diff --git a/NEWS b/NEWS
index d24d911fc..d63e07b4c 100644
--- a/NEWS
+++ b/NEWS
@@ -13,6 +13,10 @@ New in spot 2.3.0.dev (not yet released)
 
   - spot::twa_run::as_twa() has an option to preserve state names.
 
+  - the method spot::twa::is_alternating(), introduced in Spot 2.3 was
+    badly named and has been deprecated.  Use the negation of the new
+    spot::twa::is_existential() instead.
+
   Bugs fixed:
 
   - spot::otf_product() was incorrectly registering atomic
diff --git a/bin/autfilt.cc b/bin/autfilt.cc
index 41ce76c9f..3142dcf84 100644
--- a/bin/autfilt.cc
+++ b/bin/autfilt.cc
@@ -485,7 +485,7 @@ static bool opt_highlight_languages = false;
 static spot::twa_graph_ptr
 ensure_deterministic(const spot::twa_graph_ptr& aut, bool nonalt = false)
 {
-  if (!(nonalt && aut->is_alternating()) && spot::is_deterministic(aut))
+  if ((!nonalt || aut->is_existential()) && spot::is_deterministic(aut))
     return aut;
   spot::postprocessor p;
   p.set_type(spot::postprocessor::Generic);
@@ -1044,7 +1044,7 @@ namespace
           matched &= opt_used_ap_n.contains(aut->ap().size() - unused);
         }
       if (matched && opt_is_alternating)
-        matched &= aut->is_alternating();
+        matched &= !aut->is_existential();
       if (matched && opt_is_complete)
         matched &= is_complete(aut);
       if (matched && (opt_sccs_set | opt_art_sccs_set))
diff --git a/bin/ltlcross.cc b/bin/ltlcross.cc
index 5a55df9d3..5cbed97a1 100644
--- a/bin/ltlcross.cc
+++ b/bin/ltlcross.cc
@@ -648,7 +648,7 @@ namespace
               if (verbose)
                 std::cerr << "info: getting statistics\n";
               st->ok = true;
-              st->alternating = res->is_alternating();
+              st->alternating = !res->is_existential();
               spot::twa_sub_statistics s = sub_stats_reachable(res);
               st->states = s.states;
               st->edges = s.edges;
@@ -1118,7 +1118,7 @@ namespace
               std::cerr << "info:   " << prefix << i << "\t(";
               printsize(x[i]);
               std::cerr << ')';
-              if (x[i]->is_alternating())
+              if (!x[i]->is_existential())
                 std::cerr << " univ-edges";
               if (is_deterministic(x[i]))
                 std::cerr << " deterministic";
@@ -1142,7 +1142,7 @@ namespace
           auto unalt = [&](std::vector<spot::twa_graph_ptr>& x,
                            unsigned i, char prefix)
             {
-              if (!(x[i] && x[i]->is_alternating()))
+              if (!x[i] || x[i]->is_existential())
                 return;
               if (verbose)
                 {
diff --git a/spot/graph/graph.hh b/spot/graph/graph.hh
index 4dd47b37c..31e7f264d 100644
--- a/spot/graph/graph.hh
+++ b/spot/graph/graph.hh
@@ -656,11 +656,23 @@ namespace spot
       return edges_.size() - killed_edge_ - 1;
     }
 
-    /// Whether the automaton is alternating
+    /// Whether the automaton uses only existential branching.
+    bool is_existential() const
+    {
+      return dests_.empty();
+    }
+
+#ifndef SWIG
+    /// \brief Whether the automaton has universal branching
+    ///
+    /// The name of this function is confusing since non-deterministic
+    /// automata should be a subclass of alternating automata.
+    SPOT_DEPRECATED("use !is_existential() instead")
     bool is_alternating() const
     {
-      return !dests_.empty();
+      return !is_existential();
     }
+#endif
 
     /// \brief Create a new states
     ///
diff --git a/spot/misc/common.hh b/spot/misc/common.hh
index 94ed98234..554644615 100644
--- a/spot/misc/common.hh
+++ b/spot/misc/common.hh
@@ -32,17 +32,21 @@
 #endif
 
