ltlcross: add support for alternating automata

* bin/ltlcross.cc: Add an alternation-removal pass, and
adjust CSV output.
* doc/org/ltlcross.org: Update.
* tests/core/ltl3dra.test, tests/core/ltl3ba.test: Add more tests.
* tests/Makefile.am: Add tests/core/ltl3ba.test.
* NEWS: Mention it.

NEWS

 New in spot 2.2.2.dev (Not yet released)
 
+  Tools:
+
+  * ltlcross supports translators that output weak alternating
+    automata in the HOA format (not necessarily *very* weak).
+
   Library:
 
   * A twa is required to have at least one state, the initial state.

bin/ltlcross.cc

@@ -56,6 +56,7 @@
 #include <spot/twaalgos/word.hh>
 #include <spot/twaalgos/complement.hh>
 #include <spot/twaalgos/cleanacc.hh>
+#include <spot/twaalgos/alternation.hh>
 #include <spot/misc/formater.hh>
 #include <spot/twaalgos/stats.hh>
 #include <spot/twaalgos/isdet.hh>
@@ -146,9 +147,10 @@ static const argp_option options[] =
       "store automata (in the HOA format) into the CSV or JSON output", 0 },
     { "strength", OPT_STRENGTH, nullptr, 0,
       "output statistics about SCC strengths (non-accepting, terminal, weak, "
-      "strong)", 0 },
+      "strong) [not supported for alternating automata]", 0 },
     { "ambiguous", OPT_AMBIGUOUS, nullptr, 0,
-      "output statistics about ambiguous automata", 0 },
+      "output statistics about ambiguous automata "
+      "[not supported for alternating automata]", 0 },
     { "unambiguous", 0, nullptr, OPTION_ALIAS, nullptr, 0 },
     /**************************************************/
     { nullptr, 0, nullptr, 0, "Miscellaneous options:", -2 },
@@ -257,6 +259,7 @@ struct statistics
 {
   statistics()
     : ok(false),
+      alternating(false),
       status_str(nullptr),
       status_code(0),
       time(0),
@@ -280,6 +283,7 @@ struct statistics
   // If OK is false, only the status_str, status_code, and time fields
   // should be valid.
   bool ok;
+  bool alternating;
   const char* status_str;
   int status_code;
   double time;
@@ -351,18 +355,33 @@ struct statistics
            << acc << ','
            << scc << ',';
         if (opt_strength)
-          os << nonacc_scc << ','
-             << terminal_scc << ','
-             << weak_scc << ','
-             << strong_scc << ',';
+          {
+            if (alternating)
+              os << ",,,,";
+            else
+              os << nonacc_scc << ','
+                 << terminal_scc << ','
+                 << weak_scc << ','
+                 << strong_scc << ',';
+          }
         os << nondetstates << ','
            << nondeterministic << ',';
         if (opt_strength)
-          os << terminal_aut << ','
-             << weak_aut << ','
-             << strong_aut << ',';
+          {
+            if (alternating)
+              os << ",,,";
+            else
+              os << terminal_aut << ','
+                 << weak_aut << ','
+                 << strong_aut << ',';
+          }
         if (opt_ambiguous)
-          os << ambiguous << ',';
+          {
+            if (alternating)
+              os << ',';
+            else
+              os << ambiguous << ',';
+          }
         os << complete;
         if (!products_avg)
           {
@@ -627,6 +646,7 @@ namespace
               if (verbose)
                 std::cerr << "info: getting statistics\n";
               st->ok = true;
+              st->alternating = res->is_alternating();
               spot::twa_sub_statistics s = sub_stats_reachable(res);
               st->states = s.states;
               st->edges = s.edges;
@@ -637,7 +657,7 @@ namespace
               st->scc = c;
               st->nondetstates = spot::count_nondet_states(res);
               st->nondeterministic = st->nondetstates != 0;
-              if (opt_strength)
+              if (opt_strength && !st->alternating)
                 {
                   m.determine_unknown_acceptance();
                   for (unsigned n = 0; n < c; ++n)
@@ -658,7 +678,7 @@ namespace
                   else
                     st->terminal_aut = true;
                 }
-              if (opt_ambiguous)
+              if (opt_ambiguous && !st->alternating)
                 st->ambiguous = !spot::is_unambiguous(res);
               st->complete = spot::is_complete(res);
 
@@ -1037,11 +1057,6 @@ namespace
           bool prob;
           pos[n] = runner.translate(n, 'P', pstats, prob);
           problems += prob;
-
-          // If the automaton is deterministic, compute its complement
-          // as well.
-          if (!no_complement && pos[n] && is_deterministic(pos[n]))
-            comp_pos[n] = dtwa_complement(pos[n]);
         }
 
