Deciding fast termination for probabilistic VASS with nondeterminism

T. Brázdil, K. Chatterjee, A. Kucera, P. Novotný, D. Velan, in:, International Symposium on Automated Technology for Verification and Analysis, Springer Nature, 2019, pp. 462–478.


Conference Paper | Published | English
Author
; ; ; ;
Department
Series Title
LNCS
Abstract
A probabilistic vector addition system with states (pVASS) is a finite state Markov process augmented with non-negative integer counters that can be incremented or decremented during each state transition, blocking any behaviour that would cause a counter to decrease below zero. The pVASS can be used as abstractions of probabilistic programs with many decidable properties. The use of pVASS as abstractions requires the presence of nondeterminism in the model. In this paper, we develop techniques for checking fast termination of pVASS with nondeterminism. That is, for every initial configuration of size n, we consider the worst expected number of transitions needed to reach a configuration with some counter negative (the expected termination time). We show that the problem whether the asymptotic expected termination time is linear is decidable in polynomial time for a certain natural class of pVASS with nondeterminism. Furthermore, we show the following dichotomy: if the asymptotic expected termination time is not linear, then it is at least quadratic, i.e., in Ω(n2).
Publishing Year
Date Published
2019-10-21
Proceedings Title
International Symposium on Automated Technology for Verification and Analysis
Volume
11781
Page
462-478
Conference
ATVA: Automated TEchnology for Verification and Analysis
Conference Location
Taipei, Taiwan
Conference Date
2019-10-28 – 2019-10-31
ISSN
eISSN
IST-REx-ID

Cite this

Brázdil T, Chatterjee K, Kucera A, Novotný P, Velan D. Deciding fast termination for probabilistic VASS with nondeterminism. In: International Symposium on Automated Technology for Verification and Analysis. Vol 11781. Springer Nature; 2019:462-478. doi:10.1007/978-3-030-31784-3_27
Brázdil, T., Chatterjee, K., Kucera, A., Novotný, P., & Velan, D. (2019). Deciding fast termination for probabilistic VASS with nondeterminism. In International Symposium on Automated Technology for Verification and Analysis (Vol. 11781, pp. 462–478). Taipei, Taiwan: Springer Nature. https://doi.org/10.1007/978-3-030-31784-3_27
Brázdil, Tomás, Krishnendu Chatterjee, Antonín Kucera, Petr Novotný, and Dominik Velan. “Deciding Fast Termination for Probabilistic VASS with Nondeterminism.” In International Symposium on Automated Technology for Verification and Analysis, 11781:462–78. Springer Nature, 2019. https://doi.org/10.1007/978-3-030-31784-3_27.
T. Brázdil, K. Chatterjee, A. Kucera, P. Novotný, and D. Velan, “Deciding fast termination for probabilistic VASS with nondeterminism,” in International Symposium on Automated Technology for Verification and Analysis, Taipei, Taiwan, 2019, vol. 11781, pp. 462–478.
Brázdil T, Chatterjee K, Kucera A, Novotný P, Velan D. 2019. Deciding fast termination for probabilistic VASS with nondeterminism. International Symposium on Automated Technology for Verification and Analysis. ATVA: Automated TEchnology for Verification and Analysis, LNCS, vol. 11781. 462–478.
Brázdil, Tomás, et al. “Deciding Fast Termination for Probabilistic VASS with Nondeterminism.” International Symposium on Automated Technology for Verification and Analysis, vol. 11781, Springer Nature, 2019, pp. 462–78, doi:10.1007/978-3-030-31784-3_27.

Link(s) to Main File(s)
Access Level
OA Open Access

Export

Marked Publications

Open Data IST Research Explorer

Sources

arXiv 1907.11010

Search this title in

Google Scholar
ISBN Search