Computer Science Department
School of Computer Science, Carnegie Mellon University


Abstraction and Counterexample-Guided Refinement
in Model Checking of Hybrid Systems

Edmund Clarke, Ansgar Fehnker, Zhi Han, Bruce Krogh,
Joel Ouaknine, Olaf Stursberg, Michael Theobald

January 2003

Keywords: Formal verification, abstraction, model checking, hybrid systems, refinement, counterexamples

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 hybrid systems. Following an approach originally developed for finite-state systems, 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. Examples illustrate our counterexample-guided refinement procedure and experimental results for a prototype implementation of the procedure indicate significant advantages over existing methods.

27 pages

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