       // ---------- Negative Formula ----------
@@ -1073,11 +1088,6 @@ namespace
               bool prob;
               neg[n] = runner.translate(n, 'N', nstats, prob);
               problems += prob;
-
-              // If the automaton is deterministic, compute its
-              // complement as well.
-              if (!no_complement && neg[n] && is_deterministic(neg[n]))
-                comp_neg[n] = dtwa_complement(neg[n]);
             }
         }
 
@@ -1102,6 +1112,8 @@ namespace
               std::cerr << "info:   " << prefix << i << "\t(";
               printsize(x[i]);
               std::cerr << ')';
+              if (x[i]->is_alternating())
+                std::cerr << " univ-edges";
               if (is_deterministic(x[i]))
                 std::cerr << " deterministic";
               if (is_complete(x[i]))
@@ -1120,9 +1132,51 @@ namespace
           std::cerr << "Performing sanity checks and gathering statistics..."
                     << std::endl;
 
+          bool print_first = verbose;
+          auto unalt = [&](std::vector<spot::twa_graph_ptr>& x,
+                           unsigned i, char prefix)
+            {
+              if (!(x[i] && x[i]->is_alternating()))
+                return;
+              if (verbose)
+                {
+                  if (print_first)
+                    {
+                      std::cerr <<
+                        "info: getting rid of universal edges...\n";
+                      print_first = false;
+                    }
+                  std::cerr << "info:   " << prefix << i << "\t(";
+                  printsize(x[i]);
+                  std::cerr << ") ->";
+                }
+              x[i] = remove_alternation(x[i]);
+              if (verbose)
+                {
+                  std::cerr << " (";
+                  printsize(x[i]);
+                  std::cerr << ")\n";
+                }
+            };
+          auto complement = [&](const std::vector<spot::twa_graph_ptr>& x,
+                                std::vector<spot::twa_graph_ptr>& comp,
+                                unsigned i)
+            {
+              if (!no_complement && x[i] && is_deterministic(x[i]))
+                comp[i] = dtwa_complement(x[i]);
+            };
+
+          for (unsigned i = 0; i < m; ++i)
+            {
+              unalt(pos, i, 'P');
+              complement(pos, comp_pos, i);
+              unalt(neg, i, 'N');
+              complement(neg, comp_neg, i);
+            }
+
           if (determinize && !no_complement)
             {
-              bool print_first = verbose;
+              print_first = verbose;
               auto tmp = [&](std::vector<spot::twa_graph_ptr>& from,
                              std::vector<spot::twa_graph_ptr>& to, unsigned i,
                              char prefix)
@@ -1157,7 +1211,7 @@ namespace
                 }
             }
 
-          bool print_first = verbose;
+          print_first = verbose;
           auto tmp = [&](std::vector<spot::twa_graph_ptr>& x, unsigned i,
                          const char* prefix, const char* suffix)
             {

doc/org/ltlcross.org

@@ -9,19 +9,22 @@ translators.  It is actually a Spot-based clone of [[http://www.tcs.hut.fi/Softw
 /LTL-to-Büchi Translator Testbench/, that essentially performs the
 same sanity checks.
 
-The main differences are:
-  - support for PSL formulas in addition to LTL
-  - more statistics, especially:
+The main differences with LBTT are:
+  - *support for PSL formulas in addition to LTL*
+  - support for (non-alternating) automata with *any type of acceptance condition*,
+  - support for *weak alternating automata*,
+  - additional intersection *checks with the complement*, allowing
+    to check equivalence of automata more precisely,
+  - *more statistics*, especially:
     - the number of logical transitions represented by each physical edge,
     - the number of deterministic states and automata
     - the number of SCCs with their various strengths (nonaccepting, terminal, weak, strong)
     - the number of terminal, weak, and strong automata
-  - statistics output in a format that can be more easily be post-processed,
-  - more precise time measurement (LBTT was only precise to
-    1/100 of a second, reporting most times as "0.00s"),
-  - support for any type of acceptance condition,
-  - additional intersection checks with the complement, allowing
-    to check equivalence of automata more precisely.
+  - an option to *reduce counterexample* by attempting to mutate and
+    shorten troublesome formulas,
+  - statistics output in *CSV* for easier post-processing,
+  - *more precise time measurement* (LBTT was only precise to
+    1/100 of a second, reporting most times as "0.00s").
 
 Although =ltlcross= performs the same sanity checks as LBTT, it does
 not implement any of the interactive features of LBTT.  In our almost
@@ -120,6 +123,7 @@ be rewritten using the other supported operators.
     --lbtt=.
   - Non-alternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]] with any acceptance
     condition.
+  - [[file:concepts.org::#property-flags][Weak]] alternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]].
   - [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]], which supports deterministic Rabin or Streett
     automata.
 
