Adding function to canonicalize an automaton.

* src/tgbaalgos/are_isomorphic.cc, src/tgbaalgos/are_isomorphic.hh,
src/bin/autfilt.cc: are_isomorphic now uses canonicalize. It returns a
bool, because the mapping cannot be deduced easily from the
canonicalized automaton.
* src/graph/graph.hh: Add equality operator to trans_storage_t
for easy comparison of transition vectors.
* src/tgba/tgbagraph.hh: Add equality operator to tgba_graph_trans_data
and to tgba_digraph.
* src/tgbaalgos/canonicalize.cc, src/tgbaalgos/canonicalize.hh:
New files.
* src/tgbaalgos/Makefile.am: Add them.
* src/tgbatest/isomorph.test: Test them.

src/tgbaalgos/canonicalize.cc

@@ -0,0 +1,109 @@
+// -*- coding: utf-8 -*-
+// Copyright (C) 2014 Laboratoire de Recherche et
+// Developpement 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 "canonicalize.hh"
+#include "tgba/tgbagraph.hh"
+#include <set>
+#include <vector>
+
+namespace
+{
+  typedef std::pair<spot::tgba_digraph::graph_t::trans_data_t, unsigned>
+    trans_sig_t;
+
+  struct signature_t
+  {
+    std::vector<trans_sig_t> ingoing;
+    std::vector<trans_sig_t> outgoing;
+    unsigned classnum;
+
+    bool
+    operator<(const signature_t& o) const
+    {
+      return ingoing != o.ingoing ? ingoing < o.ingoing :
+        outgoing != o.outgoing ? outgoing < o.outgoing :
+        classnum < o.classnum;
+    }
+  };
+
+  typedef std::map<signature_t, std::vector<unsigned>> sig2states_t;
+
+  static sig2states_t
+  sig_to_states(spot::tgba_digraph_ptr aut, std::vector<unsigned>& state2class)
+  {
+    std::vector<signature_t> signature(aut->num_states(), signature_t());
+
+    for (auto& t : aut->transitions())
+      {
+        signature[t.dst].ingoing.emplace_back(t.data(), state2class[t.src]);
+        signature[t.src].outgoing.emplace_back(t.data(), state2class[t.dst]);
+      }
+
+    sig2states_t sig2states;
+    for (unsigned s = 0; s < aut->num_states(); ++s)
+      {
+        std::sort(signature[s].ingoing.begin(), signature[s].ingoing.end());
+        std::sort(signature[s].outgoing.begin(), signature[s].outgoing.end());
+        signature[s].classnum = state2class[s];
+        sig2states[signature[s]].push_back(s);
+      }
+
+    return sig2states;
+  }
+}
+
+namespace spot
+{
+  tgba_digraph_ptr
+  canonicalize(tgba_digraph_ptr aut)
+  {
+    std::vector<unsigned> state2class(aut->num_states(), 0);
+    state2class[aut->get_init_state_number()] = 1;
+    size_t distinct_classes = 2;
+    sig2states_t sig2states = sig_to_states(aut, state2class);
+
+    while (sig2states.size() != distinct_classes &&
+           sig2states.size() != aut->num_states())
+      {
+        distinct_classes = sig2states.size();
+
+        unsigned classnum = 0;
+        for (auto& s: sig2states)
+          {
+            for (auto& state: s.second)
+              state2class[state] = classnum;
+            ++classnum;
+          }
+
+        sig2states = sig_to_states(aut, state2class);
+      }
+
+    unsigned classnum = 0;
+    for (auto& s: sig2states)
+      for (auto& state: s.second)
+        state2class[state] = classnum++;
+
+    auto& g = aut->get_graph();
+    g.rename_states_(state2class);
+    aut->set_init_state(state2class[aut->get_init_state_number()]);
+    g.sort_transitions_();
+    g.chain_transitions_();
+    return aut;
+  }
+}