Comparing the expressiveness of the π -calculus and CCS

Abstract

This paper shows that the π -calculus with implicit matching is no more expressive than CCS γ, a variant of CCS in which the result of a synchronisation of two actions is itself an action subject to relabelling or restriction, rather than the silent action τ. This is done by exhibiting a compositional translation from the π -calculus with implicit matching to CCS γ that is valid up to strong barbed bisimilarity. The full π -calculus can be similarly expressed in CCS γ enriched with the triggering operation of Meije. I also show that these results cannot be recreated with CCS in the rôle of CCS γ, not even up to reduction equivalence, and not even for the asynchronous π -calculus without restriction or replication. Finally I observe that CCS cannot be encoded in the π -calculus.