From 7a65bdf6bc381ce57b96b1bddfaa51a9cfd296fc Mon Sep 17 00:00:00 2001
From: Alexandre Duret-Lutz <adl@lrde.epita.fr>
Date: Wed, 28 Mar 2018 10:32:38 +0200
Subject: [PATCH] specialized translation for GF(guarantee) and FG(safety)
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

This is adapted from a proposition in a paper by J. Esparza,
J. Křentínský, and S. Sickert, submitted to LICS'18.  We should add
proper references to the code and documentation once that paper is
accepted.

* spot/twaalgos/gfguarantee.cc, spot/twaalgos/gfguarantee.hh:
New files.
* spot/twaalgos/Makefile.am, python/spot/impl.i: Add them.
* spot/twa/fwd.hh: Add a forward declaration of bdd_dict_ptr.
* spot/twaalgos/postproc.cc, spot/twaalgos/postproc.hh: Make it
possible to call finalize() from the translator subclass.  Constify
all the do_* functions while we are there.
* spot/twaalgos/translate.cc, spot/twaalgos/translate.hh: Add
a "gf-guarantee" option to decide whether to use the new translation.
* bin/spot-x.cc: Document it.
* tests/core/dca2.test, tests/core/genltl.test,
tests/core/ltl2tgba2.test, tests/core/parity2.test,
tests/core/satmin.test, tests/python/automata.ipynb,
tests/python/sbacc.py: Adjust test cases.
* tests/python/except.py: Add a couple more tests.
---
 NEWS                         |   13 +
 bin/spot-x.cc                |   10 +-
 python/spot/impl.i           |    2 +
 spot/twa/fwd.hh              |    5 +-
 spot/twaalgos/Makefile.am    |    2 +
 spot/twaalgos/gfguarantee.cc |  193 ++
 spot/twaalgos/gfguarantee.hh |   96 +
 spot/twaalgos/postproc.cc    |   71 +-
 spot/twaalgos/postproc.hh    |   13 +-
 spot/twaalgos/translate.cc   |   40 +-
 spot/twaalgos/translate.hh   |    4 +-
 tests/core/dca2.test         |    7 +-
 tests/core/genltl.test       |   10 +-
 tests/core/ltl2tgba2.test    |    6 +-
 tests/core/parity2.test      |  400 +++-
 tests/core/satmin.test       |    4 +-
 tests/python/automata.ipynb  | 4174 +++++++++++++++++++---------------
 tests/python/except.py       |   12 +
 tests/python/sbacc.py        |   10 +-
 19 files changed, 3140 insertions(+), 1932 deletions(-)
 create mode 100644 spot/twaalgos/gfguarantee.cc
 create mode 100644 spot/twaalgos/gfguarantee.hh

diff --git a/NEWS b/NEWS
index 62c838c6b..48b5d1bfd 100644
--- a/NEWS
+++ b/NEWS
@@ -27,6 +27,19 @@ New in spot 2.5.2.dev (not yet released)
     simplified to {1} or {SERE} depending on whether SERE accepts
     the empty word or not.
 
+  - gf_guarantee_to_ba() is a specialized construction for
+    translating formulas of the form GF(guarantee) to BA or DBA,
+    and fg_safety_to_dca() is a specialized construction for
+    translating formulas of the form FG(safety) to DCA.  These
+    are slight generalizations of some constructions proposed
+    by J. Esparza, J. Křentínský, and S. Sickert in a submitted
+    paper.
+
+    These are now used by the main translation routine, and can be
+    disabled by passing -x '!gf-guarantee' to ltl2tgba.  As an
+    example, the translation of GF(a <-> XXb) to transition-based
+    Büchi went from 9 to 5 states using that construction.
+
   Bugs fixed:
 
   - "autfilt --cobuchi --small/--det" would turn a transition-based
diff --git a/bin/spot-x.cc b/bin/spot-x.cc
index 511ff49d3..d5b23ffa3 100644
--- a/bin/spot-x.cc
+++ b/bin/spot-x.cc
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013, 2014, 2015, 2016, 2017 Laboratoire de Recherche et
+// Copyright (C) 2013, 2014, 2015, 2016, 2017, 2018 Laboratoire de Recherche et
 // Développement de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -107,6 +107,14 @@ the determinization algorithm.") },
 the determinization algorithm.") },
     { DOC("det-stutter", "Set to 0 to disable optimizations based on \
 the stutter-invariance in the determinization algorithm.") },
+    // FIXME: Add bibliographic reference to their paper ASAP.
+    { DOC("gf-guarantee", "Set to 0 to disable alternate constructions \
+for GF(guarantee)->[D]BA and FG(safety)->DCA.  Those constructions \
+are based on work by J. Esparza, J. Křentínský, and S. Sickert.  \
+This is enabled by default for medium and high optimization \
+levels.  Unless we are building deterministic automata, the \
+resulting automata are compared to the automata built using the \
+more traditional pipeline, and only kept if they are better.") },
     { DOC("simul", "Set to 0 to disable simulation-based reductions. \
 Set to 1 to use only direct simulation. Set to 2 to use only reverse \
 simulation. Set to 3 to iterate both direct and reverse simulations. \
diff --git a/python/spot/impl.i b/python/spot/impl.i
index 9043c6676..9be7eb296 100644
--- a/python/spot/impl.i
+++ b/python/spot/impl.i
@@ -131,6 +131,7 @@
 #include <spot/twaalgos/lbtt.hh>
 #include <spot/twaalgos/ltl2taa.hh>
 #include <spot/twaalgos/ltl2tgba_fm.hh>
+#include <spot/twaalgos/gfguarantee.hh>
 #include <spot/twaalgos/compsusp.hh>
 #include <spot/twaalgos/determinize.hh>
 #include <spot/twaalgos/magic.hh>
@@ -571,6 +572,7 @@ def state_is_accepting(self, src) -> "bool":
 %include <spot/twaalgos/lbtt.hh>
 %include <spot/twaalgos/ltl2taa.hh>
 %include <spot/twaalgos/ltl2tgba_fm.hh>
+%include <spot/twaalgos/gfguarantee.hh>
 %include <spot/twaalgos/compsusp.hh>
 %include <spot/twaalgos/determinize.hh>
 %include <spot/twaalgos/dualize.hh>
diff --git a/spot/twa/fwd.hh b/spot/twa/fwd.hh
index 5318e940f..4563f8766 100644
--- a/spot/twa/fwd.hh
+++ b/spot/twa/fwd.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2014, 2015 Laboratoire de Recherche et Développement
+// Copyright (C) 2014, 2015, 2018 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -23,6 +23,9 @@
 
