strength: generalize is_safety_automaton to any type of automata

Reported by Samuel Judson.

* spot/twaalgos/strength.cc (is_safety_automaton): Reimplement it.
* spot/twaalgos/strength.hh (is_safety_automaton): Update
documentation.
* tests/python/safety.py: New file.
* tests/Makefile.am: Add it.
* NEWS: Mention this change.
* THANKS: Add Samuel.

NEWS

@@ -120,6 +120,12 @@ New in spot 2.11.6.dev  (not yet released)
   - ltsmin's interface will now point to README.ltsmin in case an
     error is found while running divine or spins.
 
+  - spot::is_safety_automaton() was generalized to detect any
+    automaton for which the acceptance could be changed to "t" without
+    changing the language.  In previous versions this function assumed
+    weak automata as input, but the documentation did not reflect
+    this.
+
   Python:
 
   - The spot.automata() and spot.automaton() functions now accept a

THANKS

@@ -56,6 +56,7 @@ Raven Beutner
 Reuben Rowe
 Roei Nahum
 Rüdiger Ehlers
+Samuel Judson
 Shachar Itzhaky
 Shengping Shaw
 Shufang Zhu

spot/twaalgos/strength.cc

@@ -23,6 +23,8 @@
 #include <spot/twaalgos/minimize.hh>
 #include <spot/twaalgos/isdet.hh>
 #include <spot/twaalgos/sccfilter.hh>
+#include <spot/twaalgos/contains.hh>
+#include <spot/twaalgos/stripacc.hh>
 
 using namespace std::string_literals;
 
@@ -182,23 +184,55 @@ namespace spot
   {
     if (aut->acc().is_t())
       return true;
+    if (!aut->is_existential())
+      throw std::runtime_error
+        ("is_safety_automaton() does not support alternation");
 
-    bool need_si = !si;
-    if (need_si)
-      si = new scc_info(aut);
+    std::unique_ptr<scc_info> localsi;
+    if (!si)
+      {
+        localsi = std::make_unique<scc_info>(aut);
+        si = localsi.get();
+      }
+    si->determine_unknown_acceptance();
 
-    bool res = true;
-    unsigned scount = si->scc_count();
-    for (unsigned scc = 0; scc < scount; ++scc)
-      if (!si->is_trivial(scc) && si->is_rejecting_scc(scc))
+    // a trim automaton without rejecting cycle is a safety automaton
+    bool has_rejecting_cycle = false;
+
+    // first, look for rejecting SCCs.
+    unsigned scccount = si->scc_count();
+    for (unsigned scc = 0; scc < scccount; ++scc)
+      if (si->is_useful_scc(scc)
+          && !si->is_trivial(scc)
+          && si->is_rejecting_scc(scc))
         {
-          res = false;
+          has_rejecting_cycle = true;
           break;
         }
+    if (!has_rejecting_cycle && !aut->prop_inherently_weak().is_true())
+      {
+        // maybe we have rejecting cycles inside accepting SCCs?
+        for (unsigned scc = 0; scc < scccount; ++scc)
+          if (si->is_useful_scc(scc)
+              && !si->is_trivial(scc)
+              && si->is_accepting_scc(scc)
+              && scc_has_rejecting_cycle(*si, scc))
+            {
+              has_rejecting_cycle = true;
+              break;
+            }
+      }
+    if (!has_rejecting_cycle)
+      return true;
 
-    if (need_si)
-      delete si;
-    return res;
+    // If the automaton has a rejecting loop and is deterministic, it
+    // cannot be a safety automaton.
+    if (is_universal(aut))
+      return false;
+
+    twa_graph_ptr b = make_twa_graph(aut, twa::prop_set::all());
+    strip_acceptance_here(b);
+    return spot::contains(aut, b);
   }
 
 

spot/twaalgos/strength.hh

@@ -104,12 +104,24 @@ namespace spot
 
   /// \brief Check whether an automaton is a safety automaton.
   ///
-  /// A safety automaton has only accepting SCCs (or trivial
-  /// SCCs).
+  /// An automaton is a safety automaton if its acceptance condition
+  /// can be changed to "true" without changing its language.
   ///
-  /// A minimized WDBA (as returned by a successful run of
-  /// minimize_obligation()) represents safety property if it is a
-  /// safety automaton.
+  /// The test performed by this function differs depending on
+  /// the nature of the input \a aut.
+  ///
+  /// If \a aut is an automaton with `t` acceptance, it is necessarily
+  /// a safety automaton.
+  ///
+  /// Else we check for the absence of rejecting cycle in the
+  /// useful part of the automaton.  This absence is only a sufficient
+  /// condition in the non-deterministic case, because a rejecting
+  /// run might correspond to a word that is accepted by another run.
+  ///
+  /// If the previous test could not conclude, we build the automaton
+  /// B that is a copy of \a aut with acceptance set to true, and we
+  /// check that \a aut contains all words of B.  This last test
+  /// requires complementing \a aut.
   ///
   /// \param aut the automaton to check
   ///

tests/Makefile.am

@@ -446,6 +446,7 @@ TESTS_python = \
   python/relabel.py \
   python/remfin.py \
   python/removeap.py \
+  python/safety.py \
   python/satmin.py \
   python/sbacc.py \
   python/sccfilter.py \

tests/python/safety.py

@@ -0,0 +1,52 @@
+# -*- 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()
+
+
+for f in ['Fb', 'GFa & GFb',
+          '(p0 W Fp0) R ((Gp1 & Fp1) | (F!p1 & G!p1)) & GFp0',
+          'GFp0 xor GFp1']:
+    aut = spot.translate(f, 'BA')
+    tc.assertFalse(spot.is_safety_automaton(aut))
+
+    aut = spot.translate(f, 'BA')
+    tc.assertFalse(spot.is_safety_automaton(aut))
+
+    aut = spot.translate(f, 'deterministic', 'complete')
+    tc.assertFalse(spot.is_safety_automaton(aut))
+
+    aut = spot.translate(f, 'generic', 'sbacc')
+    tc.assertFalse(spot.is_safety_automaton(aut))
+
+for f in ['Gb', 'Ga|Gb|Gc', 'Fr->(!p U r)', 'p1 M F(p1 U (Gp0 U X(0)))',
+          '((p1 U !p0) M !FXp1) W p0', 'p0 & ((!p1 | (p1 W X!p1)) M p1)',
+          '(p0 W Fp0) R ((Gp1 & Fp1) | (F!p1 & G!p1))']:
+    aut = spot.translate(f, 'BA')
+    tc.assertTrue(spot.is_safety_automaton(aut))
+
+    ba = spot.translate(f, 'BA', 'complete')
+    tc.assertTrue(spot.is_safety_automaton(aut))
+
+    ba = spot.translate(f, 'deterministic', 'complete')
+    tc.assertTrue(spot.is_safety_automaton(aut))
+
+    ba = spot.translate(f, 'generic', 'sbacc')
+    tc.assertTrue(spot.is_safety_automaton(aut))