalized_buchi(const const_twa_graph_ptr& aut);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Convert Streett acceptance into generalized Büchi
   /// acceptance.
   SPOT_API twa_graph_ptr
   streett_to_generalized_buchi(const const_twa_graph_ptr& in);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Convert Streett acceptance into generalized Büchi
   ///
   /// This version only works SPOT_STREET_CONF_MIN is set to a number
@@ -53,7 +53,7 @@ namespace spot
   SPOT_API twa_graph_ptr
   streett_to_generalized_buchi_maybe(const const_twa_graph_ptr& in);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Take an automaton with any acceptance condition and return
   /// an equivalent Generalized Rabin automaton.
   ///
@@ -68,7 +68,7 @@ namespace spot
   to_generalized_rabin(const const_twa_graph_ptr& aut,
                        bool share_inf = false);
 
-  /// \ingroup twa_algorithms
+  /// \ingroup twa_acc_transform
   /// \brief Take an automaton with any acceptance condition and return
   /// an equivalent Generalized Streett automaton.
   ///
@@ -83,6 +83,7 @@ namespace spot
   to_generalized_streett(const const_twa_graph_ptr& aut,
                          bool share_fin = false);
 
+  /// \ingroup twa_acc_transform
   /// \brief Converts any DNF acceptance condition into Streett-like.
   ///
   /// This function is an optimized version of the construction described