On the Asynchronous Nature of the Asynchronous π-Calculus

  • Romain Beauxis
  • Catuscia Palamidessi
  • Frank D. Valencia
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5065)


We address the question of what kind of asynchronous communication is exactly modeled by the asynchronous π-calculus (π a ). To this purpose we define a calculus \(\pi_\mathfrak{B}\) where channels are represented explicitly as special buffer processes. The base language for \(\pi_\mathfrak{B}\) is the (synchronous) π-calculus, except that ordinary processes communicate only via buffers. Then we compare this calculus with π a . It turns out that there is a strong correspondence between π a and \(\pi_\mathfrak{B}\) in the case that buffers are bags: we can indeed encode each π a process into a strongly asynchronous bisimilar \(\pi_\mathfrak{B}\) process, and each \(\pi_\mathfrak{B}\) process into a weakly asynchronous bisimilar π a process. In case the buffers are queues or stacks, on the contrary, the correspondence does not hold. We show indeed that it is not possible to translate a stack or a queue into a weakly asynchronous bisimilar π a process. Actually, for stacks we show an even stronger result, namely that they cannot be encoded into weakly (asynchronous) bisimilar processes in a π-calculus without mixed choice.


Turing Machine Input Action Base Language Asynchronous Communication Synchronous Communication 
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© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Romain Beauxis
    • 1
  • Catuscia Palamidessi
    • 1
  • Frank D. Valencia
    • 1
  1. 1.INRIA Saclay and LIX, École Polytechnique 

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