Abstract

The Sπ-calculus is a synchronous π-calculus which is based on the SL model. The latter is a relaxation of the Esterel model where the reaction to the absence of a signal within an instant can only happen at the next instant. In the present work, we present and characterize a compositional semantics of the Sπ-calculus based on suitable notions of labelled transition system and bisimulation. Based on this semantic framework, we explore the notion of determinacy and the related one of (local) confluence.

Introduction

Let P be a program that can repeatedly interact with its environment. A derivative of P is a program to which P reduces after a finite number of interactions with the environment. A program terminates if all its internal computations terminate and it is reactive if all its derivatives are guaranteed to terminate. A program is determinate if after any finite number of interactions with the environment the resulting derivative is unique up to semantic equivalence.

Most conditions found in the literature that entail determinacy are rather intuitive, however the formal statement of these conditions and the proof that they indeed guarantee determinacy can be rather intricate in particular in the presence of name mobility, as available in a paradigmatic form in the π-calculus.

Our purpose here is to provide a streamlined theory of determinacy for the synchronous π-calculus introduced in.