 #ifdef __has_cpp_attribute
-#  if __has_cpp_attribute(deprecated)
-#    define SPOT_DEPRECATED [[deprecated]]
+#  if __has_cpp_attribute(deprecated) && __cplusplus >= 201402L
+#    define SPOT_DEPRECATED(msg) [[deprecated(msg)]]
+#  elif __has_cpp_attribute(gnu::deprecated)
+#    define SPOT_DEPRECATED(msg) [[gnu::deprecated(msg)]]
+#  elif __has_cpp_attribute(clang::deprecated)
+#    define SPOT_DEPRECATED(msg) [[clang::deprecated(msg)]]
 #  endif
 #endif
 #ifndef SPOT_DEPRECATED
 #  ifdef __GNUC__
-#    define SPOT_DEPRECATED __attribute__ ((deprecated))
+#    define SPOT_DEPRECATED(msg) __attribute__ ((deprecated))
 #  elif defined(_MSC_VER)
-#    define SPOT_DEPRECATED __declspec(deprecated)
+#    define SPOT_DEPRECATED(msg) __declspec(deprecated)
 #  else
-#    define SPOT_DEPRECATED
+#    define SPOT_DEPRECATED(msg)
 #  endif
 #endif
 
diff --git a/spot/parseaut/parseaut.yy b/spot/parseaut/parseaut.yy
index 63de3bf1d..a3a81f75c 100644
--- a/spot/parseaut/parseaut.yy
+++ b/spot/parseaut/parseaut.yy
@@ -2436,7 +2436,7 @@ namespace spot
     fix_acceptance(r);
     fix_initial_state(r);
     fix_properties(r);
-    if (r.h->aut && r.h->aut->is_alternating())
+    if (r.h->aut && !r.h->aut->is_existential())
       r.h->aut->merge_univ_dests();
     return r.h;
   };
diff --git a/spot/twa/twa.cc b/spot/twa/twa.cc
index 75b6e721d..81dd490ee 100644
--- a/spot/twa/twa.cc
+++ b/spot/twa/twa.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2014-2016 Laboratoire de Recherche et Developpement de
+// Copyright (C) 2011, 2014-2017 Laboratoire de Recherche et Developpement de
 // l'EPITA (LRDE).
 // Copyright (C) 2003, 2004, 2005 Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
@@ -53,7 +53,7 @@ namespace spot
     const_twa_ptr remove_fin_maybe(const const_twa_ptr& a)
     {
       auto aa = std::dynamic_pointer_cast<const twa_graph>(a);
-      if ((!aa || !aa->is_alternating()) && !a->acc().uses_fin_acceptance())
+      if ((!aa || aa->is_existential()) && !a->acc().uses_fin_acceptance())
         return a;
       if (!aa)
         aa = make_twa_graph(a, twa::prop_set::all());
diff --git a/spot/twa/twagraph.cc b/spot/twa/twagraph.cc
index 04ea0cb81..28733cab6 100644
--- a/spot/twa/twagraph.cc
+++ b/spot/twa/twagraph.cc
@@ -86,7 +86,7 @@ namespace spot
   {
     set_named_prop("highlight-edges", nullptr);
     g_.remove_dead_edges_();
-    if (is_alternating())
+    if (!is_existential())
       merge_univ_dests();
 
     typedef graph_t::edge_storage_t tr_t;
@@ -245,7 +245,7 @@ namespace spot
     std::vector<unsigned> order;
     order.reserve(num_states);
 
-    if (!is_alternating())
+    if (is_existential())
       {
         std::vector<std::pair<unsigned, unsigned>> todo; // state, edge
         useful[get_init_state_number()] = 1;
@@ -399,7 +399,7 @@ namespace spot
   void twa_graph::defrag_states(std::vector<unsigned>&& newst,
                                 unsigned used_states)
   {
-    if (is_alternating())
+    if (!is_existential())
       {
         auto& g = get_graph();
         auto& dests = g.dests_vector();
diff --git a/spot/twa/twagraph.hh b/spot/twa/twagraph.hh
index 9c3f77014..18732b7f0 100644
--- a/spot/twa/twagraph.hh
+++ b/spot/twa/twagraph.hh
@@ -294,7 +294,7 @@ namespace spot
     virtual const twa_graph_state* get_init_state() const override
     {
       unsigned n = get_init_state_number();
-      if (SPOT_UNLIKELY(is_alternating()))
+      if (SPOT_UNLIKELY(!is_existential()))
         throw std::runtime_error
           ("the abstract interface does not support alternating automata");
       return state_from_number(n);
@@ -479,10 +479,23 @@ namespace spot
       return g_.univ_dests(e);
     }
 
