tra2tba: Implement transformation of TRA to TBA acceptance condition

* python/spot/impl.i: Add bindings for tra2tba
* spot/twaalgos/Makefile.am: Record tra2tba.cc, tra2tba.hh
* spot/twaalgos/tra2tba.cc: Implement transformation of TRA to TBA
* spot/twaalgos/tra2tba.hh: Introduce declaration of tra_to_tba
* tests/Makefile.am: Record tra2tba tests
* tests/core/tra2tba.cc: Add driver for tests
* tests/core/tra2tba.test: Add tests of tra2tba transformation

python/spot/impl.i

@@ -151,6 +151,7 @@
 #include <spot/twaalgos/postproc.hh>
 #include <spot/twaalgos/product.hh>
 #include <spot/twaalgos/stutter.hh>
+#include <spot/twaalgos/tra2tba.hh>
 #include <spot/twaalgos/translate.hh>
 #include <spot/twaalgos/hoa.hh>
 #include <spot/twaalgos/dtwasat.hh>
@@ -581,6 +582,7 @@ def state_is_accepting(self, src) -> "bool":
 %include <spot/twaalgos/split.hh>
 %include <spot/twaalgos/sum.hh>
 %include <spot/twaalgos/stutter.hh>
+%include <spot/twaalgos/tra2tba.hh>
 %include <spot/twaalgos/translate.hh>
 %include <spot/twaalgos/hoa.hh>
 %include <spot/twaalgos/dtwasat.hh>

spot/twaalgos/Makefile.am

@@ -84,6 +84,7 @@ twaalgos_HEADERS = \
   tau03.hh \
   tau03opt.hh \
   totgba.hh \
+  tra2tba.hh \
   translate.hh \
   word.hh
 
@@ -145,6 +146,7 @@ libtwaalgos_la_SOURCES = \
   tau03.cc \
   tau03opt.cc \
   totgba.cc \
+  tra2tba.cc \
   translate.cc \
   word.cc
 

