Analysing and Comparing Encodability Criteria

TL;DR

This paper provides a formal framework for analyzing and comparing encodability criteria in process calculi by relating them to relations between source and target processes, clarifying their roles and differences.

Contribution

It introduces a formal method to reason about and compare various encodability criteria through relations induced by encodings, unifying their analysis.

Findings

Formal mapping of criteria to process relations

Analysis of simulation relations like bisimulation and coupled simulation

Clarification of criteria applicability across different settings

Abstract

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.