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Probabilistic Bisimulation: Naturally on Distributions

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CONCUR 2014 – Concurrency Theory (CONCUR 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8704))

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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.

This work is supported by the EU 7th Framework Programme under grant agreements 295261 (MEALS) and 318490 (SENSATION), European Research Council (ERC) under grant agreement 267989 (QUAREM), Austrian Science Fund (FWF) project S11402-N23 (RiSE), 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. Jan Křetínský is currently on leave from Faculty of Informatics, Masaryk University, Czech Republic.

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Authors and Affiliations

  1. Saarland University – Computer Science, Saarbrücken, Germany

    Holger Hermanns & Jan Krčál

  2. IST, Austria

    Jan Křetínský

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  1. Holger Hermanns
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  2. Jan Krčál
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Editors and Affiliations

  1. Department of Mathematics, University of Padova, Via Trieste, 63, 35121, Padova, Italy

    Paolo Baldan

  2. Department of Computer Science, University of Roma “La Sapienza”, Via Salaria, 113, 00198, Rome, Italy

    Daniele Gorla

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Hermanns, H., Krčál, J., Křetínský, J. (2014). Probabilistic Bisimulation: Naturally on Distributions. In: Baldan, P., Gorla, D. (eds) CONCUR 2014 – Concurrency Theory. CONCUR 2014. Lecture Notes in Computer Science, vol 8704. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44584-6_18

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  • DOI: https://doi.org/10.1007/978-3-662-44584-6_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44583-9

  • Online ISBN: 978-3-662-44584-6

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