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

D 2015

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

KUČERA, Antonín

Basic information

Original name

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

Authors

KUČERA, Antonín (203 Czech Republic, guarantor, belonging to the institution)

Edition

Heidelberg, Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings. p. 12-24, 13 pp. 2015

Publisher

Springer

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10201 Computer sciences, information science, bioinformatics

Country of publisher

Germany

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

printed version "print"

Impact factor

Impact factor: 0.402 in 2005

RIV identification code

RIV/00216224:14330/15:00081424

Organization unit

Faculty of Informatics

ISBN

978-3-319-22176-2

ISSN

DOI

http://dx.doi.org/10.1007/978-3-319-22177-9_2

Keywords in English

Vector Addition Systems; Markov chains

Abstract

V originále

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 contradics 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.

Links

GA15-17564S, research and development project

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

Investor: Czech Science Foundation

Citovat

KUČERA, Antonín. On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS. In Adrian Kosowski, Igor Walukiewicz. Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings. Heidelberg: Springer, 2015, p. 12-24. ISBN 978-3-319-22176-2. Available from: https://dx.doi.org/10.1007/978-3-319-22177-9_2.

@inproceedings{1323103,
   author = {Kučera, Antonín},
   address = {Heidelberg},
   booktitle = {Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Gdańsk, Poland, August 17-19, 2015, Proceedings.},
   doi = {http://dx.doi.org/10.1007/978-3-319-22177-9_2},
   editor = {Adrian Kosowski, Igor Walukiewicz},
   keywords = {Vector Addition Systems; Markov chains},
   howpublished = {tištěná verze "print"},
   language = {eng},
   location = {Heidelberg},
   isbn = {978-3-319-22176-2},
   pages = {12-24},
   publisher = {Springer},
   title = {On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS},
   year = {2015}
}

TY  - JOUR
ID  - 1323103
AU  - Kučera, Antonín
PY  - 2015
TI  - On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS
PB  - Springer
CY  - Heidelberg
SN  - 9783319221762
KW  - Vector Addition Systems
KW  - Markov chains
N2  - 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 contradics 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.
ER  -

KUČERA, Antonín. On the Existence and Computability of Long-Run Average Properties in Probabilistic VASS. In Adrian Kosowski, Igor Walukiewicz. \textit{Fundamentals of Computation Theory - 20th International Symposium, FCT 2015, Gda\'nsk, Poland, August 17-19, 2015, Proceedings.}. Heidelberg: Springer, 2015, p.~12-24. ISBN~978-3-319-22176-2. Available from: https://dx.doi.org/10.1007/978-3-319-22177-9\_{}2.

Detailed Information on Publication Record