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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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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