Modal abstractions of concurrent behavior

Abstract

We present an effective algorithm for the automatic construction of finite modal transition systems as abstractions of potentially infinite concurrent processes. Modal transition systems are recognized as valuable abstractions for model checking because they allow for the validation as well as refutation of safety and liveness properties. However, the algorithmic construction of finite abstractions from potentially infinite concurrent processes is a missing link that prevents their more widespread usage for model checking of concurrent systems. Our algorithm is a worklist algorithm using concepts from abstract interpretation and operating upon mappings from sets to intervals in order to express simultaneous over- and underapproximations of the multisets of process actions available in a particular state. We obtain a finite abstraction that is 3-valued in both states and transitions and that supports the definition of a 3-valued modal logic for validating as well as refuting properties of systems. The construction is illustrated on a few examples, including the Ingemarsson-Tang-Wong key agreement protocol.