 namespace spot
 {
+  class bdd_dict;
+  typedef std::shared_ptr<bdd_dict> bdd_dict_ptr;
+
   class twa;
   typedef std::shared_ptr<twa> twa_ptr;
   typedef std::shared_ptr<const twa> const_twa_ptr;
diff --git a/spot/twaalgos/Makefile.am b/spot/twaalgos/Makefile.am
index 500115a51..daff17f09 100644
--- a/spot/twaalgos/Makefile.am
+++ b/spot/twaalgos/Makefile.am
@@ -49,6 +49,7 @@ twaalgos_HEADERS = \
   dualize.hh \
   emptiness.hh \
   emptiness_stats.hh \
+  gfguarantee.hh \
   gv04.hh \
   hoa.hh \
   iscolored.hh \
@@ -114,6 +115,7 @@ libtwaalgos_la_SOURCES = \
   dtwasat.cc \
   dualize.cc \
   emptiness.cc \
+  gfguarantee.cc \
   gv04.cc \
   hoa.cc \
   iscolored.cc \
diff --git a/spot/twaalgos/gfguarantee.cc b/spot/twaalgos/gfguarantee.cc
new file mode 100644
index 000000000..9b43c6a0e
--- /dev/null
+++ b/spot/twaalgos/gfguarantee.cc
@@ -0,0 +1,193 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2018 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
+//
+// This file is part of Spot, a model checking library.
+//
+// Spot is free software; you can redistribute it and/or modify it
+// under the terms of the GNU General Public License as published by
+// the Free Software Foundation; either version 3 of the License, or
+// (at your option) any later version.
+//
+// Spot is distributed in the hope that it will be useful, but WITHOUT
+// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+// License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+#include "config.h"
+#include "gfguarantee.hh"
+#include <spot/twa/twagraph.hh>
+#include <spot/twaalgos/sccinfo.hh>
+#include <spot/twaalgos/isweakscc.hh>
+#include <spot/twaalgos/strength.hh>
+#include <spot/twaalgos/ltl2tgba_fm.hh>
+#include <spot/twaalgos/minimize.hh>
+#include <spot/twaalgos/dualize.hh>
+
+namespace spot
+{
+  namespace
+  {
+    // F(φ₁)&F(φ₂)&F(φ₃) ≡ F(φ₁ & F(φ₂ & F(φ₃))
+    // because we assume this is all under G.
+    static formula
+    nest_f(formula input)
+    {
+      assert(input.is(op::And));
+      formula res = formula::tt();
+      unsigned n = input.size();
+      do
+        {
+          --n;
+          assert(input[n].is(op::F));
+          res = formula::F(formula::And({input[n][0], res}));
+        }
+      while (n);
+      return res;
+    }
+
+
+    static twa_graph_ptr
+    do_g_f_terminal_inplace(scc_info& si, bool state_based)
+    {
+      twa_graph_ptr aut = std::const_pointer_cast<twa_graph>(si.get_aut());
+
+      if (!is_terminal_automaton(aut, &si, true))
+        throw std::runtime_error("g_f_terminal() expects a terminal automaton");
+
+      unsigned ns = si.scc_count();
+      std::vector<bool> term(ns, false);
+      for (unsigned n = 0; n < ns; ++n)
+        if (is_terminal_scc(si, n))
+          term[n] = true;
+
+      aut->prop_keep({ false, false, true, false, true, true });
+      aut->prop_state_acc(state_based);
+      aut->prop_inherently_weak(false);
+      aut->set_buchi();
+
+      unsigned init = aut->get_init_state_number();
+
+      if (!state_based)
+        {
+          for (auto& e: aut->edges())
+            if (term[si.scc_of(e.dst)])
+              {
+                e.dst = init;
+                e.acc = {0};
+              }
+            else
+              {
+                e.acc = {};
+              }
+        }
+      else
+        {
+          // Replace all terminal state by a single accepting state.
+          unsigned accstate = aut->new_state();
+          for (auto& e: aut->edges())
+            {
+              if (term[si.scc_of(e.dst)])
+                e.dst = accstate;
+              e.acc = {};
+            }
+          // This accepting state has the same output as the initial
+          // state.
+          for (auto& e: aut->out(init))
+            aut->new_edge(accstate, e.dst, e.cond, {0});
+          // This is not mandatory, but starting on the accepting
+          // state helps getting shorter accepting words.
+          aut->set_init_state(accstate);
+        }
+
+      aut->purge_unreachable_states();
+      return aut;
+    }
+  }
+
+  twa_graph_ptr
+  g_f_terminal_inplace(twa_graph_ptr aut, bool state_based)
+  {
+    scc_info si(aut);
+    return do_g_f_terminal_inplace(si, state_based);
+  }
+
+  twa_graph_ptr
+  gf_guarantee_to_ba_maybe(formula gf, const bdd_dict_ptr& dict,
+                           bool deterministic, bool state_based)
+  {
+    if (!gf.is(op::G))
+      return nullptr;
+    formula f = gf[0];
+    if (!f.is(op::F))
+      {
+        // F(...)&F(...)&... is also OK.
+        if (!f.is(op::And))
+          return nullptr;
+        for (auto c: f)
+          if (!c.is(op::F))
+            return nullptr;
+
+        f = nest_f(f);
+      }
+    twa_graph_ptr aut = ltl_to_tgba_fm(f, dict, true);
+    twa_graph_ptr reduced = minimize_obligation(aut, f, nullptr,
+                                                !deterministic);
+    scc_info si(reduced);
+    if (!is_terminal_automaton(aut, &si, true))
+      return nullptr;
+    do_g_f_terminal_inplace(si, state_based);
+    return reduced;
+  }
+
+  twa_graph_ptr
+  gf_guarantee_to_ba(formula gf, const bdd_dict_ptr& dict,
+                     bool deterministic, bool state_based)
+  {
+    twa_graph_ptr res = gf_guarantee_to_ba_maybe(gf, dict,
+                                              deterministic, state_based);
+    if (!res)
+      throw std::runtime_error
+        ("gf_guarantee_to_ba(): expects a formula of the form GF(guarantee)");
+    return res;
+  }
+
+  twa_graph_ptr
+  fg_safety_to_dca_maybe(formula fg, const bdd_dict_ptr& dict,
+                         bool state_based)
+  {
+    if (!fg.is(op::F))
+      return nullptr;
+    formula g = fg[0];
+    if (!g.is(op::G))
+      {
+        // G(...)|G(...)|... is also OK.
+        if (!g.is(op::Or))
+          return nullptr;
+        for (auto c: g)
+          if (!c.is(op::G))
+            return nullptr;
+      }
+
+    formula gf = negative_normal_form(fg, true);
+    twa_graph_ptr res =
+      gf_guarantee_to_ba_maybe(gf, dict, true, state_based);
+    if (!res)
+      return nullptr;
+    return dualize(res);
+  }
+
+  twa_graph_ptr
+  fg_safety_to_dca(formula gf, const bdd_dict_ptr& dict,
+                   bool state_based)
+  {
+    twa_graph_ptr res = fg_safety_to_dca_maybe(gf, dict, state_based);
+    if (!res)
+      throw std::runtime_error
+        ("fg_safety_to_dca(): expects a formula of the form FG(safety)");
+    return res;
+  }
+}
diff --git a/spot/twaalgos/gfguarantee.hh b/spot/twaalgos/gfguarantee.hh
new file mode 100644
index 000000000..97611dbdb
--- /dev/null
+++ b/spot/twaalgos/gfguarantee.hh
@@ -0,0 +1,96 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2018 Laboratoire de Recherche et Développement
+// de l'Epita (LRDE).
+//
+// This file is part of Spot, a model checking library.
+//
+// Spot is free software; you can redistribute it and/or modify it
+// under the terms of the GNU General Public License as published by
+// the Free Software Foundation; either version 3 of the License, or
+// (at your option) any later version.
+//
+// Spot is distributed in the hope that it will be useful, but WITHOUT
+// ANY WARRANTY; without even the implied warranty of MERCHANTABILITY
+// or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU General Public
+// License for more details.
+//
+// You should have received a copy of the GNU General Public License
+// along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+#pragma once
+
+#include <spot/misc/common.hh>
+#include <spot/twa/fwd.hh>
+#include <spot/tl/formula.hh>
+#include <spot/tl/nenoform.hh>
+
+namespace spot
+{
+  /// \ingroup twa_misc
+  /// \brief Given a terminal automaton \a f_terminal recognizing
+  /// some formula F(φ), modify it to recognize GF(φ).
+  ///
+  /// If \a state_based is set, the automaton all terminal states are
+  /// replaced by a unique accepting state that has the same outgoing
+  /// transitions as the initial state, and the initial state is
+  /// actually relocated to that accepting state.  The latter point is
+  /// not necessary, but it favors shorter accepting cycles.
+  ///
+  /// If \a state_based is not set, all transition going to terminal
+  /// states are made accepting and redirected to the initial state.
+  ///
+  /// This construction is inspired by a similar construction in a
+  /// submitted paper by J. Esparza, J. Křetínský, & S. Sickert.
+  SPOT_API twa_graph_ptr
+  g_f_terminal_inplace(twa_graph_ptr f_terminal, bool state_based = false);
+
+  /// \ingroup twa_ltl
+  /// \brief Convert GF(φ) into a (D)BA if φ is a guarantee property.
+  ///
+  /// If the formula \a gf has the form GΦ where Φ matches either F(φ)
+  /// or F(φ₁)|F(φ₂)|...|F(φₙ), we translate Φ into A_Φ and attempt to
+  /// minimize it to a WDBA.  If \a deterministic is not set, we keep
+  /// the minimized automaton only if A_Φ is larger.  If the resulting
+  /// automaton is terminal, we then call g_f_terminal_inplace().
+  ///
+  /// Return nullptr if the input formula is not of the supported
+  /// form.
+  ///
+  /// This construction generalized a similar construction in a
+  /// submitted paper by J. Esparza, J. Křetínský, & S. Sickert in the
+  /// sense that it will work if Φ represent a safety property, even
+  /// if it is not a syntactic safety.
+  SPOT_API twa_graph_ptr
+  gf_guarantee_to_ba_maybe(formula gf, const bdd_dict_ptr& dict,
+                           bool deterministic = true, bool state_based = false);
+
+  /// \ingroup twa_ltl
+  /// \brief Convert GF(φ) into a (D)BA if φ is a guarantee property.
+  ///
+  /// This is similar to gf_guarantee_to_ba_maybe() except it raises
+  /// an exception of the input formula is not of the supported form.
+  SPOT_API twa_graph_ptr
+  gf_guarantee_to_ba(formula gf, const bdd_dict_ptr& dict,
+                     bool deterministic = true, bool state_based = false);
+
+  /// \ingroup twa_ltl
+  /// \brief Convert FG(φ) into a DCA if φ is a safety property.
+  ///
+  /// This is the dual of gf_guarantee_to_ba_maybe().  See that
+  /// function for details.
+  ///
+  /// Return nullptr if the input formula is not of the supported
+  /// form.
+  SPOT_API twa_graph_ptr
+  fg_safety_to_dca_maybe(formula fg, const bdd_dict_ptr& dict,
+                            bool state_based);
+
+  /// \ingroup twa_ltl
+  /// \brief Convert FG(φ) into a DCA if φ is a safety property.
+  ///
+  /// This is similar to fg_safety_to_dba_maybe() except it raises
+  /// an exception of the input formula is not of the supported form.
+  SPOT_API twa_graph_ptr
+  fg_safety_to_dca(formula fg, const bdd_dict_ptr& dict,
+                      bool state_based = false);
+}
diff --git a/spot/twaalgos/postproc.cc b/spot/twaalgos/postproc.cc
index b443481df..4ad5a8b8b 100644
--- a/spot/twaalgos/postproc.cc
+++ b/spot/twaalgos/postproc.cc
@@ -105,7 +105,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_simul(const twa_graph_ptr& a, int opt)
+  postprocessor::do_simul(const twa_graph_ptr& a, int opt) const
   {
     if (!has_separate_sets(a))
       return a;
@@ -124,7 +124,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_sba_simul(const twa_graph_ptr& a, int opt)
+  postprocessor::do_sba_simul(const twa_graph_ptr& a, int opt) const
   {
     if (ba_simul_ <= 0)
       return a;
@@ -143,7 +143,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_degen(const twa_graph_ptr& a)
+  postprocessor::do_degen(const twa_graph_ptr& a) const
   {
     auto d = degeneralize(a,
                           degen_reset_, degen_order_,
@@ -153,7 +153,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_degen_tba(const twa_graph_ptr& a)
+  postprocessor::do_degen_tba(const twa_graph_ptr& a) const
   {
     return degeneralize_tba(a,
                             degen_reset_, degen_order_,
@@ -162,7 +162,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_scc_filter(const twa_graph_ptr& a, bool arg)
+  postprocessor::do_scc_filter(const twa_graph_ptr& a, bool arg) const
   {
     if (scc_filter_ == 0)
       return a;
@@ -176,7 +176,7 @@ namespace spot
   }
 
