On the Expressiveness of ACP
De Simone showed that a wide class of languages, including CCS, SCCS, CSP and ACP, are expressible up to strong bisimulation equivalence in Meije. He also showed that every recursively enumerable process graph is representable by a Meije expression. Meije in turn is expressible in aprACP (ACP with action prefixing instead of sequential composition).
Vaandrager established that both results crucially depend on the use of unguarded recursion, and its noncomputable consequences. Effective versions of CCS, SCCS, Meije and ACP, not using unguarded recursion, are incapable of expressing all effective De Simone languages. And no effective language can denote all computable process graphs.
In this paper I recreate De Simone’s results in aprACP without using unguarded recursion. The price to be payed for this is the use of a partial recursive communication function and—for the second result— a single constant denoting a simple infinitely branching process. Due to the noncomputable communication function, the version of aprACP employed is still not effective.
However, I also define a wide class of De Simone languages that are expressible in an effective version of aprACP. This class includes the effective versions of CCS, SCCS, ACP, Meije and most other languages proposed in the literature, but not CSP. An even wider class, including CSP, turns out to be expressible in an effective version of aprACP to which an effective relational renaming operator has been added.
KeywordsRecursive Function Communication Function Parallel Composition Label Transition System Process Expression
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