Using optimal simulations to reduce reachability graphs

We here discuss an approach which uses the optimal simulation — a kind of reachability relation — to enable reasoning about important dynamic properties of a concurrent system. The optimal simulation usually involves only a very small subset of the possible behaviours generated by the system, yet provides a sufficient information to reason about a number of interesting system's properties (such as deadlock-freeness and liveness). In this paper we show how the optimal simulation might be used to generate a reachability graph which is usually much smaller than the standard reachability graph of the system; however, both graphs essentially convey the same information about its dynamic behaviour.