@@ -496,7 +500,9 @@ This classification is used to fill the =terminal_aut=, =weak_aut=,
 =--strength= is passed).  Only one of these should contain =1=.  We
 usually prefer terminal automata over weak automata, and weak automata
 over strong automata, because the emptiness check of terminal (and
-weak) automata is easier.
+weak) automata is easier.  When working with alternating automata, all
+those strength-related columns will be empty, because the routines
+used to compute those statistic do not yet support universal edges.
 
 =nondetstates= counts the number of non-deterministic states in the
 automaton.  =nondeterministic= is a Boolean value indicating if the
@@ -509,7 +515,8 @@ assignment $ab$) and is therefore not deterministic.
 If option =--aumbiguous= was passed to =ltlcross=, the column
 =ambiguous_aut= holds a Boolean indicating whether the automaton is
 ambiguous, i.e., if there exists a word that can be accepted by at
-least two different runs.
+least two different runs.  (This information is not yet available for
+alternating automata.)
 
 =complete_aut= is a Boolean indicating whether the automaton is
 complete.
@@ -962,30 +969,40 @@ The verbose option can be useful to troubleshoot problems or simply
 follow the list of transformations and tests performed by =ltlcross=.
 
 For instance here is what happens if we try to cross check =ltl2tgba=
-and =ltl3ba= on the formula =FGa=.
+and =ltl3ba -H1= on the formula =FGa=.  Note that =ltl2tgba= will
+produce transition-based generalized Büchi automata, while =ltl3ba
+-H1= produces co-Büchi alternating automata.
 
 #+BEGIN_SRC sh :results verbatim :exports code
-ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose
+ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --determinize --verbose
 #+END_SRC
 
 #+BEGIN_SRC sh :results verbatim :exports results
-ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose 2>&1
+ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --determinize --verbose 2>&1
 #+END_SRC
 
 #+RESULTS:
 #+begin_example
 F(G(a))
-Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-vfVUzt'
-Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-IiXGfZ'
-Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-T02eWu'
-Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-0DpXF0'
+Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-Ak0bYx'
+Running [P1]: ltl3ba -H1 -f '<>([](a))'>'lcr-o1-5U1MyT'
+Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-sX2kaf'
+Running [N1]: ltl3ba -H1 -f '!(<>([](a)))'>'lcr-o1-4siKPA'
+info: collected automata:
+info:   P0	(2 st.,3 ed.,1 sets)
+info:   N0	(1 st.,2 ed.,1 sets) deterministic complete
+info:   P1	(2 st.,3 ed.,1 sets)
+info:   N1	(3 st.,5 ed.,1 sets) univ-edges deterministic complete
 Performing sanity checks and gathering statistics...
+info: getting rid of universal edges...
+info:   N1	(3 st.,5 ed.,1 sets) -> (2 st.,4 ed.,1 sets)
 info: complementing non-deterministic automata via determinization...
 info:   P0	(2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets)	Comp(P0)
 info:   P1	(2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets)	Comp(P1)
 info: getting rid of any Fin acceptance...
 info:	Comp(P0)	(2 st.,4 ed.,2 sets) -> (3 st.,7 ed.,2 sets)
 info:	Comp(N0)	(1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
+info:	     P1 	(2 st.,3 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
 info:	Comp(P1)	(2 st.,4 ed.,2 sets) -> (4 st.,9 ed.,2 sets)
 info:	Comp(N1)	(2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
 info: check_empty P0*N0
@@ -999,10 +1016,19 @@ No problem detected.
 #+end_example
 
 First =FGa= and its negations =!FGa= are translated with the two
-tools, resulting in four automata: to positive automata =P0= and =P1=
+tools, resulting in four automata: two positive automata =P0= and =P1=
 for =FGa=, and two negative automata =N0= and =N1=.
 
