Simpler Backward Simulation Proofs

Backward simulation relations provide a technique for verifying computer systems modelled as labelled transition systems. Recent experience suggests that backward simulation relations are useful in the verification of some highly concurrent systems. Proofs by backward simulation are complicated by the need to show that the simulation relation is total over all reachable states of the system being verified. Some reachable states exhibit complex dependencies between components of the state. We present a technique that reduces proving totality on all reachable states, to proving totality on a subset of the reachable states that are very simple. The technique exploits a very weak property of concurrent systems that we call completability: a system is completable if every operation can finish, but not every operation is required to finish in every execution.