alternation: add a states_and algorithm

This should will come handy to implement the convertion from LTL to
alternating automata, and to handle automata with multiple initial
states.

* spot/twaalgos/alternation.hh, spot/twaalgos/alternation.cc: New files.
* spot/twaalgos/Makefile.am: Add them.
* python/spot/impl.i: Add bindings.
* tests/python/alternating.py: Test states_and.

python/spot/impl.i

@@ -113,6 +113,7 @@
 #include <spot/twa/taatgba.hh>
 #include <spot/twa/twaproduct.hh>
 
+#include <spot/twaalgos/alternation.hh>
 #include <spot/twaalgos/cleanacc.hh>
 #include <spot/twaalgos/degen.hh>
 #include <spot/twaalgos/dot.hh>
@@ -507,6 +508,7 @@ def state_is_accepting(self, src) -> "bool":
 
 // Should come after the definition of twa_graph
 
+%include <spot/twaalgos/alternation.hh>
 %include <spot/twaalgos/cleanacc.hh>
 %include <spot/twaalgos/degen.hh>
 %include <spot/twaalgos/dot.hh>
@@ -932,6 +934,13 @@ unblock_signal(int signum)
   return sigprocmask(SIG_UNBLOCK, &set, 0);
 }
 
+// for alternation.hh
+unsigned states_and(const spot::twa_graph_ptr& aut,
+                    const std::vector<unsigned>& il)
+{
+  return states_and(aut, il.begin(), il.end());
+}
+
 %}
 
 %extend spot::parse_error_list {

spot/twaalgos/Makefile.am

@@ -28,6 +28,7 @@ AM_CXXFLAGS = $(WARNING_CXXFLAGS)
 twaalgosdir = $(pkgincludedir)/twaalgos
 
 twaalgos_HEADERS = \
+  alternation.hh \
   are_isomorphic.hh \
   bfssteps.hh \
   canonicalize.hh \
@@ -84,6 +85,7 @@ twaalgos_HEADERS = \
 
 noinst_LTLIBRARIES = libtwaalgos.la
 libtwaalgos_la_SOURCES = \
+  alternation.cc \
   are_isomorphic.cc \
   bfssteps.cc \
   canonicalize.cc \

spot/twaalgos/alternation.cc

@@ -0,0 +1,88 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2016 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 <spot/twaalgos/alternation.hh>
+#include <algorithm>
+#include <spot/misc/minato.hh>
+
+namespace spot
+{
+  outedge_combiner::outedge_combiner(const twa_graph_ptr& aut)
+    : aut_(aut), vars_(bddtrue)
+  {
+  }
+
+  outedge_combiner::~outedge_combiner()
+  {
+    aut_->get_dict()->unregister_all_my_variables(this);
+  }
+
+  bdd outedge_combiner::operator()(unsigned st)
+  {
+    const auto& dict = aut_->get_dict();
+    bdd res = bddtrue;
+    for (unsigned d1: aut_->univ_dests(st))
+      {
+        bdd res2 = bddfalse;
+        for (auto& e: aut_->out(d1))
+          {
+            bdd out = bddtrue;
+            for (unsigned d: aut_->univ_dests(e.dst))
+              {
+                auto p = state_to_var.emplace(d, 0);
+                if (p.second)
+                  {
+                    int v = dict->register_anonymous_variables(1, this);
+                    p.first->second = v;
+                    var_to_state.emplace(v, d);
+                    vars_ &= bdd_ithvar(v);
+                  }
+                out &= bdd_ithvar(p.first->second);
+              }
+            res2 |= e.cond & out;
+          }
+        res &= res2;
+      }
+    return res;
+  }
+
+  void outedge_combiner::new_dests(unsigned st, bdd out) const
+  {
+    minato_isop isop(out);
+    bdd cube;
+    std::vector<unsigned> univ_dest;
+    while ((cube = isop.next()) != bddfalse)
+      {
+        bdd cond = bdd_exist(cube, vars_);
+        bdd dest = bdd_existcomp(cube, vars_);
+        while (dest != bddtrue)
+          {
+            assert(bdd_low(dest) == bddfalse);
+            auto it = var_to_state.find(bdd_var(dest));
+            assert(it != var_to_state.end());
+            univ_dest.push_back(it->second);
+            dest = bdd_high(dest);
+          }
+        std::sort(univ_dest.begin(), univ_dest.end());
+        aut_->new_univ_edge(st, univ_dest.begin(), univ_dest.end(), cond);
+        univ_dest.clear();
+      }
+  }
+
+}