   twa_graph_ptr
-  postprocessor::do_scc_filter(const twa_graph_ptr& a)
+  postprocessor::do_scc_filter(const twa_graph_ptr& a) const
   {
     return do_scc_filter(a, scc_filter_ > 1);
   }
@@ -186,6 +186,36 @@ namespace spot
 #define SBACC_ (pref_ & SBAcc)
 #define COLORED_ (pref_ & Colored)
 
+
+  twa_graph_ptr
+  postprocessor::finalize(twa_graph_ptr tmp) const
+  {
+    if (COMP_)
+      tmp = complete(tmp);
+    bool want_parity = type_ & Parity;
+    if (want_parity && tmp->acc().is_generalized_buchi())
+      tmp = SBACC_ ? do_degen(tmp) : do_degen_tba(tmp);
+    if (SBACC_)
+      tmp = sbacc(tmp);
+    if (want_parity)
+      {
+        if (COLORED_)
+          colorize_parity_here(tmp);
+        parity_kind kind = parity_kind_any;
+        parity_style style = parity_style_any;
+        if ((type_ & ParityMin) == ParityMin)
+          kind = parity_kind_min;
+        else if ((type_ & ParityMax) == ParityMax)
+          kind = parity_kind_max;
+        if ((type_ & ParityOdd) == ParityOdd)
+          style = parity_style_odd;
+        else if ((type_ & ParityEven) == ParityEven)
+          style = parity_style_even;
+        change_parity_here(tmp, kind, style);
+      }
+    return tmp;
+  }
+
   twa_graph_ptr
   postprocessor::run(twa_graph_ptr a, formula f)
   {
@@ -199,38 +229,11 @@ namespace spot
       state_based_ = true;
 
     bool via_gba = (type_ == BA) || (type_ == TGBA) || (type_ == Monitor);
-    bool want_parity = (type_ & Parity) == Parity;
+    bool want_parity = type_ & Parity;
     if (COLORED_ && !want_parity)
       throw std::runtime_error("postprocessor: the Colored setting only works "
                                "for parity acceptance");
 
-    auto finalize = [&](twa_graph_ptr tmp)
-      {
-        if (COMP_)
-          tmp = complete(tmp);
-        if (want_parity && tmp->acc().is_generalized_buchi())
-          tmp = SBACC_ ? do_degen(tmp) : do_degen_tba(tmp);
-        if (SBACC_)
-          tmp = sbacc(tmp);
-        if (want_parity)
-          {
-            if (COLORED_)
-              colorize_parity_here(tmp);
-            parity_kind kind = parity_kind_any;
-            parity_style style = parity_style_any;
-            if ((type_ & ParityMin) == ParityMin)
-              kind = parity_kind_min;
-            else if ((type_ & ParityMax) == ParityMax)
-              kind = parity_kind_max;
-            if ((type_ & ParityOdd) == ParityOdd)
-              style = parity_style_odd;
-            else if ((type_ & ParityEven) == ParityEven)
-              style = parity_style_even;
-            change_parity_here(tmp, kind, style);
-          }
-        return tmp;
-      };
-
     if (!a->is_existential() &&
         // We will probably have to revisit this condition later.
         // Currently, the intent is that postprocessor should never
diff --git a/spot/twaalgos/postproc.hh b/spot/twaalgos/postproc.hh
index fd2f48a0f..948b49b96 100644
--- a/spot/twaalgos/postproc.hh
+++ b/spot/twaalgos/postproc.hh
@@ -219,12 +219,13 @@ namespace spot
     twa_graph_ptr run(twa_graph_ptr input, formula f = nullptr);
 
   protected:
-    twa_graph_ptr do_simul(const twa_graph_ptr& input, int opt);
-    twa_graph_ptr do_sba_simul(const twa_graph_ptr& input, int opt);
-    twa_graph_ptr do_degen(const twa_graph_ptr& input);
-    twa_graph_ptr do_degen_tba(const twa_graph_ptr& input);
-    twa_graph_ptr do_scc_filter(const twa_graph_ptr& a, bool arg);
-    twa_graph_ptr do_scc_filter(const twa_graph_ptr& a);
+    twa_graph_ptr do_simul(const twa_graph_ptr& input, int opt) const;
+    twa_graph_ptr do_sba_simul(const twa_graph_ptr& input, int opt) const;
+    twa_graph_ptr do_degen(const twa_graph_ptr& input) const;
+    twa_graph_ptr do_degen_tba(const twa_graph_ptr& input) const;
+    twa_graph_ptr do_scc_filter(const twa_graph_ptr& a, bool arg) const;
+    twa_graph_ptr do_scc_filter(const twa_graph_ptr& a) const;
+    twa_graph_ptr finalize(twa_graph_ptr tmp) const;
 
     output_type type_ = TGBA;
     int pref_ = Small;
diff --git a/spot/twaalgos/translate.cc b/spot/twaalgos/translate.cc
index d8fb14f3e..bd8277c7c 100644
--- a/spot/twaalgos/translate.cc
+++ b/spot/twaalgos/translate.cc
@@ -24,6 +24,8 @@
 #include <spot/misc/optionmap.hh>
 #include <spot/tl/relabel.hh>
 #include <spot/twaalgos/relabel.hh>
+#include <spot/twaalgos/gfguarantee.hh>
+#include <spot/twaalgos/isdet.hh>
 
 namespace spot
 {
@@ -32,6 +34,7 @@ namespace spot
   {
     comp_susp_ = early_susp_ = skel_wdba_ = skel_simul_ = 0;
     relabel_bool_ = tls_impl_ = -1;
+    gf_guarantee_ = level_ != Low;
 
     if (!opt)
       return;
@@ -45,6 +48,7 @@ namespace spot
         skel_simul_ = opt->get("skel-simul", 1);
       }
     tls_impl_ = opt->get("tls-impl", -1);
+    gf_guarantee_ = opt->get("gf-guarantee", gf_guarantee_);
   }
 