spot/twaalgos/tra2tba.cc

+// -*- coding: utf-8 -*-
+// Copyright (C) 2017 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/twa/acc.hh>
+#include <spot/twaalgos/tra2tba.hh>
+#include <spot/twaalgos/sccinfo.hh>
+#include <spot/twaalgos/mask.hh>
+#include <spot/twa/bddprint.hh>
+#include <spot/twa/formula2bdd.hh>
+
+namespace spot
+{
+  namespace
+  {
+    std::vector<unsigned> scc_edges(const const_twa_graph_ptr& aut,
+                                    const scc_info& si,
+                                    const unsigned scc)
+    {
+      std::vector<unsigned> edges;
+      for (unsigned s : si.states_of(scc))
+        for (const auto& t: aut->succ(aut->state_from_number(s)))
+          edges.push_back(aut->edge_number(t));
+      return edges;
+
+    }
+    //
+    std::vector<unsigned> scc_inner_edges(const const_twa_graph_ptr& aut,
+                                          const scc_info& si,
+                                          const unsigned scc)
+    {
+      auto edges = scc_edges(aut, si, scc);
+      edges.erase(std::remove_if(edges.begin(), edges.end(),
+        [&](unsigned e)
+        {
+          return si.scc_of(aut->edge_storage(e).dst) != scc;
+        }),
+        edges.end());
+      return edges;
+    }
+
+    twa_graph_ptr mask_keep_edges(const const_twa_graph_ptr& aut,
+                                  std::vector<bool>& to_keep,
+                                  unsigned int init)
+    {
+      if (to_keep.size() < aut->edge_vector().size())
+        to_keep.resize(aut->edge_vector().size(), false);
+
+      auto res = make_twa_graph(aut->get_dict());
+      res->copy_ap_of(aut);
+      res->prop_copy(aut, { false, true, false, true, false, false });
+      res->copy_acceptance_of(aut);
+
+      size_t states = aut->num_states();
+      std::vector<std::vector<bool>> edges;
+      edges.resize(states);
+      for (size_t i = 0; i < states; ++i)
+        edges[i].resize(states, false);
+
+      for (size_t i = 0; i < aut->edge_vector().size(); ++i)
+        {
+          if (to_keep[i])
+            {
+              const auto& es = aut->edge_storage(i);
+              edges[es.src][es.dst] = true;
+            }
+        }
+
+      transform_copy(aut, res,
+                     [&](unsigned src, bdd& cond, acc_cond::mark_t&,
+                         unsigned dst)
+                     {
+                       if (!edges[src][dst])
+                         cond = bddfalse;
+                     },
+                     init);
+      return res;
+    }
+
+    // Check whether the SCC contains non-accepting cycles.
+    //
+    // A cycle is accepting (in a Rabin automaton) if there exists an
+    // acceptance pair (Fᵢ, Iᵢ) such that some states from Iᵢ are
+    // visited while no states from Fᵢ are visited.
+    //
+    // Consequently, a cycle is non-accepting if for all acceptance
+    // pairs (Fᵢ, Iᵢ), either no states from Iᵢ are visited or some
+    // states from Fᵢ are visited.  (This corresponds to an accepting
+    // cycle with Streett acceptance.)
+    //
+    // final are those edges which are used in the resulting tba
+    // acceptance condition.
+    bool is_scc_tba_type(const const_twa_graph_ptr& aut,
+                         const scc_info& si,
+                         const unsigned scc,
+                         std::vector<bool>& final)
+    {
+      if (si.is_rejecting_scc(scc))
+        return true;
+
+      auto acc_pairs = aut->get_acceptance().used_inf_fin_sets();
+      auto infs = si.acc(scc) & acc_pairs.first;
+      auto infs_with_fins = (si.acc(scc) << 1U) & acc_pairs.first;
+      infs -= infs_with_fins;
+
+      auto& states = si.states_of(scc);
+      // Firstly consider whole SCC as one large cycle.
+      // If there is no inf without matching fin then the cycle formed
+      // by the entire SCC is not accepting.  However that does not
+      // necessarily imply that all cycles in the SCC are also
+      // non-accepting.  We may have a smaller cycle that is
+      // accepting, but which becomes non-accepting when extended with
+      // more states.
+      if (!infs)
+        {
+          // Check whether the SCC is accepting.  We do that by simply
+          // converting that SCC into a TGBA and running our emptiness
+          // check.  This is not a really smart implementation and
+          // could be improved.
+          std::vector<bool> keep(aut->num_states(), false);
+          for (auto s: states)
+            keep[s] = true;
+          auto sccaut = mask_keep_accessible_states(aut,
+                                                    keep,
+                                                    states.front());
+          sccaut->prop_state_acc(false);
+          return sccaut->is_empty();
+        }
+
+      // Remaining infs corresponds to I₁s that have been seen with seeing
+      // the mathing F₁. In this SCC any edge in these I₁ is therefore
+      // final. Otherwise we do not know: it is possible that there is
+      // a non-accepting cycle in the SCC that do not visit Fᵢ.
+      std::set<unsigned> unknown;
+      for (auto e: scc_inner_edges(aut, si, scc))
+        if (aut->edge_data(e).acc & infs)
+          final[e] = true;
+        else
+          unknown.insert(e);
+      // Check whether it is possible to build non-accepting cycles
+      // using only the "unknown" edges.
+      std::vector<bool> keep(aut->edge_vector().size(), false);
+      for (auto e: unknown)
+        keep[e] = true;
+
+      while (!unknown.empty())
+        {
+          unsigned init = aut->edge_storage(*unknown.begin()).src;
+          scc_info si(mask_keep_edges(aut, keep, init));
+          unsigned scc_max = si.scc_count();
+          for (unsigned uscc = 0; uscc < scc_max; ++uscc)
+            {
+              for (auto e: scc_edges(aut, si, uscc))
+                {
+                  unknown.erase(e);
+                  keep[e] = false;
+                }
+              if (si.is_rejecting_scc(uscc))
+                continue;
+              if (!is_scc_tba_type(aut, si, uscc, final))
+                return false;
+            }
+        }
+      return true;
+    }
+  }
+
+  // Specialized conversion from transition based Rabin acceptance to
+  // transition based Büchi acceptance.
+  // Is able to detect SCCs that are TBA-type (i.e., they can be
+  // converted to Büchi acceptance without chaning their structure).
+  //
+  // See "Deterministic ω-automata vis-a-vis Deterministic Büchi
+  // Automata", S. Krishnan, A. Puri, and R. Brayton (ISAAC'94) for
+  // some details about detecting Büchi-typeness.
+  //
+  // We essentially apply this method SCC-wise. The paper is
+  // concerned about *deterministic* automata, but we apply the
+  // algorithm on non-deterministic automata as well: in the worst
+  // case it is possible that a TBA-type SCC with some
+  // non-deterministic has one accepting and one rejecting run for
+  // the same word.  In this case we may fail to detect the
+  // TBA-typeness of the SCC, but the resulting automaton should
+  // be correct nonetheless.
+  twa_graph_ptr
+  tra_to_tba(const const_twa_graph_ptr& aut)
+  {
+    if (aut->prop_state_acc().is_true())
+      return nullptr;
+    std::vector<acc_cond::rs_pair> pairs;
+    if (!aut->acc().is_rabin_like(pairs))
+      return nullptr;
+
+    auto code = aut->get_acceptance();
+    if (code.is_t())
+      return nullptr;
+
+    // if is TBA type
+    scc_info si{aut};
+    std::vector<bool> scc_is_tba_type(si.scc_count(), false);
+    std::vector<bool> final(aut->edge_vector().size(), false);
+
+    for (unsigned scc = 0; scc < si.scc_count(); ++scc)
+      {
+        scc_is_tba_type[scc] = is_scc_tba_type(aut, si, scc, final);
+      }
+    // compute final edges
+    auto res = make_twa_graph(aut->get_dict());
+    res->copy_ap_of(aut);
+    res->prop_copy(aut, { false, false, false, false, false, true });
+    res->new_states(aut->num_states());
+    res->set_buchi();
+    res->set_init_state(aut->get_init_state_number());
+    trival deterministic = aut->prop_universal();
+    trival complete = aut->prop_complete();
+
+    std::vector<unsigned> state_map(aut->num_states());
+    for (unsigned scc = 0; scc < si.scc_count(); ++scc)
+      {
+        auto states = si.states_of(scc);
+
+        if (scc_is_tba_type[scc])
+          {
+            for (unsigned e: scc_edges(aut, si, scc))
+              {
+                const auto& ed = aut->edge_data(e);
+                const auto& es = aut->edge_storage(e);
+                bool acc = final[e];
+                res->new_acc_edge(es.src, es.dst, ed.cond, acc);
+              }
+          }
+        else
+          {
+            deterministic = false;
+            complete = trival::maybe();
+
+            auto acc_pairs = aut->get_acceptance().used_inf_fin_sets();
+            auto infs = si.acc(scc) & acc_pairs.first;
+            auto infs_with_fins = (si.acc(scc) << 1U) & acc_pairs.first;
+            infs -= infs_with_fins;
+
+            for (auto e: scc_edges(aut, si, scc))
+              {
+                const auto& ed = aut->edge_data(e);
+                const auto& es = aut->edge_storage(e);
+                bool acc{ ed.acc & infs };
+                res->new_acc_edge(es.src, es.dst, ed.cond, acc);
+              }
+
+            auto rem = si.acc(scc) & acc_pairs.second;
+            assert(rem != 0U);
+            for (auto r: rem.sets())
+              {
+                unsigned base = res->new_states(states.size());
+                for (auto s: states)
+                    state_map[s] = base++;
+                for (auto e: scc_inner_edges(aut, si, scc))
+                  {
+                    const auto& ed = aut->edge_data(e);
+                    const auto& es = aut->edge_storage(e);
+                    if (ed.acc.has(r))
+                      continue;
+                    auto src = state_map[es.src];
+                    auto dst = state_map[es.dst];
+                    res->new_acc_edge(src, dst, ed.cond, ed.acc.has(r + 1));
+                    // We need only one non-deterministic jump per
+                    // cycle.  As an approximation, we only do
+                    // them on back-links.
+                    bool jacc{ed.acc & inf_alone};
+                    if (es.dst <= es.src)
+                      res->new_acc_edge(es.src, dst, ed.cond, jacc);
+                  }
+              }
+          }
+      }
+    res->prop_complete(complete);
+    res->prop_universal(deterministic);
+    res->purge_dead_states();
+    return res;
+  }
+
+}

