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A Spectrum of Approximate Probabilistic Bisimulations

Authors Timm Spork , Christel Baier , Joost-Pieter Katoen , Jakob Piribauer , Tim Quatmann

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ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Random walks and Markov chains
Keywords
  • Markov chains
  • Approximate bisimulation
  • Abstraction
  • Model checking

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Abstract

This paper studies various notions of approximate probabilistic bisimulation on labeled Markov chains (LMCs). We introduce approximate versions of weak and branching bisimulation, as well as a notion of ε-perturbed bisimulation that relates LMCs that can be made (exactly) probabilistically bisimilar by small perturbations of their transition probabilities. We explore how the notions interrelate and establish their connections to other well-known notions like ε-bisimulation.

Cite As Get BibTex

Timm Spork, Christel Baier, Joost-Pieter Katoen, Jakob Piribauer, and Tim Quatmann. A Spectrum of Approximate Probabilistic Bisimulations. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 37:1-37:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.CONCUR.2024.37

Author Details

Timm Spork
  • Technische Universität Dresden, Dresden, Germany
Christel Baier
  • Technische Universität Dresden, Dresden, Germany
Joost-Pieter Katoen
  • RWTH Aachen University, Aachen, Germany
Jakob Piribauer
  • Technische Universität Dresden, Dresden, Germany
  • Universität Leipzig, Leipzig, Germany
Tim Quatmann
  • RWTH Aachen University, Aachen, Germany

Funding

Christel Baier, Jakob Piribauer and Timm Spork: This work was partly funded by the DFG Grant 389792660 as part of TRR 248 (Foundations of Perspicuous Software Systems) and the Cluster of Excellence EXC 2050/1 (CeTI, project ID 390696704, as part of Germany’s Excellence Strategy).
  • Quatmann, Tim: This research was funded by a KI-Starter grant from the Ministerium für Kultur und Wissenschaft NRW.

Acknowledgements

We thank the reviewers for their helpful feedback, comments and suggestions. In particular, we thank the reviewer who pointed out the work in [Haesaert et al., 2021; Haesaert and Soudjani, 2021] on approximate simulation relations which we were previously not aware of.

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