Verifying general safety and liveness properties with integer programming

Abstract

Analysis of concurrent systems is plagued by the state explosion problem. The constrained expression analysis technique uses necessary conditions, in the form of linear inequalities, to verify certain properties of concurrent systems, thus avoiding the enumeration of the potentially explosive number of reachable states of the system. This technique has been shown to be capable of verifying simple safety properties, like freedom from deadlock, that can be expressed in terms of the number of certain events occurring in a finite execution, and has been successfully used to analyze a variety of concurrent software systems. We extend this technique to the verification of more complex safety properties that involve the order of events and to the verification of liveness properties, which involve infinite executions.