   void translator::build_simplifier(const bdd_dict_ptr& dict)
@@ -96,6 +100,8 @@ namespace spot
 
   twa_graph_ptr translator::run(formula* f)
   {
+#define PREF_ (pref_ & (Small | Deterministic))
+
     bool unambiguous = (pref_ & postprocessor::Unambiguous);
     if (unambiguous && type_ == postprocessor::Monitor)
       {
@@ -153,12 +159,13 @@ namespace spot
     simpl_->clear_as_bdd_cache();
 
     twa_graph_ptr aut;
+    twa_graph_ptr aut2 = nullptr;
     if (comp_susp_ > 0)
       {
         // FIXME: Handle unambiguous_ automata?
         int skel_wdba = skel_wdba_;
         if (skel_wdba < 0)
-          skel_wdba = (pref_ == postprocessor::Deterministic) ? 1 : 2;
+          skel_wdba = (pref_ & postprocessor::Deterministic) ? 1 : 2;
 
         aut = compsusp(r, simpl_->get_dict(), skel_wdba == 0,
                        skel_simul_ == 0, early_susp_ != 0,
@@ -166,6 +173,24 @@ namespace spot
       }
     else
       {
+        if (gf_guarantee_ && PREF_ != Any)
+          {
+            bool det = unambiguous || (PREF_ == Deterministic);
+            bool sba = type_ == BA || (pref_ & SBAcc);
+            if ((type_ & (BA | Parity | Generic)) || type_ == TGBA)
+              aut2 = gf_guarantee_to_ba_maybe(r, simpl_->get_dict(), det, sba);
+            if (aut2 && (type_ & (BA | Parity)) && (pref_ & Deterministic))
+              return finalize(aut2);
+            if (!aut2 && (type_ & (Generic | Parity | CoBuchi)))
+              {
+                aut2 = fg_safety_to_dca_maybe(r, simpl_->get_dict(), sba);
+                if (aut2
+                    && (type_ & (CoBuchi | Parity))
+                    && (pref_ & Deterministic))
+                  return finalize(aut2);
+              }
+          }
+
         bool exprop = unambiguous || level_ == postprocessor::High;
         aut = ltl_to_tgba_fm(r, simpl_->get_dict(), exprop,
                              true, false, false, nullptr, nullptr,
@@ -173,6 +198,18 @@ namespace spot
       }
 
     aut = this->postprocessor::run(aut, r);
+    if (aut2)
+      {
+        aut2 = this->postprocessor::run(aut2, r);
+        unsigned s2 = aut2->num_states();
+        unsigned s1 = aut->num_states();
+        bool d2_more_det = !is_deterministic(aut) && is_deterministic(aut2);
+        if (((PREF_ == Deterministic) && d2_more_det)
+            || (s2 < s1)
+            || (s2 == s1
+                && ((aut2->num_sets() < aut2->num_sets()) || d2_more_det)))
+          aut = std::move(aut2);
+      }
 
     if (!m.empty())
       relabel_here(aut, &m);
@@ -188,5 +225,4 @@ namespace spot
   {
     simpl_->clear_caches();
   }
-
 }
diff --git a/spot/twaalgos/translate.hh b/spot/twaalgos/translate.hh
index 271f72ee3..10eecf908 100644
--- a/spot/twaalgos/translate.hh
+++ b/spot/twaalgos/translate.hh
@@ -1,5 +1,5 @@
 // -*- coding: utf-8 -*-
-// Copyright (C) 2013-2017 Laboratoire de Recherche et Développement
+// Copyright (C) 2013-2018 Laboratoire de Recherche et Développement
 // de l'Epita (LRDE).
 //
 // This file is part of Spot, a model checking library.
@@ -148,6 +148,8 @@ namespace spot
     int skel_simul_;
     int relabel_bool_;
     int tls_impl_;
+    bool gf_guarantee_;
   };
   /// @}
+
 }
diff --git a/tests/core/dca2.test b/tests/core/dca2.test
index e14c87ee2..ce0093c72 100755
--- a/tests/core/dca2.test
+++ b/tests/core/dca2.test
@@ -53,7 +53,8 @@ EOF
 
 while read l_f; do
     ltl2tgba --parity='max odd' "$l_f" > l.hoa
-    autfilt -q --acceptance-is='Fin(0) | Inf(1)' l.hoa
+    autfilt -q --acceptance-is='Fin(0) | Inf(1)' l.hoa ||
+        autfilt -q --acceptance-is='Fin(0)' l.hoa
     while read r_f; do
         # Dualizing a deterministic transition-based parity automaton
         # to obtain a transition-based deterministic streett
@@ -63,10 +64,10 @@ while read l_f; do
         ltl2tgba "$r_f" -D --parity='min odd' | autfilt --dualize --gsa > r.hoa
         # Streett & Streett
         autfilt r.hoa --name="($l_f)&!($r_f)" --product=l.hoa -S > and.hoa
-        autfilt -q --acceptance-is=Streett and.hoa
+        autfilt -q --acceptance-is=Streett-like and.hoa
         # Streett | Streett
         autfilt r.hoa --name="($l_f)|!($r_f)" --product-or=l.hoa -S > or.hoa
-        autfilt -q -v --acceptance-is=Streett or.hoa
+        autfilt -q -v --acceptance-is=Streett-like or.hoa
 
         autcross --language-preserved --verbose -F or.hoa -F and.hoa \
                  'autfilt %H --stats=%M | ltl2tgba >%O' \
diff --git a/tests/core/genltl.test b/tests/core/genltl.test
index 0250bd346..ff8bbc429 100755
--- a/tests/core/genltl.test
+++ b/tests/core/genltl.test
@@ -150,11 +150,11 @@ ms-phi-r=2,29
 ms-phi-s=0,5
 ms-phi-s=1,8
 ms-phi-s=2,497
-ms-phi-h=0,2
-ms-phi-h=1,4
-ms-phi-h=2,21
-ms-phi-h=3,170
-ms-phi-h=4,1816
+ms-phi-h=0,1
+ms-phi-h=1,3
+ms-phi-h=2,7
+ms-phi-h=3,15
+ms-phi-h=4,31
 gf-equiv=0,1
 gf-equiv=1,4
 gf-equiv=2,8
diff --git a/tests/core/ltl2tgba2.test b/tests/core/ltl2tgba2.test
index f88e5dd73..e249d228e 100755
--- a/tests/core/ltl2tgba2.test
+++ b/tests/core/ltl2tgba2.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2009-2017 Laboratoire de Recherche et Développement de
+# Copyright (C) 2009-2018 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
@@ -132,8 +132,8 @@ sb-patterns,26, 1,1, 1,1, 1,1, 1,1
 sb-patterns,27, 2,7, 2,7, 2,7, 2,7
 hkrss-patterns,1, 1,2, 1,2, 3,6, 3,6
 hkrss-patterns,2, 1,2, 1,2, 3,6, 3,6
-hkrss-patterns,3, 5,36, 5,36, 5,36, 5,36
-hkrss-patterns,4, 9,400, 9,400, 9,400, 9,400
+hkrss-patterns,3, 5,20, 5,20, 5,20, 5,20
+hkrss-patterns,4, 9,400, 17,272, 9,400, 17,272
 hkrss-patterns,6, 1,2, 1,2, 3,6, 3,6
 hkrss-patterns,7, 2,8, 2,8, 2,8, 2,8
 hkrss-patterns,8, 1,1, 1,1, 1,1, 1,1
diff --git a/tests/core/parity2.test b/tests/core/parity2.test
index 3759c93bc..09b7d3189 100755
--- a/tests/core/parity2.test
+++ b/tests/core/parity2.test
@@ -33,6 +33,203 @@ done
 cat >expected<<EOF
 HOA: v1
 name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: co-Buchi
+Acceptance: 1 Fin(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0
+[!0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {0}
+[!1] 0
+[!0&1] 1
+State: 1
+[0] 0 {0}
+[!0] 1
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: co-Buchi
+Acceptance: 1 Fin(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0
+[!0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Rabin 1
+Acceptance: 2 Fin(0) & Inf(1)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {1}
+[!1] 0
+[!0&1] 1
+State: 1
+[0] 0 {1}
+[!0] 1
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0 {0}
+[!0] 0 {1}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {0}
+[!1] 0
+[!0&1] 1
+State: 1
+[0] 0 {0}
+[!0] 1
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0 {0}
+[!0] 0 {1}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Streett 1
+Acceptance: 2 Fin(0) | Inf(1)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {1}
+[!1] 0 {0}
+[!0&1] 1 {0}
+State: 1
+[0] 0 {1}
+[!0] 1 {0}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: Rabin 1
+Acceptance: 2 Fin(0) & Inf(1)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0 {1}
+[!0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: parity min odd 3
+Acceptance: 3 Fin(0) & (Inf(1) | Fin(2))
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {1}
+[!1] 0 {2}
+[!0&1] 1 {2}
+State: 1
+[0] 0 {1}
+[!0] 1 {2}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0] 0 {0}
+[!0] 0 {1}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: parity max even 3
+Acceptance: 3 Inf(2) | (Fin(1) & Inf(0))
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[0&1] 0 {2}
+[!1] 0 {1}
+[!0&1] 1 {1}
+State: 1
+[0] 0 {2}
+[!0] 1 {1}
+--END--
+EOF
+
+diff expected res
+
+cat >expected2<<EOF
+HOA: v1
+name: "FGa"
 States: 2
 Start: 0
 AP: 1 "a"
@@ -236,11 +433,205 @@ State: 1
 [!0] 1 {1}
 --END--
 EOF
+diff expected2 res2
 
