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.
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Alexandre Duret-Lutz
parent
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8 changed files with 106 additions and 18 deletions
2
NEWS
2
NEWS
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@ -13,7 +13,7 @@ New in spot 2.3.3.dev (not yet released)
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- genaut is a binary to produce families of automata defined in the
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literature (in the same way as we have genltl for LTL formulas).
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It currently features only one class of automata.
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It currently features only two classes of automata.
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Library:
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@ -53,6 +53,9 @@ static const argp_option options[] =
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{ "ks-cobuchi", gen::AUT_KS_COBUCHI, "RANGE", 0,
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"A co-Büchi automaton with 2N+1 states for which any equivalent "
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"deterministic co-Büchi automaton has at least 2^N/(2N+1) states.", 0},
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{ "l-nba", gen::AUT_L_NBA, "RANGE", 0,
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"A Büchi automaton with 3N+1 states whose complementary Streett "
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"automaton needs at least n! states.", 0},
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RANGE_DOC,
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/**************************************************/
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{ nullptr, 0, nullptr, 0, "Miscellaneous options:", -1 },
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@ -7,7 +7,11 @@ Prefixes used in pattern names refer to the following papers:
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.TP
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ks
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D. Kuperberg, M. Skrzypczak: On Determinisation of Good-for-Games
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Automata. Proceddings of ICALP'15.
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Automata. Proceedings of ICALP'15.
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.TP
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l
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C. Löding: Optimal Bounds for Transformations of ω-Automata.
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Proceedings of FSTTCS'99.
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[SEE ALSO]
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.BR autfilt (1),
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@ -17,6 +17,9 @@ genaut --help | sed -n '/Pattern selection:/,/^$/p' | sed '1d;$d'
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: --ks-cobuchi=RANGE A co-Büchi automaton with 2N+1 states for which
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: any equivalent deterministic co-Büchi automaton
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: has at least 2^N/(2N+1) states.
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: --l-nba=RANGE A Büchi automaton with 3N+1 states whose
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: complementary Streett automaton needs at least n!
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: states.
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By default, the output format is [[file:hoa.org][HOA]], but this can be controlled using
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@ -88,6 +88,39 @@ namespace spot
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aut->prop_state_acc(true);
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return aut;
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}
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static twa_graph_ptr
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l_nba(unsigned n, bdd_dict_ptr dict)
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{
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if (n == 0)
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throw std::runtime_error("l_nba expects a positive argument");
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auto aut = make_twa_graph(dict);
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bdd p1 = bdd_ithvar(aut->register_ap("a"));
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bdd p2 = bdd_ithvar(aut->register_ap("b"));
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bdd a = p1 - p2;
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bdd b = p2 - p1;
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bdd s = p1 & p2;
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bdd all = p1 | p2;
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aut->new_states(3 * n + 1);
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aut->set_init_state(1);
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aut->set_buchi();
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aut->prop_state_acc(true);
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aut->new_acc_edge(0, n + 1, a);
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aut->new_edge(2 * n + 1, 0, b);
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for (unsigned s = 1; s <= n; ++s)
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{
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aut->new_edge(s + n, std::min(s + n + 1, 2 * n), a);
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aut->new_edge(s + n, s, b);
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aut->new_edge(s, s, all);
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aut->new_edge(s, s + 2 * n, a);
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aut->new_edge(std::min(s + 2 * n + 1, 3 * n), s + 2 * n, a);
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}
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return aut;
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}
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}
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twa_graph_ptr aut_pattern(aut_pattern_id pattern, int n, bdd_dict_ptr dict)
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@ -105,6 +138,8 @@ namespace spot
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// Keep this alphabetically-ordered!
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case AUT_KS_COBUCHI:
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return ks_cobuchi(n, dict);
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case AUT_L_NBA:
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return l_nba(n, dict);
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case AUT_END:
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break;
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}
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@ -116,6 +151,7 @@ namespace spot
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static const char* const class_name[] =
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{
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"ks-cobuchi",
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"l-nba",
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};
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// Make sure we do not forget to update the above table every
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// time a new pattern is added.
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@ -31,23 +31,56 @@ namespace spot
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AUT_BEGIN = 256,
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/// \brief A family of co-Büchi automata.
