On the Asynchronous Nature of the Asynchronous π-Calculus

Abstract

We address the question of what kind of asynchronous communication is exactly modeled by the asynchronous π-calculus (π _a ). To this purpose we define a calculus $\pi_\mathfrak{B}$ where channels are represented explicitly as special buffer processes. The base language for $\pi_\mathfrak{B}$ is the (synchronous) π-calculus, except that ordinary processes communicate only via buffers. Then we compare this calculus with π _a . It turns out that there is a strong correspondence between π _a and $\pi_\mathfrak{B}$ in the case that buffers are bags: we can indeed encode each π _a process into a strongly asynchronous bisimilar $\pi_\mathfrak{B}$ process, and each $\pi_\mathfrak{B}$ process into a weakly asynchronous bisimilar π _a process. In case the buffers are queues or stacks, on the contrary, the correspondence does not hold. We show indeed that it is not possible to translate a stack or a queue into a weakly asynchronous bisimilar π _a process. Actually, for stacks we show an even stronger result, namely that they cannot be encoded into weakly (asynchronous) bisimilar processes in a π-calculus without mixed choice.

This work has been partially supported by the INRIA ARC project ProNoBiS and by the INRIA DREI Équipe Associée PRINTEMPS.