Verification of hybrid systems based on counterexample-guided abstraction refinement

Abstract

Hybrid dynamic systems include both continuous and discrete state variables. Properties of hybrid systems, which have an infinite state space, can often be verified using ordinary model checking together with a finite-state abstraction. Model checking can be inconclusive, however, in which case the abstraction must be refined. This paper presents a new procedure to perform this refinement operation for abstractions of infinite-state systems, in particular of hybrid systems. Following an approach originally developed for finite-state systems [1,2], the refinement procedure constructs a new abstraction that eliminates a counterexample generated by the model checker. For hybrid systems, analysis of the counterexample requires the computation of sets of reachable states in the continuous state space. We show how such reachability computations with varying degrees of complexity can be used to refine hybrid system abstractions efficiently. A detailed example illustrates our counterexample-guided refinement procedure. Experimental results for a prototype implementation of the procedure indicate its advantages over existing methods. © Springer-Verlag Berlin Heidelberg 2003.