+    /// Whether the automaton uses only existential branching.
+    bool is_existential() const
+    {
+      return g_.is_existential();
+    }
+
+#ifndef SWIG
+    /// \brief Whether the automaton has universal branching
+    ///
+    /// The name of this function is confusing since non-deterministic
+    /// automata should be a subclass of alternating automata.
+    SPOT_DEPRECATED("use !is_existential() instead")
     bool is_alternating() const
     {
-      return g_.is_alternating();
+      return !is_existential();
     }
+#endif
 
 #ifndef SWIG
     auto states() const
diff --git a/spot/twaalgos/alternation.cc b/spot/twaalgos/alternation.cc
index 9af21b332..0f4f0492c 100644
--- a/spot/twaalgos/alternation.cc
+++ b/spot/twaalgos/alternation.cc
@@ -479,7 +479,7 @@ namespace spot
   twa_graph_ptr remove_alternation(const const_twa_graph_ptr& aut,
                                    bool named_states)
   {
-    if (!aut->is_alternating())
+    if (aut->is_existential())
       // Nothing to do, why was this function called at all?
       return std::const_pointer_cast<twa_graph>(aut);
 
diff --git a/spot/twaalgos/are_isomorphic.cc b/spot/twaalgos/are_isomorphic.cc
index fbb327822..4876def46 100644
--- a/spot/twaalgos/are_isomorphic.cc
+++ b/spot/twaalgos/are_isomorphic.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et
-// Développement de l'Epita (LRDE).
+// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
+// 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.
@@ -132,7 +132,7 @@ namespace spot
   bool
   isomorphism_checker::is_isomorphic_(const const_twa_graph_ptr aut)
   {
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       throw std::runtime_error
         ("isomorphism_checker does not yet support alternation");
     trival autdet = aut->prop_deterministic();
diff --git a/spot/twaalgos/canonicalize.cc b/spot/twaalgos/canonicalize.cc
index 5bc93235b..9b3cbaa39 100644
--- a/spot/twaalgos/canonicalize.cc
+++ b/spot/twaalgos/canonicalize.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et
-// Developpement de l Epita (LRDE).
+// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -73,7 +73,7 @@ namespace spot
   twa_graph_ptr
   canonicalize(twa_graph_ptr aut)
   {
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       throw std::runtime_error
         ("canonicalize does not yet support alternation");
     std::vector<unsigned> state2class(aut->num_states(), 0);
diff --git a/spot/twaalgos/couvreurnew.cc b/spot/twaalgos/couvreurnew.cc
index fb67593f4..e38c208fc 100644
--- a/spot/twaalgos/couvreurnew.cc
+++ b/spot/twaalgos/couvreurnew.cc
@@ -1,5 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2016 Laboratoire de Recherche et Développement de l'Epita.
+// Copyright (C) 2016-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -219,7 +220,7 @@ namespace spot
       state_t
       initial_state(const const_twa_graph_ptr& twa_p)
       {
-        if (twa_p->is_alternating())
+        if (!twa_p->is_existential())
           throw std::runtime_error
             ("couvreur99_new does not support alternation");
         return twa_p->get_init_state_number();
diff --git a/spot/twaalgos/cycles.cc b/spot/twaalgos/cycles.cc
index 2d52aaeed..90deed5b3 100644
--- a/spot/twaalgos/cycles.cc
+++ b/spot/twaalgos/cycles.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2014, 2015, 2016 Laboratoire de Recherche et
-// Developpement de l'Epita (LRDE).
+// Copyright (C) 2012, 2014-2017 Laboratoire de Recherche et
+// Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -27,7 +27,7 @@ namespace spot
       info_(aut_->num_states(), aut_->num_states()),
       sm_(map)
   {
-    if (aut_->is_alternating())
+    if (!aut_->is_existential())
       throw std::runtime_error
         ("enumerate_cycles does not support alternation");
   }
diff --git a/spot/twaalgos/degen.cc b/spot/twaalgos/degen.cc
index 9256afc1b..175c10e83 100644
--- a/spot/twaalgos/degen.cc
+++ b/spot/twaalgos/degen.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014, 2015, 2016 Laboratoire de Recherche
-// et Développement de l'Epita.
+// Copyright (C) 2012-2017 Laboratoire de Recherche
+// et Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -197,7 +197,7 @@ namespace spot
       if (!a->acc().is_generalized_buchi())
         throw std::runtime_error
           ("degeneralize() can only works with generalized Büchi acceptance");
-      if (a->is_alternating())
+      if (!a->is_existential())
         throw std::runtime_error
           ("degeneralize() does not support alternation");
 
