Using Abstraction to Verify Arbitrary Temporal Properties

Abstract

Summary form only given. It is a known fact that finitary state abstraction methods (i.e. methods in which the abstract domain is finite), such as predicate abstraction, are inadequate for verifying general liveness properties or even termination of sequential programs. In this talk we will present an abstraction approach called ranking abstraction which is sound and complete for verifying all temporally specified properties, including all liveness properties. We will start by presenting a general simple framework for state abstraction emphasizing that, in order to get soundness, it is necessary to apply an over-approximating abstraction to the system and an under-approximating abstraction to the (temporal) property. We show that finitary version of this abstraction are complete for verifying all safety properties. We also show examples of simple programs whose termination provably cannot be established by finitary abstraction. We then consider abstraction approaches to the verification of deadlock freedom, presenting some sufficient conditions guaranteeing that deadlock freedom is inherited from the concrete to the abstract. Finally, we introduce the method of ranking abstraction and illustrate its application to the verification of termination and more general liveness properties. In this presentation we emphasize the similarity between predicate abstraction and its extension into ranking abstraction. In particular, the fact that the user does not have to provide a full ranking function but only to specify the ingredients from which such a function can be constructed. We also sketch how abstraction refinement can be applied to ranking abstraction, thus opening the way to a CEGAR-like methodology. Time permitting, we will present a brief comparison between ranking abstraction and the methods of transition abstraction developed by Podelski, Rybalchenko, and Cook which underly the Terminator system. The talk is based on results obtained through joint research with I. Balaban, Y. Kesten, and L.D. Zuck.