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On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS

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Fundamentals of Computation Theory (FCT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9210))

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Abstract

We present recent results about the long-run average properties of probabilistic vector additions systems with states (pVASS). Interestingly, for probabilistic pVASS with two or more counters, long-run average properties may take several different values with positive probability even if the underlying state space is strongly connected. This contradicts the previous results about stochastic Petri nets established in 80s. For pVASS with three or more counters, it may even happen that the long-run average properties are undefined (i.e., the corresponding limits do not exist) for almost all runs, and this phenomenon is stable under small perturbations in transition probabilities. On the other hand, one can effectively approximate eligible values of long-run average properties and the corresponding probabilities for some sublasses of pVASS. These results are based on new exponential tail bounds achieved by designing and analyzing appropriate martingales. The paper focuses on explaining the main underlying ideas.

A. Kučera—Based on a joint work with Tomáš Brázdil, Joost-Pieter Katoen, Stefan Kiefer, and Petr Novotný. The author is supported by the Czech Science Foundation, grant No. 15-17564S.

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Antonín Kučera

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  1. Antonín Kučera
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Correspondence to Antonín Kučera .

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Editors and Affiliations

  1. Université Paris Diderot, Paris, France

    Adrian Kosowski

  2. Université Bordeaux 1, Talence, France

    Igor Walukiewicz

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Kučera, A. (2015). On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS. In: Kosowski, A., Walukiewicz, I. (eds) Fundamentals of Computation Theory. FCT 2015. Lecture Notes in Computer Science(), vol 9210. Springer, Cham. https://doi.org/10.1007/978-3-319-22177-9_2

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  • DOI: https://doi.org/10.1007/978-3-319-22177-9_2

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-22176-2

  • Online ISBN: 978-3-319-22177-9

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