Analysing and Comparing Encodability Criteria

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.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

Comparing Process Calculi Using Encodings

“…in [45]) or explicitly distinguishes between source and target terms (as e.g. in [50]). Intuitively, it is required that the encoding respects the semantics of the source modulo the chosen relation.…”

“…Moreover it is not always clear whether the criteria used to obtain a result in a particular setting do indeed fit to this setting. A way to formally reason about and compare encodability criteria is presented in [50]. The main idea of this approach is to map encodability criteria on requirements on a relation between source and target terms that is induced by the encoding function.…”

“…According to [50] every encoding · : P S → P T induces a relation R · ⊆ (P S ⊎ P T ) 2 on the disjoint union of its source and target terms by relating source terms and their literal translations, i.e., (S, S ) ∈ R · for all S ∈ P S . Encodability criteria induce further properties on such relations.…”

“…By analysing the different kinds of such properties the semantic effect of an encodability criterion can be studied and different criteria can be compared in a model-independent and formal way. In order to completely capture the effect of a criterion, [50] aims at iff-results of the form · satisfies C iff there exists a relation R · such that ∀S. (S, S ) ∈ R · and P R · , where P is the condition that captures the effect of C. For example, an encoding reflects divergence iff there exists a relation R · such that ∀S.…”

On the Relative Expressiveness of Higher-Order Session Processes

“…A vast literature on expressiveness in concurrency theory also studies compilations (or encodings) [26,10,8,16,31]: they are used to transfer reasoning techniques across calculi, and to implement process constructs using simpler ones. In this work, we study relative expressiveness via type-preserving encodings for HOπ, a higher-order process language that integrates message-passing concurrency with functional features.…”