twaalgos: introduce match_states(a,b)

This is a useful part for issue #591.

* spot/twaalgos/matchstates.cc, spot/twaalgos/matchstates.hh: New
files.
* spot/twaalgos/Makefile.am: Add them.
* python/spot/impl.i: Add python bindings.
* tests/python/matchstates.py: New file.
* tests/Makefile.am: Add it.
* NEWS: Mention this new function.

NEWS

@@ -56,6 +56,12 @@ New in spot 2.12.0.dev (not yet released)
      were missing the rule "[*0]|f ≡ f" when f already accepts the
      empty word.  (Issue #545.)
 
+   - spot::match_states(A, B) is a new function that returns a vector
+     V such that V[x] contains all states y such that state (x, y) can
+     reach an accepting cycle in product(A, B).  In particular, if A
+     and B accept the same language, any word accepted by A from state
+     x can be accepted in B from some state in V[x].
+
   Bug fixes:
 
   - Generating random formulas without any unary opertor would very

python/spot/impl.i

@@ -132,6 +132,7 @@
 #include <spot/twaalgos/contains.hh>
 #include <spot/twaalgos/determinize.hh>
 #include <spot/twaalgos/magic.hh>
+#include <spot/twaalgos/matchstates.hh>
 #include <spot/twaalgos/minimize.hh>
 #include <spot/twaalgos/mealy_machine.hh>
 #include <spot/twaalgos/neverclaim.hh>
@@ -522,6 +523,7 @@ namespace std {
   %template(pairintacccond) pair<int, spot::acc_cond>;
   %template(vectorformula) vector<spot::formula>;
   %template(vectorunsigned) vector<unsigned>;
+  %template(vectorvectorunsigned) vector<vector<unsigned>>;
   %template(vectorpairunsigned) vector<pair<unsigned, unsigned>>;
   %template(vectoracccond) vector<spot::acc_cond>;
   %template(vectoracccode) vector<spot::acc_cond::acc_code>;
@@ -739,6 +741,7 @@ def state_is_accepting(self, src) -> "bool":
 %include <spot/twaalgos/contains.hh>
 %include <spot/twaalgos/langmap.hh>
 %include <spot/twaalgos/magic.hh>
+%include <spot/twaalgos/matchstates.hh>
 %include <spot/twaalgos/minimize.hh>
 %include <spot/twaalgos/mealy_machine.hh>
 %include <spot/twaalgos/neverclaim.hh>

spot/twaalgos/Makefile.am

@@ -64,6 +64,7 @@ twaalgos_HEADERS = \
   ltl2tgba_fm.hh \
   magic.hh \
   mask.hh \
+  matchstates.hh \
   minimize.hh \
   mealy_machine.hh \
   couvreurnew.hh \
@@ -139,6 +140,7 @@ libtwaalgos_la_SOURCES = \
   ltl2tgba_fm.cc \
   magic.cc \
   mask.cc \
+  matchstates.cc \
   minimize.cc \
   mealy_machine.cc \
   couvreurnew.cc \

spot/twaalgos/matchstates.cc

@@ -0,0 +1,50 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) by the Spot authors, see the AUTHORS file for details.
+//
+// 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 <spot/twaalgos/matchstates.hh>
+#include <spot/twaalgos/sccinfo.hh>
+#include <spot/twaalgos/product.hh>
+
+namespace spot
+{
+  std::vector<std::vector<unsigned>>
+  match_states(const const_twa_graph_ptr& aut1,
+               const const_twa_graph_ptr& aut2)
+  {
+    twa_graph_ptr prod = product(aut1, aut2);
+    product_states* ps = prod->get_named_prop<product_states>("product-states");
+    if (!ps)
+      return {};
+    scc_info si(prod, scc_info_options::TRACK_SUCCS);
+
+    std::vector<std::vector<unsigned>> v(aut1->num_states());
+    unsigned sz = ps->size();
+    assert(sz == prod->num_states());
+    for (unsigned sp = 0; sp < sz; ++sp)
+      if (si.is_useful_state(sp))
+        {
+          auto [sl, sr] = (*ps)[sp];
+          v[sl].push_back(sr);
+        }
+    return v;
+  }
+
+
+
+}

spot/twaalgos/matchstates.hh

@@ -0,0 +1,40 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) by the Spot authors, see the AUTHORS file for details.
+//
+// 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 <vector>
+
+namespace spot
+{
+  /// \ingroup twa_algorithms
+  /// \brief match the state of \a aut1 with the states of \a aut2.
+  ///
+  /// Return a vector `V` such that for each state `x` of
+  /// \a aut1, `V[x]` contains the set of states `y` such that
+  /// `(x,y)` is a useful state of `product(aut1,aut2)`.
+  ///
+  /// In particular, if the language of \a aut2 includes the language
+  /// of \a aut1, then any word accepted from state `x` in \a aut1
+  /// is also accepted from one of the states in `V[x]`.
+  SPOT_API std::vector<std::vector<unsigned>>
+  match_states(const const_twa_graph_ptr& aut1,
+               const const_twa_graph_ptr& aut2);
+}

tests/Makefile.am

@@ -435,6 +435,7 @@ TESTS_python = \
   python/ltlf.py \
   python/ltlparse.py \
   python/ltlsimple.py \
+  python/matchstates.py \
   python/mealy.py \
   python/_mealy.ipynb \
   python/merge.py \

tests/python/matchstates.py

@@ -0,0 +1,62 @@
+#!/usr/bin/python3
+# -*- mode: python; coding: utf-8 -*-
+# Copyright (C) by the Spot authors, see the AUTHORS file for details.
+#
+# 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/>.
+
+import spot
+from unittest import TestCase
+tc = TestCase()
+
+a = spot.automaton("""HOA: v1
+States: 4
+Start: 0
+AP: 3 "a" "b" "c"
+acc-name: all
+Acceptance: 0 t
+properties: trans-labels explicit-labels state-acc stutter-invariant
+properties: very-weak
+--BODY--
+State: 0 "Ga | Gb | Gc"
+[0] 1
+[1] 2
+[2] 3
+State: 1 "Ga"
+[0] 1
+State: 2 "Gb"
+[1] 2
+State: 3 "Gc"
+[2] 3
+--END--""")
+
+b = spot.automaton("""HOA: v1 States: 7 Start: 6 AP: 3 "a" "b" "c"
+acc-name: all Acceptance: 0 t properties: trans-labels explicit-labels
+state-acc deterministic properties: stutter-invariant very-weak
+--BODY-- State: 0 [2] 0 State: 1 [!1&2] 0 [1&2] 1 [1&!2] 2 State: 2
+[1] 2 State: 3 [0] 3 State: 4 [!0&2] 0 [0&!2] 3 [0&2] 4 State: 5
+[!0&1] 2 [0&!1] 3 [0&1] 5 State: 6 [!0&!1&2] 0 [!0&1&2] 1 [!0&1&!2] 2
+[0&!1&!2] 3 [0&!1&2] 4 [0&1&!2] 5 [0&1&2] 6 --END--""")
+
+m1 = spot.match_states(a, b)
+tc.assertEqual(m1, ((6,), (3, 4, 5, 6), (1, 2, 5, 6), (0, 1, 4, 6)))
+m2 = spot.match_states(b, a)
+tc.assertEqual(m2, ((3,), (2, 3), (2,), (1,), (1, 3), (1, 2), (0, 1, 2, 3)))
+
+c = spot.translate('false')
+m3 = spot.match_states(a, c)
+tc.assertEqual(m3, ((), (), (), ()))
+m4 = spot.match_states(c, a)
+tc.assertEqual(m4, ((), ))