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Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions

Authors Matias David Lee, Erik P. de Vink



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Matias David Lee
Erik P. de Vink

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Matias David Lee and Erik P. de Vink. Logical Characterization of Bisimulation for Transition Relations over Probability Distributions with Internal Actions. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 29:1-29:14, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2016)
https://doi.org/10.4230/LIPIcs.MFCS.2016.29

Abstract

In recent years the study of probabilistic transition systems has shifted to transition relations over distributions to allow for a smooth adaptation of the standard non-probabilistic apparatus. In this paper we study transition relations over probability distributions in a setting with internal actions. We provide new logics that characterize probabilistic strong, weak and branching bisimulation. Because these semantics may be considered too strong in the probabilistic context, Eisentraut et al. recently proposed weak distribution bisimulation. To show the flexibility of our approach based on the framework of van Glabbeek for the non-deterministic setting, we provide a novel logical characterization for the latter probabilistic equivalence as well.
Keywords
  • probabilistic transition systems
  • weak bisimulations
  • logical characterization
  • transition relation over distributions
  • modal logics

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