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.
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Alexandre Duret-Lutz
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6 changed files with 205 additions and 51 deletions
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@ -9,19 +9,22 @@ translators. It is actually a Spot-based clone of [[http://www.tcs.hut.fi/Softw
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/LTL-to-Büchi Translator Testbench/, that essentially performs the
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same sanity checks.
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The main differences are:
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- support for PSL formulas in addition to LTL
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- more statistics, especially:
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The main differences with LBTT are:
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- *support for PSL formulas in addition to LTL*
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- support for (non-alternating) automata with *any type of acceptance condition*,
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- support for *weak alternating automata*,
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- additional intersection *checks with the complement*, allowing
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to check equivalence of automata more precisely,
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- *more statistics*, especially:
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- the number of logical transitions represented by each physical edge,
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- the number of deterministic states and automata
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- the number of SCCs with their various strengths (nonaccepting, terminal, weak, strong)
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- the number of terminal, weak, and strong automata
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- statistics output in a format that can be more easily be post-processed,
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- more precise time measurement (LBTT was only precise to
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1/100 of a second, reporting most times as "0.00s"),
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- support for any type of acceptance condition,
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- additional intersection checks with the complement, allowing
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to check equivalence of automata more precisely.
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- an option to *reduce counterexample* by attempting to mutate and
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shorten troublesome formulas,
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- statistics output in *CSV* for easier post-processing,
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- *more precise time measurement* (LBTT was only precise to
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1/100 of a second, reporting most times as "0.00s").
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Although =ltlcross= performs the same sanity checks as LBTT, it does
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not implement any of the interactive features of LBTT. In our almost
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@ -120,6 +123,7 @@ be rewritten using the other supported operators.
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--lbtt=.
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- Non-alternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]] with any acceptance
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condition.
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- [[file:concepts.org::#property-flags][Weak]] alternating automata in [[file:http://adl.github.io/hoaf/][the HOA format]].
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- [[http://www.ltl2dstar.de/docs/ltl2dstar.html][=ltl2dstar='s format]], which supports deterministic Rabin or Streett
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automata.
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@ -496,7 +500,9 @@ This classification is used to fill the =terminal_aut=, =weak_aut=,
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=--strength= is passed). Only one of these should contain =1=. We
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usually prefer terminal automata over weak automata, and weak automata
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over strong automata, because the emptiness check of terminal (and
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weak) automata is easier.
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weak) automata is easier. When working with alternating automata, all
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those strength-related columns will be empty, because the routines
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used to compute those statistic do not yet support universal edges.
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=nondetstates= counts the number of non-deterministic states in the
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automaton. =nondeterministic= is a Boolean value indicating if the
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@ -509,7 +515,8 @@ assignment $ab$) and is therefore not deterministic.
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If option =--aumbiguous= was passed to =ltlcross=, the column
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=ambiguous_aut= holds a Boolean indicating whether the automaton is
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ambiguous, i.e., if there exists a word that can be accepted by at
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least two different runs.
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least two different runs. (This information is not yet available for
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alternating automata.)
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=complete_aut= is a Boolean indicating whether the automaton is
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complete.
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@ -962,30 +969,40 @@ The verbose option can be useful to troubleshoot problems or simply
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follow the list of transformations and tests performed by =ltlcross=.
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For instance here is what happens if we try to cross check =ltl2tgba=
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and =ltl3ba= on the formula =FGa=.
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and =ltl3ba -H1= on the formula =FGa=. Note that =ltl2tgba= will
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produce transition-based generalized Büchi automata, while =ltl3ba
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-H1= produces co-Büchi alternating automata.
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#+BEGIN_SRC sh :results verbatim :exports code
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ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose
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ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --determinize --verbose
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#+END_SRC
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#+BEGIN_SRC sh :results verbatim :exports results
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ltlcross -f 'FGa' ltl2tgba ltl3ba --determinize --verbose 2>&1
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ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --determinize --verbose 2>&1
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#+END_SRC
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#+RESULTS:
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#+begin_example
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F(G(a))
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Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-vfVUzt'
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Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-IiXGfZ'
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Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-T02eWu'
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Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-0DpXF0'
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Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-Ak0bYx'
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Running [P1]: ltl3ba -H1 -f '<>([](a))'>'lcr-o1-5U1MyT'
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Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-sX2kaf'
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Running [N1]: ltl3ba -H1 -f '!(<>([](a)))'>'lcr-o1-4siKPA'
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info: collected automata:
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info: P0 (2 st.,3 ed.,1 sets)
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info: N0 (1 st.,2 ed.,1 sets) deterministic complete
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info: P1 (2 st.,3 ed.,1 sets)
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info: N1 (3 st.,5 ed.,1 sets) univ-edges deterministic complete
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Performing sanity checks and gathering statistics...