-diff expected res
-diff expected res2
+cat >expected3<<EOF
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: co-Buchi
+Acceptance: 1 Fin(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 0
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0
+[1] 1 {0}
+State: 1
+[0&!1] 0
+[!0] 1
+[0&1] 1 {0}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: co-Buchi
+Acceptance: 1 Fin(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 0
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: Rabin 1
+Acceptance: 2 Fin(0) & Inf(1)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0
+[1] 1 {1}
+State: 1
+[0&!1] 0
+[!0] 1
+[0&1] 1 {1}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {1}
+[0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0
+[1] 1 {0}
+State: 1
+[0&!1] 0
+[!0] 1
+[0&1] 1 {0}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {1}
+[0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: Streett 1
+Acceptance: 2 Fin(0) | Inf(1)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0 {0}
+[1] 1 {1}
+State: 1
+[0&!1] 0 {0}
+[!0] 1 {0}
+[0&1] 1 {1}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: Rabin 1
+Acceptance: 2 Fin(0) & Inf(1)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 0 {1}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: parity min odd 3
+Acceptance: 3 Fin(0) & (Inf(1) | Fin(2))
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0 {2}
+[1] 1 {1}
+State: 1
+[0&!1] 0 {2}
+[!0] 1 {2}
+[0&1] 1 {1}
+--END--
+HOA: v1
+name: "FGa"
+States: 1
+Start: 0
+AP: 1 "a"
+acc-name: parity max even 2
+Acceptance: 2 Fin(1) & Inf(0)
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!0] 0 {1}
+[0] 0 {0}
+--END--
+HOA: v1
+name: "G(Fa & Fb)"
+States: 2
+Start: 1
+AP: 2 "a" "b"
+acc-name: parity max even 3
+Acceptance: 3 Inf(2) | (Fin(1) & Inf(0))
+properties: trans-labels explicit-labels trans-acc colored complete
+properties: deterministic stutter-invariant
+--BODY--
+State: 0
+[!1] 0 {1}
+[1] 1 {2}
+State: 1
+[0&!1] 0 {1}
+[!0] 1 {1}
+[0&1] 1 {2}
+--END--
+EOF
+diff expected3 res3
 
-cat >expected2<<EOF
+cat >expected4<<EOF
 HOA: v1
 name: "FGa"
 States: 2
@@ -452,8 +843,7 @@ State: 1
 [!0] 1 {1}
 --END--
 EOF
-diff expected2 res3
-diff expected2 res4
+diff expected4 res4
 