diff --git a/spot/twaalgos/determinize.cc b/spot/twaalgos/determinize.cc
index 37e9ede1f..3f4f68dbf 100644
--- a/spot/twaalgos/determinize.cc
+++ b/spot/twaalgos/determinize.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2016, 2017 Laboratoire de Recherche et
+// Copyright (C) 2015-2017 Laboratoire de Recherche et
 // Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
@@ -579,7 +579,7 @@ namespace spot
                    bool pretty_print, bool use_scc,
                    bool use_simulation, bool use_stutter)
   {
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("tgba_determinize() does not support alternation");
     if (a->prop_deterministic())
diff --git a/spot/twaalgos/dot.cc b/spot/twaalgos/dot.cc
index 274fa9031..1fec69255 100644
--- a/spot/twaalgos/dot.cc
+++ b/spot/twaalgos/dot.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2012, 2014, 2015, 2016 Laboratoire de Recherche
-// et Developpement de l'Epita (LRDE).
+// Copyright (C) 2011, 2012, 2014-2017 Laboratoire de Recherche
+// et Développement de l'Epita (LRDE).
 // Copyright (C) 2003, 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
 // et Marie Curie.
@@ -707,7 +707,7 @@ namespace spot
         start();
         if (si)
           {
-            if (!aut->is_alternating())
+            if (aut->is_existential())
               si->determine_unknown_acceptance();
 
             unsigned sccs = si->scc_count();
diff --git a/spot/twaalgos/dtbasat.cc b/spot/twaalgos/dtbasat.cc
index e9b2e029e..908e7dcd8 100644
--- a/spot/twaalgos/dtbasat.cc
+++ b/spot/twaalgos/dtbasat.cc
@@ -715,7 +715,7 @@ namespace spot
   dtba_sat_synthetize(const const_twa_graph_ptr& a,
                       int target_state_number, bool state_based)
   {
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("dtba_sat_synthetize() does not support alternating automata");
     if (!a->acc().is_buchi())
diff --git a/spot/twaalgos/dtwasat.cc b/spot/twaalgos/dtwasat.cc
index e5ad46210..5e6ed6d1b 100644
--- a/spot/twaalgos/dtwasat.cc
+++ b/spot/twaalgos/dtwasat.cc
@@ -992,7 +992,7 @@ namespace spot
                       int target_state_number,
                       bool state_based, bool colored)
   {
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("dtwa_sat_synthetize() does not support alternating automata");
     if (target_state_number == 0)
diff --git a/spot/twaalgos/hoa.cc b/spot/twaalgos/hoa.cc
index 7a6c416a7..469b66a32 100644
--- a/spot/twaalgos/hoa.cc
+++ b/spot/twaalgos/hoa.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2011, 2012, 2014, 2015, 2016 Laboratoire de Recherche et
+// Copyright (C) 2011, 2012, 2014, 2015, 2016, 2017 Laboratoire de Recherche et
 // Developpement de l'Epita (LRDE).
 // Copyright (C) 2003, 2004  Laboratoire d'Informatique de Paris 6 (LIP6),
 // département Systèmes Répartis Coopératifs (SRC), Université Pierre
@@ -445,7 +445,7 @@ namespace spot
     // property.  The "univ-branch" property seems more important to
     // announce that the automaton might not be parsable by tools that
     // do not support alternating automata.
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       {
         prop(" univ-branch");
       }
diff --git a/spot/twaalgos/isunamb.cc b/spot/twaalgos/isunamb.cc
index c481a910c..fe22ce140 100644
--- a/spot/twaalgos/isunamb.cc
+++ b/spot/twaalgos/isunamb.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013, 2015, 2016 Laboratoire de Recherche et Developpement
-// de l'Epita (LRDE).
+// Copyright (C) 2013, 2015-2017 Laboratoire de Recherche et
+// Developpement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -37,7 +37,7 @@ namespace spot
   // we used to have, was motivated by issue #188.
   bool is_unambiguous(const const_twa_graph_ptr& aut)
   {
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       throw std::runtime_error
         ("is_unambiguous() does not support alternation");
 