spot/twaalgos/tra2tba.hh

+// -*- coding: utf-8 -*-
+// Copyright (C) 2017 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/>.
+
+#pragma once
+
+#include <spot/twa/twagraph.hh>
+
+namespace spot
+{
+  /// \brief Convert a transition-based Rabin automaton to Büchi automaton,
+  /// preserving determinism when possible.
+  ///
+  /// Return nullptr if the input is not a Rabin automaton, or is not
+  /// transition-based.
+  ///
+  /// This modifies the algorithm from "Deterministic
+  /// ω-automata vis-a-vis Deterministic Büchi Automata", S. Krishnan,
+  /// A. Puri, and R. Brayton (ISAAC'94), but SCC-wise.
+  SPOT_API twa_graph_ptr
+  tra_to_tba(const const_twa_graph_ptr& aut);
+}

tests/Makefile.am

@@ -92,6 +92,7 @@ check_PROGRAMS = \
   core/sccif \
   core/syntimpl \
   core/taatgba \
+  core/tra2tba \
   core/trival \
   core/tgbagraph \
   core/tostring \
@@ -139,6 +140,7 @@ core_safra_SOURCES = core/safra.cc
 core_sccif_SOURCES = core/sccif.cc
 core_syntimpl_SOURCES = core/syntimpl.cc
 core_tostring_SOURCES = core/tostring.cc
+core_tra2tba_SOURCES = core/tra2tba.cc
 core_trival_SOURCES = core/trival.cc
 core_tunabbrev_SOURCES = core/equalsf.cc
 core_tunabbrev_CPPFLAGS = $(AM_CPPFLAGS) -DUNABBREV='"^ieFG"'
@@ -296,8 +298,8 @@ TESTS_twa = \
   core/complementation.test \
   core/randpsl.test \
   core/cycles.test \
-  core/acc_word.test
-
+  core/acc_word.test \
+  core/tra2tba.test
 
