A criterion for separating process calculi

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.Comment: In Proceedings EXPRESS'10, arXiv:1011.601

Replacement freeness: A criterion for separating process calculi

We introduce a new criterion to discern the relative expressiveness of process calculi. Intuitively, a calculus is replacement free if replacing a sub-process that cannot perform any visible action by an arbitrary one never affects the capability of the resulting process to perform a visible action. By relying on two slightly different formulations of our criterion we partition the set of process calculi into three classes. Then, we prove that no suitable encodings between any two of such classes exist; hence calculi belonging to different classes have different relative expressiveness. Finally, we classify many well-known variants of the mainstream calculi CCS and the π-calculus, thus demonstrating their expressiveness gaps