diff --git a/spot/twaalgos/isweakscc.cc b/spot/twaalgos/isweakscc.cc
index b9c03cb3f..feafb2cd3 100644
--- a/spot/twaalgos/isweakscc.cc
+++ b/spot/twaalgos/isweakscc.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014, 2015, 2016 Laboratoire de Recherche
-// et Developpement de l'Epita (LRDE).
+// Copyright (C) 2012-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -27,7 +27,7 @@ namespace spot
   scc_has_rejecting_cycle(scc_info& map, unsigned scc)
   {
     auto aut = map.get_aut();
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       throw std::runtime_error
         ("scc_has_rejecting_cycle() does not support alternation");
     // We check that by cloning the SCC and complementing its
@@ -45,7 +45,7 @@ namespace spot
   bool
   is_inherently_weak_scc(scc_info& map, unsigned scc)
   {
-    if (map.get_aut()->is_alternating())
+    if (!map.get_aut()->is_existential())
       throw std::runtime_error
         ("is_inherently_weak_scc() does not support alternation");
      // Weak SCCs are inherently weak.
@@ -60,7 +60,7 @@ namespace spot
   bool
   is_weak_scc(scc_info& map, unsigned scc)
   {
-    if (map.get_aut()->is_alternating())
+    if (!map.get_aut()->is_existential())
       throw std::runtime_error
         ("is_weak_scc() does not support alternation");
 
@@ -75,7 +75,7 @@ namespace spot
   is_complete_scc(scc_info& map, unsigned scc)
   {
     auto a = map.get_aut();
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("is_complete_scc() does not support alternation");
     for (auto s: map.states_of(scc))
@@ -99,7 +99,7 @@ namespace spot
   bool
   is_terminal_scc(scc_info& map, unsigned scc)
   {
-    if (map.get_aut()->is_alternating())
+    if (!map.get_aut()->is_existential())
       throw std::runtime_error
         ("is_terminal_scc() does not support alternation");
 
diff --git a/spot/twaalgos/mask.hh b/spot/twaalgos/mask.hh
index 83b5404a5..3ce03b700 100644
--- a/spot/twaalgos/mask.hh
+++ b/spot/twaalgos/mask.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2016 Laboratoire de Recherche et Développement
+// Copyright (C) 2015, 2016, 2017 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -43,7 +43,7 @@ namespace spot
                             twa_graph_ptr& cpy,
                             Trans trans, unsigned int init)
   {
-    if (old->is_alternating())
+    if (!old->is_existential())
       throw std::runtime_error
         ("transform_accessible() does not support alternation");
 
@@ -105,7 +105,7 @@ namespace spot
                       twa_graph_ptr& cpy,
                       Trans trans, unsigned int init)
   {
-    if (old->is_alternating())
+    if (!old->is_existential())
       throw std::runtime_error
         ("transform_copy() does not support alternation");
 
diff --git a/spot/twaalgos/minimize.cc b/spot/twaalgos/minimize.cc
index 39685caf3..4a199fbd5 100644
--- a/spot/twaalgos/minimize.cc
+++ b/spot/twaalgos/minimize.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2010, 2011, 2012, 2013, 2014, 2015, 2016, 2017 Laboratoire de
-// Recherche et Développement de l'Epita (LRDE).
+// Copyright (C) 2010-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -474,7 +474,7 @@ namespace spot
 
   twa_graph_ptr minimize_monitor(const const_twa_graph_ptr& a)
   {
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("minimize_monitor() does not support alternation");
 
@@ -495,7 +495,7 @@ namespace spot
 
   twa_graph_ptr minimize_wdba(const const_twa_graph_ptr& a)
   {
-    if (a->is_alternating())
+    if (!a->is_existential())
       throw std::runtime_error
         ("minimize_wdba() does not support alternation");
 
