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@inproceedings{1323104,
author = {Brázdil, Tomáš and Kiefer, Stefan and Kučera, Antonín and Novotný, Petr},
address = {Neuveden},
booktitle = {30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015.},
doi = {http://dx.doi.org/10.1109/LICS.2015.15},
editor = {Neuveden},
keywords = {Probabilistic Vector Addition Systems; Markov Chains},
howpublished = {tištěná verze "print"},
language = {eng},
location = {Neuveden},
isbn = {978-1-4799-8875-4},
pages = {44-55},
publisher = {IEEE},
title = {Long-Run Average Behaviour of Probabilistic Vector Addition Systems},
year = {2015}
}
TY - JOUR
ID - 1323104
AU - Brázdil, Tomáš - Kiefer, Stefan - Kučera, Antonín - Novotný, Petr
PY - 2015
TI - Long-Run Average Behaviour of Probabilistic Vector Addition Systems
PB - IEEE
CY - Neuveden
SN - 9781479988754
KW - Probabilistic Vector Addition Systems
KW - Markov Chains
N2 - 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.
ER -
BRÁZDIL, Tomáš, Stefan KIEFER, Antonín KUČERA a Petr NOVOTNÝ. Long-Run Average Behaviour of Probabilistic Vector Addition Systems. In Neuveden. \textit{30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015.}. Neuveden: IEEE. s.~44-55. ISBN~978-1-4799-8875-4. doi:10.1109/LICS.2015.15. 2015.
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