A Modal Characterisation of Distributed Bisimulation

Abstract

In this paper we consider the distributed bisimulation equivalence defined by Hennessy and Castellani and later developed by Castellani. We present a logic in the style of Hennessy-Milner logic to charaterize the equivalence, i.e. we seek a logic such that whenever two processes are distributed bisimulation equivalent, they satisfy the same set of formulae and vice versa. Furthermore, for a small subset of CCS we provide a proof system which is shown to be sound and complete. The proof system is structural both in the structure of formulae and in the structure of processes. For the case of parallel composition of processes we present inference rules defined via a new combinator introduced. The combinator in question is left merge, a special kind of parallel composition in which the left operand has precedence over the other and must perform the first action observed.