 ############################## PYTHON ##############################
 

tests/core/tra2tba.cc

+// -*- coding: utf-8 -*-
+// Copyright (C) 2017 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 <iostream>
+#include <spot/parseaut/public.hh>
+#include <spot/twaalgos/tra2tba.hh>
+#include <spot/twaalgos/hoa.hh>
+
+int main(int, char* argv[])
+{
+  char* input = argv[1];
+  if (!input)
+    return 1;
+  auto pa = parse_aut(input, spot::make_bdd_dict());
+  if (pa->format_errors(std::cerr))
+    return 1;
+  if (pa->aborted)
+    {
+      std::cerr << "--ABORT-- read\n";
+      return 1;
+    }
+  auto tba = spot::tra_to_tba(pa->aut);
+  spot::print_hoa(std::cout, tba) << '\n';
+  return 0;
+}

tests/core/tra2tba.test

+#!/bin/sh
+# -*- coding: utf-8 -*-
+# Copyright (C) 2017 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/>.
+
+. ./defs
+
+set -e
+
+cat >test1.hoa <<EOF
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+Acceptance: 2 (Fin(0) & Inf(1))
+--BODY--
+State: 0
+[!0] 0 {1}
+[0] 1
+State: 1
+[0] 1 {0}
+--END--
+EOF
+
+cat >out.exp << EOF
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc deterministic
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 1
+State: 1
+[0] 1
+--END--
+EOF
+
+run 0 ../tra2tba test1.hoa > out.hoa
+diff out.hoa out.exp
+
+cat >test2.hoa <<EOF
+HOA: v1
+States: 3
+Start: 0
+AP: 1 "a"
+Acceptance: 2 (Inf(1) & Fin(0))
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 1
+State: 1
+[0] 2 {}
+State: 2
+[!0] 1 {}
+[0] 2 {1}
+--END--
+EOF
+
+cat >out.exp << EOF
+HOA: v1
+States: 3
+Start: 0
+AP: 1 "a"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels trans-acc deterministic
+--BODY--
+State: 0
+[!0] 0
+[0] 1
+State: 1
+[0] 2
+State: 2
+[!0] 1
+[0] 2 {0}
+--END--
+EOF
+
+run 0 ../tra2tba test2.hoa > out.hoa
+diff out.hoa out.exp
+
+cat >test3.hoa <<EOF
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+Acceptance: 4 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))
+--BODY--
+State: 0
+[!0] 0 {0}
+[0] 1
+State: 1
+[0] 1 {2}
+--END--
+EOF
+
+cat >out.exp << EOF
+HOA: v1
+States: 2
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels state-acc deterministic
+--BODY--
+State: 0
+[!0] 0
+[0] 1
+State: 1
+[0] 1
+--END--
+EOF
+
+run 0 ../tra2tba test3.hoa > out.hoa
+diff out.hoa out.exp
+
+cat >test4.hoa <<EOF
+HOA: v1
+States: 3
+Start: 0
+Acceptance: 4 (Fin(0) & Inf(1)) | (Fin(2) & Inf(3))
+AP: 2 "a" "b"
+--BODY--
+State: 0
+[0 & 1] 0 {0 2}
+  [!0] 1
+  [!1] 2
+State: 1
+  [t] 1 {1}
+State: 2
+  [t] 2 {3}
+--END--
+EOF
+
+cat >out.exp << EOF
+HOA: v1
+States: 3
+Start: 0
+AP: 2 "a" "b"
+acc-name: Buchi
+Acceptance: 1 Inf(0)
+properties: trans-labels explicit-labels state-acc complete
+--BODY--
+State: 0
+[0&1] 0
+[!0] 1
+[!1] 2
+State: 1 {0}
+[t] 1
+State: 2 {0}
+[t] 2
+--END--
+EOF
+
+run 0 ../tra2tba test4.hoa > out.hoa
+diff out.hoa out.exp
+
+cat >test5.hoa <<EOF
+HOA: v1
+States: 4
+Start: 0