Comparing the expressiveness of the π-calculus and CCS

03/22/2022
by   Rob van Glabbeek, et al.
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This paper shows that the π-calculus with implicit matching is no more expressive than CCSγ, 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 CCSγ that is valid up to strong barbed bisimilarity. The full π-calculus can be similarly expressed in CCSγ enriched with the triggering operation of Meije. I also show that these results cannot be recreated with CCS in the role of CCSγ, 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.

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