The -calculus with synchronous output and mixed-guarded choices is strictly more expressive than the -calculus with asynchronous output and no choice. As a corollary, Palamidessi recently proved that there is no fully compositional encoding from the former into the latter that preserves divergence-freedom and symmetries. This paper shows

We study two bisimilarities for ν-calculus, a small but expressive formalism with asynchronous communication primitive. Weak bisimilarities based on two different notions of observables are formulated and studied. Both bisimilarities are congruence relations, while asynchronous bisimilarity is proved to be more inclusive than the synchronous counterpart. Equivalence of two semantic theories in expressive power is studied via mutual embeddings of modal logics characterizing their respective bisimilarities. Apart from the interest in their own right, our results strongly relativize the notion of observables as a semantic foundation of concurrency. They also lay basis for operational study of ν-calculus.

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