@@ -610,7 +610,7 @@ namespace spot
                       const_twa_graph_ptr aut_neg_f,
                       bool reject_bigger)
   {
-    if (aut_f->is_alternating())
+    if (!aut_f->is_existential())
       throw std::runtime_error
         ("minimize_obligation() does not support alternation");
 
diff --git a/spot/twaalgos/postproc.cc b/spot/twaalgos/postproc.cc
index e9f8b6f16..2191b8924 100644
--- a/spot/twaalgos/postproc.cc
+++ b/spot/twaalgos/postproc.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014, 2015, 2016 Laboratoire de Recherche et
-// Développement de l'Epita (LRDE).
+// Copyright (C) 2012-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -182,7 +182,7 @@ namespace spot
     if (type_ == BA || SBACC_)
       state_based_ = true;
 
-    if (a->is_alternating() &&
+    if (!a->is_existential() &&
         // We will probably have to revisit this condition later.
         // Currently, the intent is that postprocessor should never
         // return an alternating automaton, unless it is called with
diff --git a/spot/twaalgos/product.cc b/spot/twaalgos/product.cc
index cd3752aca..601b23a1d 100644
--- a/spot/twaalgos/product.cc
+++ b/spot/twaalgos/product.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et
-// Développement de l'Epita (LRDE).
+// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -46,7 +46,7 @@ namespace spot
                               unsigned right_state,
                               bool and_acc)
     {
-      if (left->is_alternating() || right->is_alternating())
+      if (!(left->is_existential() && right->is_existential()))
         throw std::runtime_error
           ("product() does not support alternating automata");
       std::unordered_map<product_state, unsigned, product_state_hash> s2n;
diff --git a/spot/twaalgos/randomize.cc b/spot/twaalgos/randomize.cc
index 963751101..a38435ba9 100644
--- a/spot/twaalgos/randomize.cc
+++ b/spot/twaalgos/randomize.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et Développement
+// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -29,7 +29,7 @@ namespace spot
   randomize(twa_graph_ptr& aut, bool randomize_states,
             bool randomize_edges)
   {
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       throw std::runtime_error
         ("randomize() does not yet support alternation");
 
diff --git a/spot/twaalgos/remfin.cc b/spot/twaalgos/remfin.cc
index 26c6919e4..87d8c90ef 100644
--- a/spot/twaalgos/remfin.cc
+++ b/spot/twaalgos/remfin.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2016, 2017 Laboratoire de Recherche et
-// Développement de l'Epita.
+// Copyright (C) 2015-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -494,7 +494,7 @@ namespace spot
     if (aut->prop_weak().is_true())
       return remove_fin_weak(aut);
 
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       return remove_fin(remove_alternation(aut));
 
     if (auto maybe = streett_to_generalized_buchi_maybe(aut))
diff --git a/spot/twaalgos/sbacc.cc b/spot/twaalgos/sbacc.cc
index 7ad03f0ca..b4df91026 100644
--- a/spot/twaalgos/sbacc.cc
+++ b/spot/twaalgos/sbacc.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2015, 2016 Laboratoire de Recherche et Développement
-// de l'Epita.
+// Copyright (C) 2015-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -29,7 +29,7 @@ namespace spot
   {
     if (old->prop_state_acc())
       return old;
-    if (old->is_alternating())
+    if (!old->is_existential())
       throw std::runtime_error
         ("sbacc() does not support alternation");
 
diff --git a/spot/twaalgos/sccfilter.cc b/spot/twaalgos/sccfilter.cc
index 9ce0cffee..b2ca23908 100644
--- a/spot/twaalgos/sccfilter.cc
+++ b/spot/twaalgos/sccfilter.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2009, 2010, 2011, 2012, 2013, 2014, 2015, 2016
-// Laboratoire de Recherche et Développement de l'Epita (LRDE).
+// Copyright (C) 2009-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -276,7 +276,7 @@ namespace spot
     twa_graph_ptr scc_filter_apply(const_twa_graph_ptr aut,
                                    scc_info* given_si, Args&&... args)
     {
-      if (aut->is_alternating())
+      if (!aut->is_existential())
         throw std::runtime_error
           ("scc_filter() does yet not support alternation");
 
diff --git a/spot/twaalgos/sccinfo.cc b/spot/twaalgos/sccinfo.cc
index c806552da..c15308403 100644
--- a/spot/twaalgos/sccinfo.cc
+++ b/spot/twaalgos/sccinfo.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et Développement
-// de l'Epita.
+// Copyright (C) 2014-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -353,7 +353,7 @@ namespace spot
 
