, Volume 33, Issue 1, pp 69-97

A theory of bisimulation for the π-calculus

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Abstract

We study a new formulation of bisimulation for the π-calculus [MPW92], which we have called open bisimulation ( ∼ ). In contrast with the previously known bisimilarity equivalences, ∼ is preserved by all π-calculus operators, including input prefix. The differences among all these equivalences already appear in the sublanguage without name restrictions: Here the definition of ∼ can be factorised into a “standard” part which, modulo the different syntax of actions, is the CCS bisimulation, and a part specific to the π-calculus, which requires name instantiation. Attractive features of ∼ are: A simple axiomatisation (of the finite terms), with a completeness proof which leads to the construction of minimal canonical representatives for the equivalence classes of ∼; an “efficient” characterisation, based on a modified transition system. This characterisation seems promising for the development of automated-verification tools and also shows the call-by-need flavour of ∼. Although in the paper we stick to the π-calculus, the issues developed may be relevant to value-passing calculi in general.