-=ltlcross= then proceeds to compute the complement of these four
+Some basic information about the collected automata are displayed.
+For instance we can see that although =ltl3ba -H1= outputs co-Büchi
+alternating automata, only automaton =N1= uses universal edges: the
+automaton =P1= can be used like a non-alternating co-Büchi automaton.
+
+=ltlcross= then proceeds to transform alternating automata (only weak
+alternating automata are supported) into non-alternating automata.
+Here only =N1= needs this transformation.
+
+Then =ltlcross= computes the complement of these four
 automata.  Since =P0= and =P1= are nondeterministic and the
 =--determinize= option was given, a first pass determinize and
 complete these two automata, creating =Comp(P0)= and =Comp(P1)=.
@@ -1030,23 +1056,31 @@ Note that if we had not used the =--determinize= option, the procedure
 would look slightly more complex:
 
 #+BEGIN_SRC sh :results verbatim :exports code
-ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose
+ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --verbose
 #+END_SRC
 
 #+BEGIN_SRC sh :results verbatim :exports results
-ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose 2>&1
+ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --verbose 2>&1
 #+END_SRC
 
 #+RESULTS:
 #+begin_example
 F(G(a))
-Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-YvMdzU'
-Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-Ixj7RI'
-Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-uBbTbx'
-Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-eo0fzl'
+Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-jD32mW'
+Running [P1]: ltl3ba -H1 -f '<>([](a))'>'lcr-o1-w6IJYI'
+Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-dac1Av'
+Running [N1]: ltl3ba -H1 -f '!(<>([](a)))'>'lcr-o1-OZL7fi'
+info: collected automata:
+info:   P0	(2 st.,3 ed.,1 sets)
+info:   N0	(1 st.,2 ed.,1 sets) deterministic complete
+info:   P1	(2 st.,3 ed.,1 sets)
+info:   N1	(3 st.,5 ed.,1 sets) univ-edges deterministic complete
 Performing sanity checks and gathering statistics...
+info: getting rid of universal edges...
+info:   N1	(3 st.,5 ed.,1 sets) -> (2 st.,4 ed.,1 sets)
 info: getting rid of any Fin acceptance...
 info:	Comp(N0)	(1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
+info:	     P1 	(2 st.,3 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
 info:	Comp(N1)	(2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
 info: check_empty P0*N0
 info: check_empty P0*N1

tests/Makefile.am

@@ -256,6 +256,7 @@ TESTS_twa = \
   core/dra2dba.test \
   core/unambig.test \
   core/ltlcross4.test \
+  core/ltl3ba.test \
   core/streett.test \
   core/ltl3dra.test \
   core/ltl2dstar.test \

tests/core/ltl3ba.test

+#!/bin/sh
+# -*- 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/>.
+
+# Do some quick translations to make sure the neverclaims produced by
+# spot actually look correct!  We do that by parsing them via ltlcross.
+# ltl2neverclaim-lbtt.test does the same with LBTT if it is installed.
+
+. ./defs
+set -e
+
+# Skip this test if ltl3dra is not installed.
+(ltl3ba -v) || exit 77
+
+# The -H1 option will output alternating automata, so this tests
+# ltlcross's support in this area.
+randltl -n 30 2 |
+ltlcross 'ltl3ba -H1' 'ltl3ba -H2' 'ltl3ba -H3' \
+         --ambiguous --strength --csv=output.csv
+
+# Make sure all lines in output.csv have the same number of comas
+sed 's/[^,]//g' <output.csv |
+( read first
+while read l; do
+  test "x$first" = "x$l" || exit 1
+done)

tests/core/ltl3dra.test

@@ -29,7 +29,7 @@ set -e
 (ltl3dra -v) || exit 77
 
 # This used to crash ltlcross because the number of
-# acceptance sets generated was to high.
+# acceptance sets generated was too high.
 ltlcross 'ltl2tgba' 'ltl3dra' -f '(<>((((p0) &&
 (!(<>(p2)))) || ((!(p0)) && (<>(p2)))) U ((<>(((p0) && (!([](((!(p1))
 && ([](p3))) || ((p1) && (!([](p3)))))))) || ((!(p0)) && ([](((!(p1))
@@ -41,3 +41,21 @@ ltlcross 'ltl2tgba' 'ltl3dra' -f '(<>((((p0) &&
 # relabeled p0&p1, and then p0 was unregistered despite being one of
 # the new variables.
 ltldo ltl3dra -f '"a=0" & p0' | grep 'AP: 2.*p0'
+
+# ltl3dra 0.2.2 has a bug were 'ltl3dra -H1 -f true' produce an
+# empty automaton.  ltl3dra 0.2.3 fixes that but introduces another
+# bug where 'ltl3dra -f "!(a <-> Fb)" rejects cycle{!a & b}.
+#
+# # The -H1 option will output alternating automata, so this tests
+# # ltlcross's support in this area.
+# randltl -n 30 2 |
+# ltlcross 'ltl3dra -H1' 'ltl3dra -H2' 'ltl3dra -H3' \
+#          --ignore-execution-failures --ambiguous \
+#          --strength --csv=output.csv
+#
+# # Make sure all lines in output.csv have the same number of comas
+# sed 's/[^,]//g' <output.csv |
+# ( read first
+# while read l; do
+#   test "x$first" = "x$l" || exit 1
+# done)