Context-free Synchronising Graphs

Synchronising Graphs is a system of parallel graph transformation designed for modeling process interaction in a network environment. Although notions of observational equivalence are abundant in the literature for process calculi, not so for graph rewriting, where system behaviour is typically context dependent. We propose a theory of context-free synchronising graphs and a novel notion of bisimulation equivalence which is shown to be a congruence with respect to graph composition and node restriction. This notion is used to provide a proof technique for the hyperequivalence of the Fusion calculus, through an encoding which is shown to be sound and complete. This builds a bridge between graph rewriting and process algebra. As a further application, we prove the correctness of a system component, called non-deterministic commuter, with respect to its specification. The result shows that our notion of equivalence is fine enough to discriminate between different degrees of parallelism in a network.