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Probabilistic Operational Correspondence

Authors Anna Schmitt , Kirstin Peters

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Author Details

Anna Schmitt
  • TU Darmstadt, Germany
Kirstin Peters
  • Augsburg University, Germany

Acknowledgements

We thank the anonymous reviewers of a preliminary version of this paper for their comments and hints.

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Anna Schmitt and Kirstin Peters. Probabilistic Operational Correspondence. In 34th International Conference on Concurrency Theory (CONCUR 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 279, pp. 15:1-15:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.CONCUR.2023.15

Abstract

Encodings are the main way to compare process calculi. By applying quality criteria to encodings we analyse their quality and rule out trivial or meaningless encodings. Thereby, operational correspondence is one of the most common and most important quality criteria. It ensures that processes and their translations have the same abstract behaviour. We analyse probabilistic versions of operational correspondence to enable such a verification for probabilistic systems.
Concretely, we present three versions of probabilistic operational correspondence: weak, middle, and strong. We show the relevance of the weaker version using an encoding from a sublanguage of probabilistic CCS into the probabilistic π-calculus. Moreover, we map this version of probabilistic operational correspondence onto a probabilistic behavioural relation that directly relates source and target terms. Then we can analyse the quality of the criterion by analysing the relation it induces between a source term and its translation. For the second version of probabilistic operational correspondence we proceed in the opposite direction. We start with a standard simulation relation for probabilistic systems and map it onto a probabilistic operational correspondence criterion.

Subject Classification

ACM Subject Classification
  • Theory of computation → Process calculi
Keywords
  • Probabilistic Process Calculi
  • Encodings
  • Operational Correspondence

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