gen: introduce a new automaton family

* spot/gen/automata.cc, spot/gen/automata.hh: Define AUT_L_NBA.
* bin/genaut.cc (--l-nba): New option.
* bin/man/genaut.x, doc/org/genaut.org, NEWS: Document it.
* tests/python/gen.py, tests/core/genaut.test: Test it.

NEWS

@@ -13,7 +13,7 @@ New in spot 2.3.3.dev (not yet released)
 
   - genaut is a binary to produce families of automata defined in the
     literature (in the same way as we have genltl for LTL formulas).
-    It currently features only one class of automata.
+    It currently features only two classes of automata.
 
   Library:
 

bin/genaut.cc

@@ -53,6 +53,9 @@ static const argp_option options[] =
     { "ks-cobuchi", gen::AUT_KS_COBUCHI, "RANGE", 0,
       "A co-Büchi automaton with 2N+1 states for which any equivalent "
       "deterministic co-Büchi automaton has at least 2^N/(2N+1) states.", 0},
+    { "l-nba", gen::AUT_L_NBA, "RANGE", 0,
+      "A Büchi automaton with 3N+1 states whose complementary Streett "
+      "automaton needs at least n! states.", 0},
     RANGE_DOC,
   /**************************************************/
     { nullptr, 0, nullptr, 0, "Miscellaneous options:", -1 },

bin/man/genaut.x

@@ -7,7 +7,11 @@ Prefixes used in pattern names refer to the following papers:
 .TP
 ks
 D. Kuperberg, M. Skrzypczak: On Determinisation of Good-for-Games
-Automata.  Proceddings of ICALP'15.
+Automata.  Proceedings of ICALP'15.
+.TP
+l
+C. Löding: Optimal Bounds for Transformations of ω-Automata.
+Proceedings of FSTTCS'99.
 
 [SEE ALSO]
 .BR autfilt (1),

doc/org/genaut.org

@@ -17,6 +17,9 @@ genaut --help | sed -n '/Pattern selection:/,/^$/p' | sed '1d;$d'
 :       --ks-cobuchi=RANGE     A co-Büchi automaton with 2N+1 states for which
 :                              any equivalent deterministic co-Büchi automaton
 :                              has at least 2^N/(2N+1) states.
+:       --l-nba=RANGE          A Büchi automaton with 3N+1 states whose
+:                              complementary Streett automaton needs at least n!
+:                              states.
 
 
 By default, the output format is [[file:hoa.org][HOA]], but this can be controlled using

spot/gen/automata.cc

@@ -88,6 +88,39 @@ namespace spot
         aut->prop_state_acc(true);
         return aut;
       }
+
+      static twa_graph_ptr
+      l_nba(unsigned n, bdd_dict_ptr dict)
+      {
+        if (n == 0)
+          throw std::runtime_error("l_nba expects a positive argument");
+
+        auto aut = make_twa_graph(dict);
+
+        bdd p1 = bdd_ithvar(aut->register_ap("a"));
+        bdd p2 = bdd_ithvar(aut->register_ap("b"));
+        bdd a = p1 - p2;
+        bdd b = p2 - p1;
+        bdd s = p1 & p2;
+        bdd all = p1 | p2;
+
+        aut->new_states(3 * n + 1);
+        aut->set_init_state(1);
+        aut->set_buchi();
+        aut->prop_state_acc(true);
+
+        aut->new_acc_edge(0, n + 1, a);
+        aut->new_edge(2 * n + 1, 0, b);
+        for (unsigned s = 1; s <= n; ++s)
+          {
+            aut->new_edge(s + n, std::min(s + n + 1, 2 * n), a);
+            aut->new_edge(s + n, s, b);
+            aut->new_edge(s, s, all);
+            aut->new_edge(s, s + 2 * n, a);
+            aut->new_edge(std::min(s + 2 * n + 1, 3 * n), s + 2 * n, a);
+          }
+        return aut;
+      }
     }
 
     twa_graph_ptr aut_pattern(aut_pattern_id pattern, int n, bdd_dict_ptr dict)
@@ -105,6 +138,8 @@ namespace spot
           // Keep this alphabetically-ordered!
         case AUT_KS_COBUCHI:
           return ks_cobuchi(n, dict);
+        case AUT_L_NBA:
+          return l_nba(n, dict);
         case AUT_END:
           break;
         }
@@ -116,6 +151,7 @@ namespace spot
       static const char* const class_name[] =
         {
           "ks-cobuchi",
+          "l-nba",
         };
       // Make sure we do not forget to update the above table every
       // time a new pattern is added.

