Analysing and Comparing Encodability Criteria for Process Calculi

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 for reduction semantics; e.g. we analyse the exact nature of the simulation relation (coupled simulation versus bisimulation) that is induced by different variants of operational correspondence. Additionally, we analyse divergence reflection and operational correspondence for labelled semantics. This way we reduce the problem of analysing or comparing encodability criteria to the better understood problem of comparing relations on processes.