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///
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/// ks_cobuchi(n) is a co-Büchi automaton of size 2n+1 that is
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/// good-for-games and that has no equivalent deterministic co-Büchi
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/// automaton with less than 2^n / (2n+1) states.
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/// For details and other classes, see:
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///
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/// @InProceedings{kuperberg2015determinisation,
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/// author={Kuperberg, Denis and Skrzypczak, Micha{\l}},
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/// title={On Determinisation of Good-for-Games Automata},
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/// booktitle={International Colloquium on Automata, Languages, and
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/// Programming},
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/// pages={299--310},
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/// year={2015},
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/// organization={Springer}
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/// }
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/// Builds a co-Büchi automaton of size 2n+1 that is
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/// good-for-games and that has no equivalent deterministic
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/// co-Büchi automaton with less than 2^n / (2n+1) states.
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///
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/// Only defined for n>0
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///
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/** \verbatim
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@InProceedings{ kuperberg.15.icalp,
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author = {Denis Kuperberg and Micha{\l} Skrzypczak },
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title = {On Determinisation of Good-for-Games Automata},
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booktitle = {Proceedings of the 42nd International Colloquium on
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Automata, Languages, and Programming (ICALP'15)},
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pages = {299--310},
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year = {2015},
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publisher = {Springer},
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series = {Lecture Notes in Computer Science},
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volume = 9135,
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doi = {10.1007/978-3-662-47666-6_24}
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}
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\endverbatim */
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AUT_KS_COBUCHI = AUT_BEGIN,
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/// \brief Hard-to-complement non-deterministic Büchi automata
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///
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/// Build a non-deterministic Büchi automaton with 3n+1 states
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/// and whose complementary language requires an automaton with
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/// at least n! states if Streett acceptance is used.
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///
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/// Only defined for n>0. The automaton constructed corresponds
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/// to the right part of Fig.1 in the following paper, except
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/// that only state q_1 is initial. (The fact that states q_2,
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/// q_3, ..., and q_n are not initial as in the paper does not
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/// change the recognized language.)
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///
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/** \verbatim
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@InProceedings{loding.99.fstts,
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author = {Christof L{\"o}ding},
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title = {Optimal Bounds for Transformations of
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$\omega$-Automata},
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booktitle = {Proceedings of the 19th Conference on Foundations of
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Software Technology and Theoretical Computer Science
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(FSTTCS'99)},
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year = 1999,
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publisher = {Springer},
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pages = {97--109},
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series = {Lecture Notes in Computer Science},
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volume = 1738,
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doi = {10.1007/3-540-46691-6_8}
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}
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\endverbatim */
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AUT_L_NBA,
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AUT_END
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};
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@ -29,13 +29,18 @@ s/[=[].*/=1/p
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res=`genaut $opts --stats="--%F=%L"`
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test "$opts" = "$res"
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genaut --ks-cobuchi=..3 --stats=%s,%e,%t,%c,%g >out
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genaut --ks-cobuchi=..3 --l-nba=..3 --stats=%s,%e,%t,%c,%g >out
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cat >expected <<EOF
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3,7,16,1,Fin(0)
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5,14,32,1,Fin(0)
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7,20,48,1,Fin(0)
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4,7,9,1,Inf(0)
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7,12,16,1,Inf(0)
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10,17,23,1,Inf(0)
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EOF
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diff out expected
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genaut --ks-cobuchi=0 2>err && exit 1
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grep positive err
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genaut --l-nba=0 2>err && exit 1
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grep positive err
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@ -31,7 +31,7 @@ assert k2.num_states() == 5
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# the type returned by spot.gen.ks_cobuchi() is the correct one.
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assert 'to_str' in dir(k2)
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k3 = gen.aut_pattern(gen.AUT_KS_COBUCHI, 3)
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k3 = gen.aut_pattern(gen.AUT_L_NBA, 3)
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assert k2.get_dict() == k3.get_dict()
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try:
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@ -63,3 +63,7 @@ else:
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assert 40 == sum(p.size() for p in gen.ltl_patterns((gen.LTL_OR_G, 1, 5),
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(gen.LTL_GH_Q, 3),
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gen.LTL_EH_PATTERNS))
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assert 32 == sum(p.num_states()
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for p in gen.aut_patterns((gen.AUT_L_NBA, 1, 3),
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(gen.AUT_KS_COBUCHI, 5)))
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