On the Asynchronous Nature of the Asynchronous Π-Calculus

  • Authors:

  • Romain Beauxis;Catuscia Palamidessi;Frank D. Valencia

  • Affiliations:

  • INRIA Saclay and LIX, École Polytechnique,;INRIA Saclay and LIX, École Polytechnique,;INRIA Saclay and LIX, École Polytechnique,

  • Venue:
  • Concurrency, Graphs and Models
  • Year:
  • 2008

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Abstract

We address the question of what kind of asynchronouscommunication is exactly modeled by the asynchronous Π-calculus (Πa). To this purposewe define a calculus $\pi_\mathfrak{B}$ where channels arerepresented explicitly as special buffer processes. The baselanguage for $\pi_\mathfrak{B}$ is the (synchronous) Π-calculus, except that ordinary processes communicate only viabuffers. Then we compare this calculus with Πa. It turns out that there is a strongcorrespondence between Πaand$\pi_\mathfrak{B}$ in the case that buffers are bags: we can indeedencode each Πaprocess into astrongly asynchronous bisimilar $\pi_\mathfrak{B}$ process, andeach $\pi_\mathfrak{B}$ process into a weakly asynchronousbisimilar Πaprocess. In case thebuffers are queues or stacks, on the contrary, the correspondencedoes not hold. We show indeed that it is not possible to translatea stack or a queue into a weakly asynchronous bisimilarΠaprocess. Actually, for stackswe show an even stronger result, namely that they cannot be encodedinto weakly (asynchronous) bisimilar processes in a Π-calculus without mixed choice.