   void scc_info::determine_unknown_acceptance()
   {
-    if (aut_->is_alternating())
+    if (!aut_->is_existential())
       throw std::runtime_error("scc_info::determine_unknown_acceptance() "
                                "does not support alternating automata");
     std::vector<bool> k;
diff --git a/spot/twaalgos/simulation.cc b/spot/twaalgos/simulation.cc
index 3db2c06f8..e59ed5e4a 100644
--- a/spot/twaalgos/simulation.cc
+++ b/spot/twaalgos/simulation.cc
@@ -1,6 +1,6 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2012, 2013, 2014, 2015, 2016 Laboratoire de Recherche
-// et Développement de l'Epita (LRDE).
+// Copyright (C) 2012-2017 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
 //
@@ -160,7 +160,7 @@ namespace spot
         if (!has_separate_sets(in))
           throw std::runtime_error
             ("direct_simulation() requires separate Inf and Fin sets");
-        if (in->is_alternating())
+        if (!in->is_existential())
           throw std::runtime_error
             ("direct_simulation() does not yet support alternation");
 
diff --git a/spot/twaalgos/strength.cc b/spot/twaalgos/strength.cc
index 926da171c..8826ee92d 100644
--- a/spot/twaalgos/strength.cc
+++ b/spot/twaalgos/strength.cc
@@ -172,7 +172,7 @@ namespace spot
 
   void check_strength(const twa_graph_ptr& aut, scc_info* si)
   {
-    if (aut->is_alternating())
+    if (!aut->is_existential())
       is_type_automaton<false, false, true>(aut, si);
     else
       is_type_automaton<true, true, true>(aut, si);
diff --git a/tests/core/graph.cc b/tests/core/graph.cc
index 1de3b6481..3de1d51f0 100644
--- a/tests/core/graph.cc
+++ b/tests/core/graph.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015, 2016 Laboratoire de Recherche et
+// Copyright (C) 2014, 2015, 2016, 2017 Laboratoire de Recherche et
 // Développement de l'Epita.
 //
 // This file is part of Spot, a model checking library.
@@ -225,7 +225,7 @@ f6()
       f += t.first;
       h += t.second;
     }
-  return f == 3 && (h > 2.49 && h < 2.51) && !g.is_alternating();
+  return f == 3 && (h > 2.49 && h < 2.51) && g.is_existential();
 }
 
 static bool
@@ -247,7 +247,7 @@ f7()
 
   g.dump_storage(std::cout);
 
-  return f == 15 && g.is_alternating();
+  return f == 15 && !g.is_existential();
 }
 
 
diff --git a/tests/core/ngraph.cc b/tests/core/ngraph.cc
index 793329981..8ae18c963 100644
--- a/tests/core/ngraph.cc
+++ b/tests/core/ngraph.cc
@@ -264,7 +264,7 @@ static bool f6()
       f += t.first;
       h += t.second;
     }
-  return f == 3 && (h > 2.49 && h < 2.51) && !g.is_alternating();
+  return f == 3 && (h > 2.49 && h < 2.51) && g.is_existential();
 }
 
 static bool f7()
@@ -287,7 +287,7 @@ static bool f7()
     for (unsigned tt: g.univ_dests(t.dst))
       f += t.label * g.state_data(tt);
 
-  return f == 15 && g.is_alternating();
+  return f == 15 && !g.is_existential();
 }
 
 
diff --git a/tests/python/alternating.py b/tests/python/alternating.py
index d1bb47f9a..1ed9d1567 100755
--- a/tests/python/alternating.py
+++ b/tests/python/alternating.py
@@ -1,6 +1,6 @@
 #!/usr/bin/python3
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2016 Laboratoire de Recherche et Développement de
+# Copyright (C) 2016, 2017 Laboratoire de Recherche et Développement de
 # l'EPITA.
 #
 # This file is part of Spot, a model checking library.
@@ -40,7 +40,7 @@ tr = [(s, [[x for x in aut.univ_dests(i)] for i in aut.out(s)])
       for s in range(3)]
 print(tr)
 assert [(0, [[1, 2], [0, 1]]), (1, [[0, 2, 1]]), (2, [[2]])] == tr
-assert aut.is_alternating()
+assert not aut.is_existential()
 
 received = False
 try: