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Long-Run Average Behaviour of Probabilistic Vector Addition Systems

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BRÁZDIL Tomáš KIEFER Stefan KUČERA Antonín NOVOTNÝ Petr

Druh Článek ve sborníku
Konference 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015.
Fakulta / Pracoviště MU

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Citace
Doi http://dx.doi.org/10.1109/LICS.2015.15
Obor Informatika
Klíčová slova Probabilistic Vector Addition Systems; Markov Chains
Popis We study the pattern frequency vector for runs in probabilistic Vector Addition Systems with States (pVASS). Intuitively, each configuration of a given pVASS is assigned one of finitely many \emph{patterns}, and every run can thus be seen as an infinite sequence of these patterns. The pattern frequency vector assigns to each run the limit of pattern frequencies computed for longer and longer prefixes of the run. If the limit does not exist, then the vector is undefined. We show that for one-counter pVASS, the pattern frequency vector is defined and takes one of finitely many values for almost all runs. Further, these values and their associated probabilities can be approximated up to an arbitrarily small relative error in polynomial time. For stable two-counter pVASS, we show the same result, but we do not provide any upper complexity bound. As a byproduct of our study, we discover counterexamples falsifying some classical results about stochastic Petri nets published in the 80s.
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