A criterion for separating process calculi

TL;DR

This paper introduces the concept of replacement freeness to compare the expressiveness of process calculi, showing that certain calculi with priorities cannot be encoded into mainstream calculi like CCS or pi-calculus.

Contribution

It defines replacement freeness and its variants, proving non-encodability results that distinguish calculi with priorities from standard calculi.

Findings

Calculi with priority are not replacement free.

Mainstream calculi like CCS and pi-calculus are strongly replacement free.

Variants of pi-calculus with pattern matching are only weakly replacement free.

Abstract

We introduce a new criterion, replacement freeness, to discern the relative expressiveness of process calculi. Intuitively, a calculus is strongly replacement free if replacing, within an enclosing context, a process that cannot perform any visible action by an arbitrary process never inhibits the capability of the resulting process to perform a visible action. We prove that there exists no compositional and interaction sensitive encoding of a not strongly replacement free calculus into any strongly replacement free one. We then define a weaker version of replacement freeness, by only considering replacement of closed processes, and prove that, if we additionally require the encoding to preserve name independence, it is not even possible to encode a non replacement free calculus into a weakly replacement free one. As a consequence of our encodability results, we get that many calculi equipped with priority are not replacement free and hence are not encodable into mainstream calculi like CCS and pi-calculus, that instead are strongly replacement free. We also prove that variants of pi-calculus with match among names, pattern matching or polyadic synchronization are only weakly replacement free, hence they are separated both from process calculi with priority and from mainstream calculi.