spot/twaalgos/alternation.hh

@@ -0,0 +1,96 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2016 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/twa/twagraph.hh>
+#include <utility>
+
+namespace spot
+{
+  /// \brief Helper class combine outgoing edges in alternating
+  /// automata
+  ///
+  /// The idea is that you can the operator() on some state to get an
+  /// BDD representation of its outgoing edges (labels and
+  /// destinations, but not acceptance marks).  The BDD representation
+  /// of different states can combined using & or | to build a new
+  /// representation of some outgoing edges that can be attached to
+  /// some state with new_dests.  The use of BDDs helps removing
+  /// superfluous edges.
+  ///
+  /// Beware that new_dests() just *appends* the transitions to the
+  /// supplied state, it does not remove existing ones.
+  ///
+  /// operator() can be called on states with universal branching
+  /// (that's actually the point), and can be called on state number
+  /// that designate groupes of destination states (in that case the
+  /// conjunction of all those states are taken).
+  class SPOT_API outedge_combiner
+  {
+  private:
+    const twa_graph_ptr& aut_;
+    std::map<unsigned, int> state_to_var;
+    std::map<int, unsigned> var_to_state;
+    bdd vars_;
+  public:
+    outedge_combiner(const twa_graph_ptr& aut);
+    ~outedge_combiner();
+    bdd operator()(unsigned st);
+    void new_dests(unsigned st, bdd out) const;
+  };
+
+  /// @{
+  /// \brief Combine two states in a conjunction.
+  ///
+  /// This creates a new state whose outgoing transitions are the
+  /// conjunctions of the compatible transitions of s1 and s2.
+  ///
+  /// Acceptance marks are dropped.
+  ///
+  /// The results is very likely to be alternating.
+  template<class I>
+  SPOT_API
+  unsigned states_and(const twa_graph_ptr& aut, I begin, I end)
+  {
+    if (begin == end)
+      throw std::runtime_error
+        ("state_and() expects an non-empty list of states");
+    outedge_combiner combiner(aut);
+    bdd combination = bddtrue;
+    while (begin != end)
+      combination &= combiner(*begin++);
+    unsigned new_s = aut->new_state();
+    combiner.new_dests(new_s, combination);
+    return new_s;
+  }
+
+  template<class T>
+  SPOT_API
+  unsigned states_and(const twa_graph_ptr& aut,
+                      const std::initializer_list<T>& il)
+  {
+    return states_and(aut, il.begin(), il.end());
+  }
+  /// @}
+
+
+
+
+}

tests/python/alternating.py

@@ -94,3 +94,41 @@ State: 1
 State: 2
 [0 | 1] 2
 --END--"""
+
+st = spot.states_and(aut, [0, 2])
+st2 = spot.states_and(aut, [1, st])
+st3 = spot.states_and(aut, [0, 1, 2])
+assert (st, st2, st3) == (3, 4, 5)
+
+received = False
+try:
+    st4 = spot.states_and(aut, [])
+except RuntimeError:
+    received = True
+assert received
+
+h = aut.to_str('hoa')
+print(h)
+assert h == """HOA: v1
+States: 6
+Start: 0
+AP: 2 "p1" "p2"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: univ-branch trans-labels explicit-labels trans-acc
+--BODY--
+State: 0
+[0] 1&2 {0}
+[1] 0&1
+State: 1
+[0&1] 0&2&1
+State: 2
+[0 | 1] 2
+State: 3
+[0] 1&2
+[1] 0&1&2
+State: 4
+[0&1] 0&1&2
+State: 5
+[0&1] 0&1&2
+--END--"""