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

In C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006] the authors studied the expressiveness of persistence in the asynchronous π-calculus (Aπ) 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 π-calculus (Aπ) wrt De Nicola and Hennessy's testing scenario which is sensitive to divergence. Following C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006], we consider Aπ and three sub-languages of it, each capturing one source of persistence: the persistent-input calculus (PIAπ), the persistent-output calculus (POAπ) and persistent calculus (PAπ). In C. Palamidessi, V. Saraswat, F. Valencia and B. Victor. On the Expressiveness of Linearity vs Persistence in the Asynchronous Pi Calculus. LICS 2006:59–68, 2006] the authors showed encodings from Aπ into the semi-persistent calculi (i.e., POAπ and PIAπ) correct wrt weak barbed congruence. In this paper we prove that, under some general conditions, there cannot be an encoding from Aπ into a (semi)-persistent calculus preserving the must testing semantics.