 ltlcross 'ltl2tgba -P' 'ltl2tgba -P"odd max"' 'ltl2tgba -P"even min"' \
          'ltl2tgba -p' 'ltl2tgba -p"odd max"' 'ltl2tgba -p"even min"' \
diff --git a/tests/core/satmin.test b/tests/core/satmin.test
index 4f91570c2..4a5b75247 100755
--- a/tests/core/satmin.test
+++ b/tests/core/satmin.test
@@ -1,6 +1,6 @@
 #!/bin/sh
 # -*- coding: utf-8 -*-
-# Copyright (C) 2013, 2017 Laboratoire de Recherche et Développement
+# Copyright (C) 2013, 2017, 2018 Laboratoire de Recherche et Développement
 # de l'Epita (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -660,7 +660,7 @@ cat >expected <<'EOF'
 "!(G((p0) -> ((p1) U (p2))))","15",3
 "!(G((p0) -> ((p1) U (p2))))","16",3
 "!(G((p0) -> ((p1) U (p2))))","17",3
-"G(F((p0) <-> (X(X(p1)))))","1",9
+"G(F((p0) <-> (X(X(p1)))))","1",7
 "G(F((p0) <-> (X(X(p1)))))","2",7
 "G(F((p0) <-> (X(X(p1)))))","3",4
 "G(F((p0) <-> (X(X(p1)))))","4",4
diff --git a/tests/python/automata.ipynb b/tests/python/automata.ipynb
index c13ea1afd..745ae3752 100644
--- a/tests/python/automata.ipynb
+++ b/tests/python/automata.ipynb
@@ -29,124 +29,142 @@
        "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
        "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
        " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
-       "<!-- Generated by graphviz version 2.38.0 (20140413.2041)\n",
+       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
        " -->\n",
        "<!-- Title: G Pages: 1 -->\n",
        "<svg width=\"419pt\" height=\"242pt\"\n",
        " viewBox=\"0.00 0.00 419.00 241.80\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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+       "<title>3-&gt;3</title>\n",
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+       "<g class=\"edge\" id=\"edge7\">\n",
+       "<title>3-&gt;3</title>\n",
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+       "<title>6-&gt;1</title>\n",
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+       "<title>6-&gt;2</title>\n",
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+       "<title>6-&gt;3</title>\n",
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+       "<ellipse cx=\"432.9654\" cy=\"-117\" fill=\"none\" rx=\"22\" ry=\"22\" stroke=\"#000000\"/>\n",
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-       "<g class=\"edge\" id=\"edge3\"><title>1-&gt;0</title>\n",
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+       "<title>1-&gt;0</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"144.883\" y=\"-113.3\">b &amp; c</text>\n",
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+       "<title>1-&gt;1</title>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"144.9654\" y=\"-113.3\">b &amp; c</text>\n",
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        "<!-- 1&#45;&gt;2 -->\n",
-       "<g class=\"edge\" id=\"edge5\"><title>1-&gt;2</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"155.883\" y=\"-65.8\">b &amp; !c</text>\n",
+       "<g class=\"edge\" id=\"edge5\">\n",
+       "<title>1-&gt;2</title>\n",
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+       "<title>2-&gt;2</title>\n",
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+       "<title>4-&gt;0</title>\n",
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@@ -1506,458 +1670,530 @@
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        "<title>G</title>\n",
-       "<polygon fill=\"white\" points=\"-4,4 -4,-124 159,-124 159,4 -4,4\" stroke=\"none\"/>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"56.5\" y=\"-105.8\">Inf(</text>\n",
+       "<polygon fill=\"#ffffff\" points=\"-4,4 -4,-124 159,-124 159,4 -4,4\" stroke=\"transparent\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"56.5\" y=\"-105.8\">Inf(</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"54.5\" y=\"-91.8\">[Büchi]</text>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"94.5\" y=\"-105.8\">)</text>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"54.5\" y=\"-91.8\">[Büchi]</text>\n",
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-       "<g class=\"node\" id=\"node2\"><title>1</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-14.3\">1</text>\n",
+       "<g class=\"node\" id=\"node2\">\n",
+       "<title>1</title>\n",
+       "<ellipse cx=\"56\" cy=\"-18\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-14.3\">1</text>\n",
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        "<!-- I&#45;&gt;1 -->\n",
-       "<g class=\"edge\" id=\"edge1\"><title>I-&gt;1</title>\n",
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-       "<polygon fill=\"black\" points=\"37.9419,-18 30.9419,-21.1501 34.4419,-18 30.9419,-18.0001 30.9419,-18.0001 30.9419,-18.0001 34.4419,-18 30.9418,-14.8501 37.9419,-18 37.9419,-18\" stroke=\"black\"/>\n",
+       "<g class=\"edge\" id=\"edge1\">\n",
+       "<title>I-&gt;1</title>\n",
+       "<path d=\"M1.1233,-18C4.178,-18 17.9448,-18 30.9241,-18\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"37.9807,-18 30.9808,-21.1501 34.4807,-18 30.9807,-18.0001 30.9807,-18.0001 30.9807,-18.0001 34.4807,-18 30.9807,-14.8501 37.9807,-18 37.9807,-18\" stroke=\"#000000\"/>\n",
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        "<!-- 1&#45;&gt;1 -->\n",
-       "<g class=\"edge\" id=\"edge4\"><title>1-&gt;1</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"37.5\" y=\"-57.8\">a &amp; !b</text>\n",
+       "<g class=\"edge\" id=\"edge4\">\n",
+       "<title>1-&gt;1</title>\n",
+       "<path d=\"M49.6208,-35.0373C48.3189,-44.8579 50.4453,-54 56,-54 60.166,-54 62.4036,-48.8576 62.7128,-42.1433\" fill=\"none\" stroke=\"#000000\"/>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"37.5\" y=\"-57.8\">a &amp; !b</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"137\" y=\"-14.3\">0</text>\n",
+       "<g class=\"node\" id=\"node3\">\n",
+       "<title>0</title>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"137\" y=\"-14.3\">0</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-21.8\">b</text>\n",
+       "<g class=\"edge\" id=\"edge3\">\n",
+       "<title>1-&gt;0</title>\n",
+       "<path d=\"M74.3802,-18C85.4352,-18 99.6622,-18 111.7609,-18\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"118.9716,-18 111.9716,-21.1501 115.4716,-18 111.9716,-18.0001 111.9716,-18.0001 111.9716,-18.0001 115.4716,-18 111.9716,-14.8501 118.9716,-18 118.9716,-18\" stroke=\"#000000\"/>\n",
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-       "<g class=\"edge\" id=\"edge2\"><title>0-&gt;0</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"132.5\" y=\"-72.8\">1</text>\n",
+       "<g class=\"edge\" id=\"edge2\">\n",
+       "<title>0-&gt;0</title>\n",
+       "<path d=\"M129.9688,-34.6641C128.4063,-44.625 130.75,-54 137,-54 141.6875,-54 144.1777,-48.7266 144.4707,-41.8876\" fill=\"none\" stroke=\"#000000\"/>\n",
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        "<svg height=\"271pt\" viewBox=\"0.00 0.00 374.00 271.00\" width=\"374pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
        "<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 267)\">\n",
        "<title>G</title>\n",
-       "<polygon fill=\"white\" points=\"-4,4 -4,-267 370,-267 370,4 -4,4\" stroke=\"none\"/>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"136\" y=\"-248.8\">Inf(</text>\n",
+       "<polygon fill=\"#ffffff\" points=\"-4,4 -4,-267 370,-267 370,4 -4,4\" stroke=\"transparent\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"136\" y=\"-248.8\">Inf(</text>\n",
        "<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"158\" y=\"-248.8\">⓿</text>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"174\" y=\"-248.8\">)&amp;Inf(</text>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"174\" y=\"-248.8\">)&amp;Inf(</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"226\" y=\"-248.8\">)</text>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"139\" y=\"-234.8\">[gen. Büchi 2]</text>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"139\" y=\"-234.8\">[gen. Büchi 2]</text>\n",
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-       "<g class=\"node\" id=\"node2\"><title>0</title>\n",
-       "<ellipse cx=\"65\" cy=\"-118\" fill=\"#ffffaa\" rx=\"27\" ry=\"18\" stroke=\"black\"/>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"55\" y=\"-114.3\">1,1</text>\n",
+       "<g class=\"node\" id=\"node2\">\n",
+       "<title>0</title>\n",
+       "<ellipse cx=\"65\" cy=\"-118\" fill=\"#ffffaa\" rx=\"27\" ry=\"18\" stroke=\"#000000\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"55\" y=\"-114.3\">1,1</text>\n",
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        "<!-- I&#45;&gt;0 -->\n",
-       "<g class=\"edge\" id=\"edge1\"><title>I-&gt;0</title>\n",
-       "<path d=\"M1.04566,-118C1.94863,-118 16.101,-118 30.7579,-118\" fill=\"none\" stroke=\"black\"/>\n",
-       "<polygon fill=\"black\" points=\"37.9378,-118 30.9378,-121.15 34.4378,-118 30.9378,-118 30.9378,-118 30.9378,-118 34.4378,-118 30.9378,-114.85 37.9378,-118 37.9378,-118\" stroke=\"black\"/>\n",
+       "<g class=\"edge\" id=\"edge1\">\n",
+       "<title>I-&gt;0</title>\n",
+       "<path d=\"M1.2244,-118C4.383,-118 17.3969,-118 30.8528,-118\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"37.8798,-118 30.8799,-121.1501 34.3798,-118 30.8798,-118.0001 30.8798,-118.0001 30.8798,-118.0001 34.3798,-118 30.8798,-114.8501 37.8798,-118 37.8798,-118\" stroke=\"#000000\"/>\n",
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        "<!-- 0&#45;&gt;0 -->\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"32\" y=\"-172.8\">a &amp; !b &amp; !c</text>\n",
+       "<g class=\"edge\" id=\"edge5\">\n",
+       "<title>0-&gt;0</title>\n",
+       "<path d=\"M57.1448,-135.4099C55.6785,-145.0879 58.2969,-154 65,-154 69.9226,-154 72.6423,-149.1936 73.1591,-142.8073\" fill=\"none\" stroke=\"#000000\"/>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"200\" y=\"-215.8\">b &amp; c</text>\n",
+       "<g class=\"edge\" id=\"edge2\">\n",
+       "<title>0-&gt;1</title>\n",
