Probabilistic bisimulation: Naturally on distributions

H. Hermanns, J. Krčál, J. Kretinsky, in:, P. Baldan, D. Gorla (Eds.), Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014, pp. 249–265.


Conference Paper | Published | English
Author
Hermanns, Holger; Krčál, Jan; Kretinsky, JanIST Austria
Editor
Baldan, Paolo; Gorla, Daniele
Series Title
LNCS
Abstract
In contrast to the usual understanding of probabilistic systems as stochastic processes, recently these systems have also been regarded as transformers of probabilities. In this paper, we give a natural definition of strong bisimulation for probabilistic systems corresponding to this view that treats probability distributions as first-class citizens. Our definition applies in the same way to discrete systems as well as to systems with uncountable state and action spaces. Several examples demonstrate that our definition refines the understanding of behavioural equivalences of probabilistic systems. In particular, it solves a longstanding open problem concerning the representation of memoryless continuous time by memoryfull continuous time. Finally, we give algorithms for computing this bisimulation not only for finite but also for classes of uncountably infinite systems.
Publishing Year
Date Published
2014-09-01
Proceedings Title
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Acknowledgement
This work is supported by the EU 7th Framework Programme under grant agreements 295261 (MEALS) and 318490 (SENSATION), Czech Science Foundation under grant agreement P202/12/G061, the DFG Transregional Collaborative Research Centre SFB/TR 14 AVACS, and by the CAS/SAFEA International Partnership Program for Creative Research Teams.
Volume
8704
Page
249 - 265
Conference
CONCUR: Concurrency Theory
Conference Location
Rome, Italy
Conference Date
2014-09-02 – 2014-09-05
IST-REx-ID

Cite this

Hermanns H, Krčál J, Kretinsky J. Probabilistic bisimulation: Naturally on distributions. In: Baldan P, Gorla D, eds. Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Vol 8704. Schloss Dagstuhl - Leibniz-Zentrum für Informatik; 2014:249-265. doi:10.1007/978-3-662-44584-6_18
Hermanns, H., Krčál, J., & Kretinsky, J. (2014). Probabilistic bisimulation: Naturally on distributions. In P. Baldan & D. Gorla (Eds.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 8704, pp. 249–265). Rome, Italy: Schloss Dagstuhl - Leibniz-Zentrum für Informatik. https://doi.org/10.1007/978-3-662-44584-6_18
Hermanns, Holger, Jan Krčál, and Jan Kretinsky. “Probabilistic Bisimulation: Naturally on Distributions.” In Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), edited by Paolo Baldan and Daniele Gorla, 8704:249–65. Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014. https://doi.org/10.1007/978-3-662-44584-6_18.
H. Hermanns, J. Krčál, and J. Kretinsky, “Probabilistic bisimulation: Naturally on distributions,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), Rome, Italy, 2014, vol. 8704, pp. 249–265.
Hermanns H, Krčál J, Kretinsky J. 2014. Probabilistic bisimulation: Naturally on distributions. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). CONCUR: Concurrency Theory, LNCS, vol. 8704. 249–265.
Hermanns, Holger, et al. “Probabilistic Bisimulation: Naturally on Distributions.” Lecture Notes in Computer Science (Including Subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), edited by Paolo Baldan and Daniele Gorla, vol. 8704, Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 2014, pp. 249–65, doi:10.1007/978-3-662-44584-6_18.
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