spot/gen/automata.hh

@@ -31,23 +31,56 @@ namespace spot
       AUT_BEGIN = 256,
       /// \brief A family of co-Büchi automata.
       ///
-      /// ks_cobuchi(n) is a co-Büchi automaton of size 2n+1 that is
+      /// Builds a co-Büchi automaton of size 2n+1 that is
-      /// good-for-games and that has no equivalent deterministic co-Büchi
+      /// good-for-games and that has no equivalent deterministic
-      /// automaton with less than 2^n / (2n+1) states.
+      /// co-Büchi automaton with less than 2^n / (2n+1) states.
-      /// For details and other classes, see:
-      ///
-      /// @InProceedings{kuperberg2015determinisation,
-      ///     author={Kuperberg, Denis and Skrzypczak, Micha{\l}},
-      ///     title={On Determinisation of Good-for-Games Automata},
-      ///     booktitle={International Colloquium on Automata, Languages, and
-      ///                Programming},
-      ///     pages={299--310},
-      ///     year={2015},
-      ///     organization={Springer}
-      /// }
       ///
       /// Only defined for n>0
+      ///
+      /** \verbatim
+          @InProceedings{   kuperberg.15.icalp,
+            author        = {Denis Kuperberg and Micha{\l} Skrzypczak },
+            title         = {On Determinisation of Good-for-Games Automata},
+            booktitle     = {Proceedings of the 42nd International Colloquium on
+                            Automata, Languages, and Programming (ICALP'15)},
+            pages         = {299--310},
+            year          = {2015},
+            publisher     = {Springer},
+            series        = {Lecture Notes in Computer Science},
+            volume        = 9135,
+            doi           = {10.1007/978-3-662-47666-6_24}
+          }
+          \endverbatim */
       AUT_KS_COBUCHI = AUT_BEGIN,
+      /// \brief Hard-to-complement non-deterministic Büchi automata
+      ///
+      /// Build a non-deterministic Büchi automaton with 3n+1 states
+      /// and whose complementary language requires an automaton with
+      /// at least n! states if Streett acceptance is used.
+      ///
+      /// Only defined for n>0.  The automaton constructed corresponds
+      /// to the right part of Fig.1 in the following paper, except
+      /// that only state q_1 is initial.  (The fact that states q_2,
+      /// q_3, ..., and q_n are not initial as in the paper does not
+      /// change the recognized language.)
+      ///
+      /** \verbatim
+          @InProceedings{loding.99.fstts,
+            author	= {Christof L{\"o}ding},
+            title	= {Optimal Bounds for Transformations of
+                           $\omega$-Automata},
+            booktitle	= {Proceedings of the 19th Conference on Foundations of
+                           Software Technology and Theoretical Computer Science
+                           (FSTTCS'99)},
+            year        = 1999,
+            publisher	= {Springer},
+            pages       = {97--109},
+            series	= {Lecture Notes in Computer Science},
+            volume	= 1738,
+            doi		= {10.1007/3-540-46691-6_8}
+          }
+          \endverbatim */
+      AUT_L_NBA,
       AUT_END
     };
 

tests/core/genaut.test

@@ -29,13 +29,18 @@ s/[=[].*/=1/p
 res=`genaut $opts --stats="--%F=%L"`
 test "$opts" = "$res"
 
-genaut --ks-cobuchi=..3 --stats=%s,%e,%t,%c,%g >out
+genaut --ks-cobuchi=..3 --l-nba=..3 --stats=%s,%e,%t,%c,%g >out
 cat >expected <<EOF
 3,7,16,1,Fin(0)
 5,14,32,1,Fin(0)
 7,20,48,1,Fin(0)
+4,7,9,1,Inf(0)
+7,12,16,1,Inf(0)
+10,17,23,1,Inf(0)
 EOF
 diff out expected
 
 genaut --ks-cobuchi=0 2>err && exit 1
 grep positive err
+genaut --l-nba=0 2>err && exit 1
+grep positive err

tests/python/gen.py

@@ -31,7 +31,7 @@ assert k2.num_states() == 5
 # the type returned by spot.gen.ks_cobuchi() is the correct one.
 assert 'to_str' in dir(k2)
 
-k3 = gen.aut_pattern(gen.AUT_KS_COBUCHI, 3)
+k3 = gen.aut_pattern(gen.AUT_L_NBA, 3)
 assert k2.get_dict() == k3.get_dict()
 
 try:
@@ -63,3 +63,7 @@ else:
 assert 40 == sum(p.size() for p in gen.ltl_patterns((gen.LTL_OR_G, 1, 5),
                                                     (gen.LTL_GH_Q, 3),
                                                     gen.LTL_EH_PATTERNS))
+
+assert 32 == sum(p.num_states()
+                 for p in gen.aut_patterns((gen.AUT_L_NBA, 1, 3),
+                                           (gen.AUT_KS_COBUCHI, 5)))