A general approach to partial order reductions in symbolic verification

The purpose of partial-order reduction techniques is to avoid exploring several interleavings of independent transitions when model checking the temporal properties of a concurrent system. The purpose of symbolic verification techniques is to perform basic manipulations on sets of states rather than on individual states. We present a general method for applying partial order reductions to improve symbolic verification. The method is equally applicable to the verification of finite-state and infinite-state systems. It considers methods that check safety properties, either by forward reachability analysis or by backward reachability analysis. We base the method on the concept of commutativity (in one direction) between predicate transformers. Since the commutativity relation is not necessarily symmetric, this generalizes those existing approaches to partial order verification which are based on a symmetric dependency relation. We show how our method can be applied to several models of infinite-state systems: systems communicating over unbounded lossy FIFO channels, and unsafe (infinite-state Petri Nets. We show by a simple example how partial order reduction can significantly speed up symbolic backward analysis of Petri Nets.