An Improvement in Formal Verification

Critical safety and liveness properties of a concurrent system can often be proven with the help of a reachability analysis of a finite state model. This type of analysis is usually implemented as a depth−first search of the product state−space of all components in the system, with each (finite state) component modeling the behavior of one asynchronously executing process. Formal verification is achieved by coupling the depth−first search with a method for identifying those states or sequences of states that violate the correctness requirements. It is well known, however, that an exhaustive depth−first search of this type performs redundant work. The redundancy is caused by the many possible interleavings of independent actions in a concurrent system. Few of these interleavings can alter the truth or falsity of the correctness properties being studied. The standard depth−first search algorithm can be modified to track additional information about the interleavings that have already been inspected, and use this information to avoid the exploration of redundant interleavings. Care must be taken to perform the reductions in such a way that the capability to prove both safety and liveness properties is fully preserved. Not all known methods have this property. Another potential drawback of the existing methods is that the additional computations required to enforce a reduction during the search can introduce overhead that diminishes the benefits. In this paper we discuss a new reduction method that solves some of these problems.