ltlsynt: improve construction of turn-based games

Improve the way transitions are duplicated when preparing the turn-based
game for synthesis. The resulting arena should now be deterministic on
nodes owned by the environment. Also move the code to another file, so
that it is easier to test (e.g. in Python).

* bin/ltlsynt.cc: move the code
* spot/twaalgos/split.cc, spot/twaalgos/split.hh: move the code and
  implement the improvements
* tests/Makefile.am, tests/python/split.py: test it
* tests/core/ltlsynt.test: update existing tests to reflect the changes

tests/python/split.py

@@ -0,0 +1,103 @@
+# -*- mode: python; coding: utf-8 -*-
+# Copyright (C) 2018 Laboratoire de Recherche et
+# Développement de l'Epita
+#
+# 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
+
+def incl(a,b):
+    return not b.intersects(spot.dualize(spot.tgba_determinize(a)))
+def equiv(a,b):
+    return incl(a,b) and incl(b,a)
+
+def do_split(f, in_list):
+    aut = spot.translate(f)
+    inputs = spot.buddy.bddtrue
+    for a in in_list:
+        inputs &= spot.buddy.bdd_ithvar(aut.get_dict().varnum(spot.formula(a)))
+    s = spot.split_2step(aut, inputs)
+    return aut,s
+
+aut, s = do_split('(FG !a) <-> (GF b)', ['a'])
+assert equiv(aut, spot.unsplit_2step(s))
+
+aut, s = do_split('GFa && GFb', ['a'])
+assert equiv(aut, spot.unsplit_2step(s))
+assert s.to_str() == """HOA: v1
+States: 3
+Start: 0
+AP: 2 "a" "b"
+acc-name: generalized-Buchi 2
+Acceptance: 2 Inf(0)&Inf(1)
+properties: trans-labels explicit-labels trans-acc complete
+properties: deterministic
+--BODY--
+State: 0
+[!0] 1
+[0] 2
+State: 1
+[!1] 0
+[1] 0 {1}
+State: 2
+[!1] 0 {0}
+[1] 0 {0 1}
+--END--"""
+
+aut, s = do_split('! ((G (req -> (F ack))) && (G (go -> (F grant))))', ['go',
+    'req'])
+assert equiv(aut, spot.unsplit_2step(s))
+# FIXME s.to_str() is NOT the same on Debian stable and on Debian unstable
+#       we should investigate this
+#assert s.to_str() == """HOA: v1
+#States: 9
+#Start: 0
+#AP: 4 "ack" "req" "go" "grant"
+#acc-name: Buchi
+#Acceptance: 1 Inf(0)
+#properties: trans-labels explicit-labels state-acc
+#--BODY--
+#State: 0
+#[1&!2] 3
+#[!1&!2] 4
+#[1&2] 5
+#[!1&2] 6
+#State: 1
+#[t] 7
+#State: 2
+#[t] 8
+#State: 3
+#[t] 0
+#[!0] 1
+#State: 4
+#[t] 0
+#State: 5
+#[t] 0
+#[!0] 1
+#[!3] 2
+#State: 6
+#[t] 0
+#[!3] 2
+#State: 7 {0}
+#[!0] 1
+#State: 8 {0}
+#[!3] 2
+#--END--"""
+
+aut, s = do_split('((G (((! g_0) || (! g_1)) && ((r_0 && (X r_1)) -> (F (g_0 \
+    && g_1))))) && (G (r_0 -> F g_0))) && (G (r_1 -> F g_1))', ['r_0', 'r_1'])
+assert equiv(aut, spot.unsplit_2step(s))
+