Abstract
We consider probabilistic automata over finite words. Such an automaton defines the language consisting of the set of words accepted with probability greater than a given threshold. We show the existence of a universally non-regular probabilistic automaton, i.e. an automaton such that the language it defines is non-regular for every threshold. As a corollary, we obtain an alternative and very simple proof of the undecidability of determining whether such a language is regular.
The Research Leading to These Results Has Received Funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) Under Grant Agreement 259454 (GALE).
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Fijalkow, N., Skrzypczak, M. (2015). Irregular Behaviours for Probabilistic Automata. In: Bojanczyk, M., Lasota, S., Potapov, I. (eds) Reachability Problems. RP 2015. Lecture Notes in Computer Science(), vol 9328. Springer, Cham. https://doi.org/10.1007/978-3-319-24537-9_4
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DOI: https://doi.org/10.1007/978-3-319-24537-9_4
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