A criterion for separating process calculi

Federico Banti
(Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze)
Rosario Pugliese
(Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze)
Francesco Tiezzi
(Dipartimento di Sistemi e Informatica, Università degli Studi di Firenze)

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.

In Sibylle Fröschle and Frank D. Valencia: Proceedings 17th International Workshop on Expressiveness in Concurrency (EXPRESS'10), Paris, France, August 30th, 2010, Electronic Proceedings in Theoretical Computer Science 41, pp. 16–30.
Published: 28th November 2010.

ArXived at: https://dx.doi.org/10.4204/EPTCS.41.2 bibtex PDF

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