Abstract
We present Stamina, a tool solving three algorithmic problems in automata theory. First, compute the star height of a regular language, i.e. the minimal number of nested Kleene stars needed for expressing the language with a complement-free regular expression. Second, decide limitedness for regular cost functions. Third, decide whether a probabilistic leaktight automaton has value 1, i.e. whether a probabilistic leaktight automaton accepts words with probability arbitrarily close to 1.
All three problems reduce to the computation of the stabilisation monoid associated with an automaton, which is computationally challenging because the monoid is exponentially larger than the automaton. The compact data structures used in Stamina, together with optimisations and heuristics, allow us to handle automata with several hundreds of states. This radically improves upon the performances of ACME, a similar tool solving a subset of these problems.
The tool Stamina is open source and available from Github, details are given on the webpage http://stamina.labri.fr.
This work was supported by The Alan Turing Institute under the EPSRC grant EP/N510129/1. H. Gimbert and E. Kelmendi are supported by the French ANR project “Stoch-MC” and “LaBEX CPU” of Université de Bordeaux. This work has been partly funded by the grant Palse Impulsion.
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References
Colcombet, T., Kuperberg, D., Löding, C., Vanden Boom, M.: Deciding the weak definability of Büchi definable tree languages. In: CSL, pp. 215–230 (2013)
Colcombet, T., Löding, C.: The nesting-depth of disjunctive \(\rm \mu \)-calculus for tree languages and the limitedness problem. In: CSL, pp. 416–430 (2008)
Colcombet, T., Löding, C.: The non-deterministic Mostowski hierarchy and distance-parity automata. In: Aceto, L., Damgård, I., Goldberg, L.A., Halldórsson, M.M., Ingólfsdóttir, A., Walukiewicz, I. (eds.) ICALP 2008. LNCS, vol. 5126, pp. 398–409. Springer, Heidelberg (2008). doi:10.1007/978-3-540-70583-3_33
Cohen, R.S.: Star height of certain families of regular events. J. Comput. Syst. Sci. 4(3), 281–297 (1970)
Colcombet, T.: The theory of stabilisation monoids and regular cost functions. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009. LNCS, vol. 5556, pp. 139–150. Springer, Heidelberg (2009). doi:10.1007/978-3-642-02930-1_12
Colcombet, T.: Regular cost-functions Part I: logic and algebra over words. Logical Meth. Comput. Sci. 9(3), 1–47 (2013)
Eggan, L.C.: Transition graphs and the star-height of regular events. Mich. Math. J. 10, 385–397 (1963)
Fijalkow, N., Gimbert, H., Kelmendi, E., Oualhadj, Y.: Deciding the value 1 problem for probabilistic leaktight automata. Logical Meth. Comput. Sci. 11(1) (2015). http://www.lmcs-online.org/ojs/viewarticle.php?id=1588
Fijalkow, N., Gimbert, H., Oualhadj, Y.: Deciding the value 1 problem for probabilistic leaktight automata. In: LICS, pp. 295–304 (2012)
Fijalkow, N., Kuperberg, A.D.: Automata with counters, monoids and equivalence. In: ATVA, pp. 163–167 (2014)
Hashiguchi, K.: Algorithms for determining relative star height and star height. Inf. Comput. 78(2), 124–169 (1988)
Kirsten, D.: Distance desert automata and the star height problem. Theor. Inf. Appl. 39(3), 455–509 (2005)
Lombardy, S., Sakarovitch, J.: Star height of reversible languages and universal automata. In: Rajsbaum, S. (ed.) LATIN 2002. LNCS, vol. 2286, pp. 76–90. Springer, Heidelberg (2002). doi:10.1007/3-540-45995-2_12
Rabin, M.O.: Probabilistic automata. Inf. Control 6(3), 230–245 (1963)
Simon, I.: On semigroups of matrices over the tropical semiring. Theor. Inf. Appl. 28(3–4), 277–294 (1994)
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Fijalkow, N., Gimbert, H., Kelmendi, E., Kuperberg, D. (2017). Stamina: Stabilisation Monoids in Automata Theory. In: Carayol, A., Nicaud, C. (eds) Implementation and Application of Automata. CIAA 2017. Lecture Notes in Computer Science(), vol 10329. Springer, Cham. https://doi.org/10.1007/978-3-319-60134-2_9
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