Formalization and verification of coherence protocols with the gamma framework

This paper presents an approach to formalize coherence protocols for shared virtual memories as multiset rewriting systems. The global state of the protocol is represented as a multiset and rewriting rules are used to describe state changes. Invariants are expressed as properties on the cardinality of subsets which characterize specific relations. We present an automatic algorithm to check that a property is an invariant of a protocol. Both the formalization and the verification steps are illustrated on the Li and Hudak single-writer/multiple-readers coherence protocol.