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+       "<g class=\"edge\" id=\"edge3\">\n",
+       "<title>0-&gt;2</title>\n",
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+       "<title>0-&gt;3</title>\n",
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+       "<title>1-&gt;1</title>\n",
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+       "<title>2-&gt;2</title>\n",
+       "<path d=\"M206.4531,-134.6641C204.1094,-144.625 207.625,-154 217,-154 224.0313,-154 227.7666,-148.7266 228.2061,-141.8876\" fill=\"none\" stroke=\"#000000\"/>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"274.5\" y=\"-96.8\">c</text>\n",
+       "<g class=\"edge\" id=\"edge9\">\n",
+       "<title>3-&gt;1</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"199\" y=\"-71.8\">a &amp; !c</text>\n",
+       "<g class=\"edge\" id=\"edge10\">\n",
+       "<title>3-&gt;3</title>\n",
+       "<path d=\"M206.4531,-34.6641C204.1094,-44.625 207.625,-54 217,-54 224.0313,-54 227.7666,-48.7266 228.2061,-41.8876\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"227.5469,-34.6641 231.3201,-41.3488 227.865,-38.1496 228.1831,-41.6351 228.1831,-41.6351 228.1831,-41.6351 227.865,-38.1496 225.0461,-41.9214 227.5469,-34.6641 227.5469,-34.6641\" stroke=\"#000000\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"199\" y=\"-71.8\">a &amp; !c</text>\n",
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        "<g class=\"graph\" id=\"graph0\" transform=\"scale(1 1) rotate(0) translate(4 267)\">\n",
        "<title>G</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"109\" y=\"-248.8\">Inf(</text>\n",
+       "<polygon fill=\"#ffffff\" points=\"-4,4 -4,-267 316,-267 316,4 -4,4\" stroke=\"transparent\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"109\" y=\"-248.8\">Inf(</text>\n",
        "<text fill=\"#1f78b4\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"131\" y=\"-248.8\">⓿</text>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"147\" y=\"-248.8\">)&amp;Inf(</text>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"147\" y=\"-248.8\">)&amp;Inf(</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"199\" y=\"-248.8\">)</text>\n",
-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"112\" y=\"-234.8\">[gen. Büchi 2]</text>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"112\" y=\"-234.8\">[gen. Büchi 2]</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-114.3\">0</text>\n",
+       "<g class=\"node\" id=\"node2\">\n",
+       "<title>0</title>\n",
+       "<ellipse cx=\"56\" cy=\"-118\" fill=\"#ffffaa\" rx=\"18\" ry=\"18\" stroke=\"#000000\"/>\n",
+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"56\" y=\"-114.3\">0</text>\n",
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        "<!-- I&#45;&gt;0 -->\n",
-       "<g class=\"edge\" id=\"edge1\"><title>I-&gt;0</title>\n",
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+       "<g class=\"edge\" id=\"edge1\">\n",
+       "<title>I-&gt;0</title>\n",
+       "<path d=\"M1.1233,-118C4.178,-118 17.9448,-118 30.9241,-118\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"37.9807,-118 30.9808,-121.1501 34.4807,-118 30.9807,-118.0001 30.9807,-118.0001 30.9807,-118.0001 34.4807,-118 30.9807,-114.8501 37.9807,-118 37.9807,-118\" stroke=\"#000000\"/>\n",
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        "<!-- 0&#45;&gt;0 -->\n",
-       "<g class=\"edge\" id=\"edge5\"><title>0-&gt;0</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"23\" y=\"-172.8\">a &amp; !b &amp; !c</text>\n",
+       "<g class=\"edge\" id=\"edge5\">\n",
+       "<title>0-&gt;0</title>\n",
+       "<path d=\"M49.6208,-135.0373C48.3189,-144.8579 50.4453,-154 56,-154 60.166,-154 62.4036,-148.8576 62.7128,-142.1433\" fill=\"none\" stroke=\"#000000\"/>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"23\" y=\"-172.8\">a &amp; !b &amp; !c</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"294\" y=\"-114.3\">1</text>\n",
+       "<g class=\"node\" id=\"node3\">\n",
+       "<title>1</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"173\" y=\"-215.8\">b &amp; c</text>\n",
+       "<g class=\"edge\" id=\"edge2\">\n",
+       "<title>0-&gt;1</title>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190\" y=\"-114.3\">2</text>\n",
+       "<g class=\"node\" id=\"node4\">\n",
+       "<title>2</title>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190\" y=\"-114.3\">2</text>\n",
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        "<!-- 0&#45;&gt;2 -->\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-136.8\">a &amp; !b &amp; c</text>\n",
+       "<g class=\"edge\" id=\"edge3\">\n",
+       "<title>0-&gt;2</title>\n",
+       "<path d=\"M74.0718,-118C97.4488,-118 138.2991,-118 164.738,-118\" fill=\"none\" stroke=\"#000000\"/>\n",
+       "<polygon fill=\"#000000\" points=\"171.7865,-118 164.7866,-121.1501 168.2865,-118 164.7865,-118.0001 164.7865,-118.0001 164.7865,-118.0001 168.2865,-118 164.7865,-114.8501 171.7865,-118 171.7865,-118\" stroke=\"#000000\"/>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190\" y=\"-14.3\">3</text>\n",
+       "<g class=\"node\" id=\"node5\">\n",
+       "<title>3</title>\n",
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+       "<text fill=\"#000000\" font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"middle\" x=\"190\" y=\"-14.3\">3</text>\n",
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-       "<text font-family=\"Lato\" font-size=\"14.00\" text-anchor=\"start\" x=\"92\" y=\"-102.8\">a &amp; b &amp; !c</text>\n",
+       "<g class=\"edge\" id=\"edge4\">\n",
+       "<title>0-&gt;3</title>\n",
+       "<path d=\"M68.8649,-104.8649C75.531,-98.3182 83.9446,-90.4447 92,-84 117.0039,-63.9959 147.954,-43.8468 168.3011,-31.1679\" fill=\"none\" stroke=\"#000000\"/>\n",
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+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fde2056bc30> >"
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@@ -3472,14 +3839,14 @@
     }
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    "source": [
-    "aut = spot.translate('FGa', 'generic', 'deterministic'); aut"
+    "spot.translate('FGa', 'generic', 'deterministic')"
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   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "Translation to co-Büchi automaton"
+    "Translation to state-based co-Büchi automaton"
    ]
   },
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-    "spot.translate('FGa', 'coBuchi').show('.b')"
+    "spot.translate('FGa', 'coBuchi', 'deterministic', 'sbacc').show('.b')"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Translation to parity automaton.  Specifying just `parity max odd` requires a parity acceptance.  Adding `colored` ensures that each transition (or state if `sbacc` is also given) has a color, as people usually expect in parity automata."
    ]
   },
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-    "spot.translate('FGa', 'coBuchi', 'deterministic').show('.b')"
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+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>I&#45;&gt;0</title>\n",
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-       "<text text-anchor=\"start\" x=\"37.5\" y=\"-72.9822\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>0&#45;&gt;0</title>\n",
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        "<!-- 1 -->\n",
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+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>1</title>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"135\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
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-       "<!-- 1&#45;&gt;0 -->\n",
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+       "<title>0&#45;&gt;1</title>\n",
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+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>1&#45;&gt;1</title>\n",
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        "</g>\n",
        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fb10019ca20> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fde2053eae0> >"
       ]
      },
-     "execution_count": 29,
      "metadata": {},
-     "output_type": "execute_result"
+     "output_type": "display_data"
+    },
+    {
+     "data": {
+      "image/svg+xml": [
+       "<?xml version=\"1.0\" encoding=\"UTF-8\" standalone=\"no\"?>\n",
+       "<!DOCTYPE svg PUBLIC \"-//W3C//DTD SVG 1.1//EN\"\n",
+       " \"http://www.w3.org/Graphics/SVG/1.1/DTD/svg11.dtd\">\n",
+       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
+       " -->\n",
+       "<!-- Title: G Pages: 1 -->\n",
+       "<svg width=\"188pt\" height=\"128pt\"\n",
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+       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 124)\">\n",
+       "<title>G</title>\n",
+       "<polygon fill=\"#ffffff\" stroke=\"transparent\" points=\"-4,4 -4,-124 184,-124 184,4 -4,4\"/>\n",
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+       "<!-- I -->\n",
+       "<!-- 0 -->\n",
+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>0</title>\n",
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+       "</g>\n",
+       "<!-- I&#45;&gt;0 -->\n",
+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>I&#45;&gt;0</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M1.1233,-18C4.178,-18 17.9448,-18 30.9241,-18\"/>\n",
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+       "</g>\n",
+       "<!-- 0&#45;&gt;0 -->\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>0&#45;&gt;0</title>\n",
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+       "<!-- 1 -->\n",
+       "<g id=\"node3\" class=\"node\">\n",
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+       "<text text-anchor=\"middle\" x=\"162\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
+       "</g>\n",
+       "<!-- 0&#45;&gt;1 -->\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>0&#45;&gt;1</title>\n",
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+       "</g>\n",
