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

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