Finding Symmetry in Models of Concurrent Systems by Static Channel Diagram Analysis

Over the last decade there has been much interest in exploiting symmetry to combat the state explosion problem in model checking. Although symmetry in a model often arises as a result of symmetry in the topology of the system being modelled, most model checkers which exploit structural symmetry are limited to topologies which exhibit total symmetries, such as stars and cliques. We define the static channel diagram of a concurrent, message passing program, and show that under certain restrictions there is a correspondence between symmetries of the static channel diagram of a program and symmetries of the Kripke structure associated with the program. This allows the detection, and potential exploitation, of structural symmetry in systems with arbitrary topologies. Our method of symmetry detection can handle mobile systems where channel references are passed on channels, resulting in a dynamic communication structure. We illustrate our results with an example using the Promela modelling language.