Comparing the expressiveness of the $π$-calculus and CCS

Abstract: This paper shows that the $\pi$-calculus with implicit matching is no more expressive than CCS$\gamma$, 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 $\tau$. This is done by exhibiting a compositional translation from the $\pi$-calculus with implicit matching to CCS$\gamma$ that is valid up to strong barbed bisimilarity. The full $\pi$-calculus can be similarly expressed in CCS$\gamma$ enriched with the triggering operation of Meije. I also show that these results cannot be recreated with CCS in the role of CCS$\gamma$, not even up to reduction equivalence, and not even for the asynchronous $\pi$-calculus without restriction or replication. Finally I observe that CCS cannot be encoded in the $\pi$-calculus.