implement a FORQ-based inclusion check for SBAs

* spot/twaalgos/forq_contains.cc, spot/twaalgos/forq_contains.hh: New
files.
* spot/twaalgos/Makefile.am, python/spot/impl.i: Add them.
* tests/python/forq_contains.py: New file.
* tests/Makefile.am: Add it.

spot/twaalgos/Makefile.am

@@ -51,6 +51,7 @@ twaalgos_HEADERS = \
   dualize.hh \
   emptiness.hh \
   emptiness_stats.hh \
+  forq_contains.hh \
   game.hh \
   genem.hh \
   gfguarantee.hh \
@@ -124,6 +125,7 @@ libtwaalgos_la_SOURCES = \
   dtwasat.cc \
   dualize.cc \
   emptiness.cc \
+  forq_contains.cc \
   genem.cc \
   gfguarantee.cc \
   gv04.cc \

spot/twaalgos/forq_contains.hh

@@ -0,0 +1,51 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2023 Laboratoire de Recherche et Développement
+// de l'Epita. IMDEA Software Institute.
+//
+// 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/twa/twagraph.hh>
+#include <spot/twaalgos/word.hh>
+
+namespace spot
+{
+  /// \brief Returns a word accepted by \a left that is rejected by \a right,
+  /// or nullptr.
+  ///
+  /// This implements the language containment algorithm from
+  /// \cite{doveriFORQBasedLanguageInclusion2022}
+  /// to check whether L(left)⊆L(right), in which case, it returns nullptr.
+  /// Otherwise, it returns a counterexample, i.e., a word that is accepted
+  /// by $L(left)\setminus L(right)$, hence the name of the function.
+  ///
+  /// \pre Automata \a left and \a right should be
+  /// non-alternating state-based Büchi-automata.
+  SPOT_API twa_word_ptr difference_word_forq(
+    const_twa_graph_ptr left, spot::const_twa_graph_ptr right);
+
+  /// \brief Returns a boolean value indicating
+  /// whether \a left is included in the language of \a right.
+  ///
+  /// This implements the language containment algorithm from
+  /// \cite{doveriFORQBasedLanguageInclusion2022}
+  /// to check whether L(left)⊆L(right).
+  ///
+  /// \pre Automata \a left and \a right should be
+  /// non-alternating state-based Büchi-automata.
+  SPOT_API bool contains_forq(
+    const_twa_graph_ptr left, const_twa_graph_ptr right);
+}