Strong Bisimulation for the Explicit Fusion Calculus

The pi calculus holds the promise of compile-time checks for whether a given program will have the correct interactive behaviour. The theory behind such checks is called bisimulation. In the synchronous pi calculus, it is well-known that the various natural definitions of (strong) bisimulation yield different relations. In contrast, for the asynchronous pi calculus, they collapse to a single relation. We show that the definitions transfer naturally from the pi calculus to the explicit fusion calculus (a symmetric variant of the synchronous pi calculus), where they also collapse and yield a simpler theory. The important property of an explicit fusion of names is that, in parallel with a term, it allow the fused names to be substituted for each other. This means that parallel contexts become as discriminating as arbitrary contexts, and that open bisimilarity is more natural for the explicit fusion calculus than it was for the pi calculus.