Stuttering Abstraction for Model Checking


Abstraction is one of the most effective approaches to improving the applicability and the scalability of model-checking. The goal of abstraction is to construct a model which is small enough to analyze, yet contains enough detail to allow conclusive analysis of properties of interest. For a given concrete model, the size of its smallest possible abstraction is intimately related to the set of temporal properties preserved by the abstraction. Thus, smaller abstractions are possible if we reduce this set, for example, by disallowing the use of the next-time operator. In this paper, we improve the conclusiveness and efficiency of the 3-valued abstraction framework. We start by proposing a number of simulation relations that preserve true properties expressed in subsets of CTL without the next-time operator. We show how these simulation relations are extended into refinement relations for defining 3-valued abstractions. Using these refinement relations, we give a new abstraction method that results in more conclusive abstract models. We also study the efficient implementation of these abstract models.