Long-Run Average Behaviour of Probabilistic Vector Addition
Systems

D 2015

Long-Run Average Behaviour of Probabilistic Vector Addition Systems

BRÁZDIL, Tomáš, Stefan KIEFER, Antonín KUČERA and Petr NOVOTNÝ

Basic information

Original name

Long-Run Average Behaviour of Probabilistic Vector Addition Systems

Authors

BRÁZDIL, Tomáš (203 Czech Republic, belonging to the institution), Stefan KIEFER (276 Germany), Antonín KUČERA (203 Czech Republic, guarantor, belonging to the institution) and Petr NOVOTNÝ (203 Czech Republic, belonging to the institution)

Edition

Neuveden, 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015. p. 44-55, 12 pp. 2015

Publisher

IEEE

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

United States of America

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

RIV identification code

RIV/00216224:14330/15:00081425

Organization unit

Faculty of Informatics

ISBN

978-1-4799-8875-4

ISSN

DOI

http://dx.doi.org/10.1109/LICS.2015.15

UT WoS

000380427100007

Keywords in English

Probabilistic Vector Addition Systems; Markov Chains

Abstract

V originále

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.

Links

GA15-17564S, research and development project

Name: Teorie her jako prostředek pro formální analýzu a verifikaci počítačových systémů

Investor: Czech Science Foundation

MUNI/A/1159/2014, interní kód MU

Name: Rozsáhlé výpočetní systémy: modely, aplikace a verifikace IV.

Investor: Masaryk University, Category A

Citovat

BRÁZDIL, Tomáš, Stefan KIEFER, Antonín KUČERA and Petr NOVOTNÝ. Long-Run Average Behaviour of Probabilistic Vector Addition Systems. In Neuveden. 30th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2015, Kyoto, Japan, July 6-10, 2015. Neuveden: IEEE, 2015, p. 44-55. ISBN 978-1-4799-8875-4. Available from: https://dx.doi.org/10.1109/LICS.2015.15.

@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 and 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, 2015, p.~44-55. ISBN~978-1-4799-8875-4. Available from: https://dx.doi.org/10.1109/LICS.2015.15.

Detailed Information on Publication Record