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arXiv · 2203.11519

Comparing the expressiveness of the $\pi$-calculus and CCS

Rob van Glabbeek
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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.

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Rob van Glabbeek. 2022-03-22. Comparing the expressiveness of the $\pi$-calculus and CCS. https://arxiv.org/abs/2203.11519

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