Persistence and Testing Semantics in the Asynchronous Pi-Calculus

In [24] the authors studied the expressiveness of persistence in the asynchronous pi-calculus (Api) wrt weak barbed congruence. The study is incomplete because it ignores the issue of divergence. In this paper, we present an expressiveness study of persistence in the asynchronous pi-calculus (Api) wrt De Nicola and Hennessy’s testing scenario which is sensitive to divergence. Following [24], we consider Api and three sub-languages of it, each capturing one source of persistence: the persistent-input calculus (PIApi), the persistent-output calculus (POApi) and persistent calculus (PApi). In [24] the authors showed encodings from Aπ into the semi-persistent calculi (i.e., POApi and PIApi) correct wrt weak barbed congruence. In this paper we prove that, under some general conditions, there cannot be an encoding from Api into a (semi)-persistent calculus preserving the must testing semantics.