Towards the hierarchical verification of reactive systems

Abstract

The hierarchical design approach for action based systems that is known as action refinement has been studied in the literature extensively. In a paper of M. Huhn published in CONCUR 1996 a refinement operator on a linear time logic is presented that mimics precisely a semantic action refinement on synchronisation structures. We present here an alternative approach where our starting point is a process algebraic setting with a syntactic action refinement. We present a refinement operator on the Modal Mu-calculus that conforms with the process algebraic refinement in the following sense: Provided some reasonable conditions are met, the transition system induced by a process term P satisfies a Modal Mu-Calculus-specification ϕ if and only if the system which is induced by a refinement of P satisfies a particular refinement of ϕ. Alleviating these conditions, we show that each of the two implications in the equivalence assertion above can be separately proven valid for a particular fragment of the Modal Mu-calculus. We demonstrate that the obtained results can indeed be used as a hierarchical verification technique. As a further application of our results, we explain how they can be employed as an abstraction technique in order to enhance model checking techniques.