Separation of synchronous and asynchronous communication via testing

Abstract

International audienceOne of the early results about the asynchronous $\pi$-calculus which significantly contributed to its popularity is the capability of encoding the output prefix of the (choiceless) $\pi$-calculus in a natural and elegant way. Encodings of this kind were proposed by Honda and Tokoro, by Nestmann and (independently) by Boudol. We investigate whether the above encodings preserve De Nicola and Hennessy's testing semantics. In this sense, it turns out that, under some general conditions, no encoding of output prefix is able to preserve the must testing. This negative result is due to (a) the non atomicity of the sequences of steps which are necessary in the asynchronous $\pi$-calculus to mimic synchronous communication, and (b) testing semantics's sensitivity to divergence

Linearity, Persistence and Testing Semantics in the Asynchronous Pi-Calculus

“…in =!x(y), and either out =xz if P = PIAπ or out =!xz if P = PAπ) is singularly-structured. 8 We also stated this kind of specialized result for POAπ but for reasons of space and its restricted nature it has been moved in the appendix Notation 6.1 Given a focusing context C{} and P ∈ P, C{P } is the term obtained by replacing each occurrence { }σ in C{ } by {P }σ. We denote by L(P ) (ranged over by B, B , ..) the set {C{P } | P ∈ P, C{ } is a focusing context}.…”

“…In particular, the encoding provided in [24] from Aπ into PIAπ is weak barbed congruent preserving but not divergence preserving. Although in some situations divergence may be ignored, in general it is an important issue to consider in the correctness of encodings [8,17,16,18,7].…”

“…In a different context, in [22] it is shown that the separate choice encoding of the π-calculus into the asynchronous π-calculus is faithful with respect to weak bisimulation, while in [8] the authors prove that no must-preserving encoding of the (choiceless) synchronous pi-calculus into the asynchronous one exists. Hence must semantics is a good candidate to study the expressiveness of persistence when divergence is taken into account.…”

“…Hence must semantics is a good candidate to study the expressiveness of persistence when divergence is taken into account. Nevertheless, differently from [8], this work does not consider any synchronous language, i.e. the must semantics is studied in a uniform and purely asynchronous framework.…”

“…As previously mentioned the study of persistence in [24] is incomplete as ignores the crucial issue of divergence. In this paper, we used the divergence-sensitive framework of testing semantics and adapted and exploited the techniques of [8] to give a more complete account of the expressiveness of persistence in asynchronous calculi. In particular, as discussed in the introduction, this work supports informal expressiveness loss claims in persistent asynchronous languages [3,14,11].…”