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info: getting rid of universal edges...
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info: N1 (3 st.,5 ed.,1 sets) -> (2 st.,4 ed.,1 sets)
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info: complementing non-deterministic automata via determinization...
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info: P0 (2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets) Comp(P0)
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info: P1 (2 st.,3 ed.,1 sets) -> (2 st.,4 ed.,2 sets) Comp(P1)
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info: getting rid of any Fin acceptance...
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info: Comp(P0) (2 st.,4 ed.,2 sets) -> (3 st.,7 ed.,2 sets)
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info: Comp(N0) (1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
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info: P1 (2 st.,3 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
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info: Comp(P1) (2 st.,4 ed.,2 sets) -> (4 st.,9 ed.,2 sets)
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info: Comp(N1) (2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
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info: check_empty P0*N0
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@ -999,10 +1016,19 @@ No problem detected.
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#+end_example
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First =FGa= and its negations =!FGa= are translated with the two
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tools, resulting in four automata: to positive automata =P0= and =P1=
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tools, resulting in four automata: two positive automata =P0= and =P1=
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for =FGa=, and two negative automata =N0= and =N1=.
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=ltlcross= then proceeds to compute the complement of these four
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Some basic information about the collected automata are displayed.
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For instance we can see that although =ltl3ba -H1= outputs co-Büchi
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alternating automata, only automaton =N1= uses universal edges: the
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automaton =P1= can be used like a non-alternating co-Büchi automaton.
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=ltlcross= then proceeds to transform alternating automata (only weak
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alternating automata are supported) into non-alternating automata.
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Here only =N1= needs this transformation.
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Then =ltlcross= computes the complement of these four
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automata. Since =P0= and =P1= are nondeterministic and the
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=--determinize= option was given, a first pass determinize and
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complete these two automata, creating =Comp(P0)= and =Comp(P1)=.
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@ -1030,23 +1056,31 @@ Note that if we had not used the =--determinize= option, the procedure
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would look slightly more complex:
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#+BEGIN_SRC sh :results verbatim :exports code
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ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose
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ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --verbose
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#+END_SRC
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#+BEGIN_SRC sh :results verbatim :exports results
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ltlcross -f 'FGa' ltl2tgba ltl3ba --verbose 2>&1
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ltlcross -f 'FGa' ltl2tgba 'ltl3ba -H1' --verbose 2>&1
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#+END_SRC
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#+RESULTS:
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#+begin_example
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F(G(a))
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Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-YvMdzU'
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Running [P1]: ltl3ba -f '<>([](a))'>'lcr-o1-Ixj7RI'
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Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-uBbTbx'
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Running [N1]: ltl3ba -f '!(<>([](a)))'>'lcr-o1-eo0fzl'
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Running [P0]: ltl2tgba -H 'F(G(a))'>'lcr-o0-jD32mW'
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Running [P1]: ltl3ba -H1 -f '<>([](a))'>'lcr-o1-w6IJYI'
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Running [N0]: ltl2tgba -H '!(F(G(a)))'>'lcr-o0-dac1Av'
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Running [N1]: ltl3ba -H1 -f '!(<>([](a)))'>'lcr-o1-OZL7fi'
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info: collected automata:
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info: P0 (2 st.,3 ed.,1 sets)
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info: N0 (1 st.,2 ed.,1 sets) deterministic complete
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info: P1 (2 st.,3 ed.,1 sets)
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info: N1 (3 st.,5 ed.,1 sets) univ-edges deterministic complete
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Performing sanity checks and gathering statistics...
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info: getting rid of universal edges...
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info: N1 (3 st.,5 ed.,1 sets) -> (2 st.,4 ed.,1 sets)
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info: getting rid of any Fin acceptance...
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info: Comp(N0) (1 st.,2 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
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info: P1 (2 st.,3 ed.,1 sets) -> (2 st.,3 ed.,1 sets)
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info: Comp(N1) (2 st.,4 ed.,1 sets) -> (3 st.,6 ed.,1 sets)
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info: check_empty P0*N0
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info: check_empty P0*N1
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