Encoding CSP into CCS

We study encodings from CSP into asynchronous CCS with name passing and matching, so in fact, the asynchronous pi-calculus. By doing so, we discuss two different ways to map the multi-way synchronisation mechanism of CSP into the two-way synchronisation mechanism of CCS. Both encodings satisfy the criteria of Gorla except for compositionality, as both use an additional top-level context. Following the work of Parrow and Sj\"odin, the first encoding uses a centralised coordinator and establishes a variant of weak bisimilarity between source terms and their translations. The second encoding is decentralised, and thus more efficient, but ensures only a form of coupled similarity between source terms and their translations.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.0634

Analysing and Comparing Encodability Criteria

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with quality criteria. There exists a bunch of different criteria and different variants of criteria in order to reason in different settings. This leads to incomparable results. Moreover it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. We show how to formally reason about and compare encodability criteria by mapping them on requirements on a relation between source and target terms that is induced by the encoding function. In particular we analyse the common criteria full abstraction, operational correspondence, divergence reflection, success sensitiveness, and respect of barbs; e.g. we analyse the exact nature of the simulation relation (coupled simulation versus bisimulation) that is induced by different variants of operational correspondence. This way we reduce the problem of analysing or comparing encodability criteria to the better understood problem of comparing relations on processes.Comment: In Proceedings EXPRESS/SOS 2015, arXiv:1508.06347. The Isabelle/HOL source files, and a full proof document, are available in the Archive of Formal Proofs, at http://afp.sourceforge.net/entries/Encodability_Process_Calculi.shtm

Probabilistic Operational Correspondence

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 ?-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

Comparing Process Calculi Using Encodings

Encodings or the proof of their absence are the main way to compare process calculi. To analyse the quality of encodings and to rule out trivial or meaningless encodings, they are augmented with encodability criteria. There exists a bunch of different criteria and different variants of criteria in order to reason in different settings. This leads to incomparable results. Moreover, it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. This paper provides a short survey on often used encodability criteria, general frameworks that try to provide a unified notion of the quality of an encoding, and methods to analyse and compare encodability criteria.Comment: In Proceedings EXPRESS/SOS 2019, arXiv:1908.0821