+       "<!-- 1&#45;&gt;1 -->\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>1&#45;&gt;1</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M153.0212,-33.916C150.679,-44.1504 153.6719,-54 162,-54 168.3762,-54 171.625,-48.2263 171.7465,-40.9268\"/>\n",
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+       "<text text-anchor=\"start\" x=\"145\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b</text>\n",
+       "<text text-anchor=\"start\" x=\"154\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "</g>\n",
+       "</g>\n",
+       "</svg>\n"
+      ],
+      "text/plain": [
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fde2053eae0> >"
+      ]
+     },
+     "metadata": {},
+     "output_type": "display_data"
     }
    ],
    "source": [
     "import buddy\n",
-    "b = buddy.bdd_ithvar(aut.register_ap('b'))\n",
-    "for e in aut.edges():\n",
+    "display(a)\n",
+    "b = buddy.bdd_ithvar(a.register_ap('b'))\n",
+    "for e in a.edges():\n",
     "    e.cond &= b\n",
-    "aut"
+    "display(a)"
    ]
   },
   {
@@ -3736,68 +4186,64 @@
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-       "<!-- Generated by graphviz version 2.38.0 (20140413.2041)\n",
+       "<!-- Generated by graphviz version 2.40.1 (20161225.0304)\n",
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-       "<g id=\"graph0\" class=\"graph\" transform=\"scale(1 1) rotate(0) translate(4 141.556)\">\n",
+       "<svg width=\"212pt\" height=\"128pt\"\n",
+       " viewBox=\"0.00 0.00 212.00 128.00\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\">\n",
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-       "<polygon fill=\"white\" stroke=\"none\" points=\"-4,4 -4,-141.556 208,-141.556 208,4 -4,4\"/>\n",
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-       "<text text-anchor=\"start\" x=\"91\" y=\"-123.356\" font-family=\"Lato\" font-size=\"14.00\">) &amp; Inf(</text>\n",
-       "<text text-anchor=\"start\" x=\"134\" y=\"-123.356\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
-       "<text text-anchor=\"start\" x=\"150\" y=\"-123.356\" font-family=\"Lato\" font-size=\"14.00\">)</text>\n",
-       "<text text-anchor=\"start\" x=\"73\" y=\"-109.356\" font-family=\"Lato\" font-size=\"14.00\">[Rabin 1]</text>\n",
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+       "<text text-anchor=\"start\" x=\"81\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">Inf(</text>\n",
+       "<text text-anchor=\"start\" x=\"103\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<text text-anchor=\"start\" x=\"119\" y=\"-105.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">)</text>\n",
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+       "<g id=\"node2\" class=\"node\">\n",
+       "<title>0</title>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"56\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"56\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">0</text>\n",
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        "<!-- I&#45;&gt;0 -->\n",
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+       "<g id=\"edge1\" class=\"edge\">\n",
+       "<title>I&#45;&gt;0</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M1.1233,-18C4.178,-18 17.9448,-18 30.9241,-18\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"37.9807,-18 30.9808,-21.1501 34.4807,-18 30.9807,-18.0001 30.9807,-18.0001 30.9807,-18.0001 34.4807,-18 30.9807,-14.8501 37.9807,-18 37.9807,-18\"/>\n",
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        "<!-- 0&#45;&gt;0 -->\n",
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-       "<text text-anchor=\"start\" x=\"37.5\" y=\"-75.3559\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
+       "<g id=\"edge2\" class=\"edge\">\n",
+       "<title>0&#45;&gt;0</title>\n",
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+       "<text text-anchor=\"start\" x=\"51.5\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">b</text>\n",
        "</g>\n",
        "<!-- 1 -->\n",
-       "<g id=\"node3\" class=\"node\"><title>1</title>\n",
-       "<ellipse fill=\"#ffffaa\" stroke=\"black\" cx=\"186\" cy=\"-35.5559\" rx=\"18\" ry=\"18\"/>\n",
-       "<text text-anchor=\"middle\" x=\"186\" y=\"-31.8559\" font-family=\"Lato\" font-size=\"14.00\">1</text>\n",
+       "<g id=\"node3\" class=\"node\">\n",
+       "<title>1</title>\n",
+       "<ellipse fill=\"#ffffaa\" stroke=\"#000000\" cx=\"186\" cy=\"-18\" rx=\"18\" ry=\"18\"/>\n",
+       "<text text-anchor=\"middle\" x=\"186\" y=\"-14.3\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">1</text>\n",
        "</g>\n",
        "<!-- 0&#45;&gt;1 -->\n",
-       "<g id=\"edge3\" class=\"edge\"><title>0&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"black\" d=\"M74.0378,-38.4844C79.731,-39.3307 86.1223,-40.1382 92,-40.5559 117.713,-42.3833 124.287,-42.3833 150,-40.5559 153.49,-40.3079 157.161,-39.9225 160.759,-39.4731\"/>\n",
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-       "<text text-anchor=\"start\" x=\"92\" y=\"-60.3559\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b &amp; c</text>\n",
-       "<text text-anchor=\"start\" x=\"113\" y=\"-45.3559\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
-       "</g>\n",
-       "<!-- 1&#45;&gt;0 -->\n",
-       "<g id=\"edge4\" class=\"edge\"><title>1&#45;&gt;0</title>\n",
-       "<path fill=\"none\" stroke=\"black\" d=\"M173.404,-22.4171C167.156,-16.3398 158.908,-9.76704 150,-6.55595 125.75,2.18532 116.25,2.18532 92,-6.55595 85.4579,-8.91409 79.2724,-13.0852 73.9732,-17.5417\"/>\n",
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-       "<text text-anchor=\"start\" x=\"102.5\" y=\"-25.3559\" font-family=\"Lato\" font-size=\"14.00\">!a &amp; b</text>\n",
-       "<text text-anchor=\"start\" x=\"113\" y=\"-10.3559\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
+       "<g id=\"edge3\" class=\"edge\">\n",
+       "<title>0&#45;&gt;1</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M74.0759,-18C96.5544,-18 135.0643,-18 160.5273,-18\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"167.6585,-18 160.6585,-21.1501 164.1585,-18 160.6585,-18.0001 160.6585,-18.0001 160.6585,-18.0001 164.1585,-18 160.6584,-14.8501 167.6585,-18 167.6585,-18\"/>\n",
+       "<text text-anchor=\"start\" x=\"92\" y=\"-21.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b &amp; c</text>\n",
        "</g>\n",
        "<!-- 1&#45;&gt;1 -->\n",
-       "<g id=\"edge5\" class=\"edge\"><title>1&#45;&gt;1</title>\n",
-       "<path fill=\"none\" stroke=\"black\" d=\"M175.292,-50.3476C171.806,-60.9724 175.375,-71.5559 186,-71.5559 194.135,-71.5559 198.134,-65.3521 197.997,-57.6757\"/>\n",
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-       "<text text-anchor=\"start\" x=\"169\" y=\"-90.3559\" font-family=\"Lato\" font-size=\"14.00\">a &amp; b</text>\n",
-       "<text text-anchor=\"start\" x=\"178\" y=\"-75.3559\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#ff4da0\">❶</text>\n",
+       "<g id=\"edge4\" class=\"edge\">\n",
+       "<title>1&#45;&gt;1</title>\n",
+       "<path fill=\"none\" stroke=\"#000000\" d=\"M175.292,-32.7917C171.8057,-43.4165 175.375,-54 186,-54 194.1348,-54 198.1336,-47.7961 197.9966,-40.1197\"/>\n",
+       "<polygon fill=\"#000000\" stroke=\"#000000\" points=\"196.708,-32.7917 201.0228,-39.1403 197.3142,-36.2388 197.9204,-39.6859 197.9204,-39.6859 197.9204,-39.6859 197.3142,-36.2388 194.818,-40.2315 196.708,-32.7917 196.708,-32.7917\"/>\n",
+       "<text text-anchor=\"start\" x=\"169\" y=\"-72.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#000000\">a &amp; b</text>\n",
+       "<text text-anchor=\"start\" x=\"178\" y=\"-57.8\" font-family=\"Lato\" font-size=\"14.00\" fill=\"#1f78b4\">⓿</text>\n",
        "</g>\n",
        "</g>\n",
        "</svg>\n"
       ],
       "text/plain": [
-       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fb10019ca20> >"
+       "<spot.impl.twa_graph; proxy of <Swig Object of type 'std::shared_ptr< spot::twa_graph > *' at 0x7fde2053eae0> >"
       ]
      },
      "execution_count": 30,
@@ -3806,11 +4252,11 @@
     }
    ],
    "source": [
-    "c = buddy.bdd_ithvar(aut.register_ap('c'))\n",
-    "for e in aut.out(0):\n",
+    "c = buddy.bdd_ithvar(a.register_ap('c'))\n",
+    "for e in a.out(0):\n",
     "    if e.dst == 1:\n",
     "        e.cond &= c\n",
-    "aut"
+    "a"
    ]
   }
  ],
@@ -3830,7 +4276,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.6.4+"
+   "version": "3.6.5rc1"
   }
  },
  "nbformat": 4,
diff --git a/tests/python/except.py b/tests/python/except.py
index 12687ec6a..d8b50af27 100644
--- a/tests/python/except.py
+++ b/tests/python/except.py
@@ -75,3 +75,15 @@ try:
     a = r.reduce()
 except RuntimeError as e:
     assert "empty cycle" in str(e)
+
+f = spot.formula('GF(a | Gb)')
+try:
+    spot.gf_guarantee_to_ba(f, spot._bdd_dict)
+except RuntimeError as e:
+    assert "guarantee" in str(e)
+
+f = spot.formula('FG(a | Fb)')
+try:
+    spot.fg_safety_to_dca(f, spot._bdd_dict)
+except RuntimeError as e:
+    assert "safety" in str(e)
diff --git a/tests/python/sbacc.py b/tests/python/sbacc.py
index e4efeb738..b0c457846 100644
--- a/tests/python/sbacc.py
+++ b/tests/python/sbacc.py
@@ -1,5 +1,5 @@
 # -*- mode: python; coding: utf-8 -*-
-# Copyright (C) 2017 Laboratoire de Recherche et Développement de l'Epita
+# Copyright (C) 2017, 2018 Laboratoire de Recherche et Développement de l'Epita
 # (LRDE).
 #
 # This file is part of Spot, a model checking library.
@@ -50,12 +50,12 @@ h = s.to_str('hoa')
 assert h == """HOA: v1
 States: 2
 Start: 0
-AP: 2 "b" "a"
+AP: 2 "a" "b"
 Acceptance: 2 Inf(0) | Inf(1)
 properties: trans-labels explicit-labels state-acc deterministic
 --BODY--
 State: 0
-[1] 1
+[0] 1
 State: 1 {1}
 [t] 1
 --END--"""
@@ -84,13 +84,13 @@ h = d.to_str('hoa')
 assert h == """HOA: v1
 States: 2
 Start: 0
-AP: 2 "b" "a"
+AP: 2 "a" "b"
 acc-name: Buchi
 Acceptance: 1 Inf(0)
 properties: trans-labels explicit-labels state-acc deterministic
 --BODY--
 State: 0
-[1] 1
+[0] 1
 State: 1 {0}
 [t] 1
 --END--"""