Parameterised Bisimulations: Some Applications

In [AK06] the first author had generalised the notion of bisimulation on labelled transition systems to that of a parameterised relation whose parameters were a pair of relations on the observables of a system. In this paper we present new results which show that notions of parameterised bisimilarity may be defined to capture congruences in process algebras. In particular, we show that observational congruence may be obtained as a parameterised bisimulation, thereby providing a co-inductive characterisation for the same. In another application, parameterisation is employed to prove that amortised bisimilarity is preserved under recursion in CCS by resorting to a generalisation of the so-called “upto”-technique. We then extend the framework to a name passing calculus and show that one can capture (hyper-)bisimulations in the fusion calculus [Vic98] as a parameterised (hyper-)bisimulation. However this involves giving a behaviourally equivalent alternative semantics for the fusion calculus, which is necessary for defining parameterised bisimulations in the fusion calculus and also allows for more natural definitions of bisimulations.