Probabilistic Operational Correspondence (Technical Report)

TL;DR

This paper extends the concept of operational correspondence to probabilistic process calculi, providing three variants and linking them to behavioral relations to assess encoding quality in probabilistic systems.

Contribution

It introduces three versions of probabilistic operational correspondence and connects them to behavioral relations for evaluating process encoding quality.

Findings

Relevance of weak probabilistic operational correspondence demonstrated.

Mapping of probabilistic operational correspondence to behavioral relations.

Technical proofs and additional material provided.

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 pi-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. This technical report contains the proofs to the lemmata and theorems of [8] as well as some additional material.