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

TLDR

Hybrid dynamic systems combine continuous and discrete variables and have infinite state spaces, so verification typically uses finite‑state abstractions, but model checking can be inconclusive, requiring refinement. The paper introduces a new procedure for refining abstractions of hybrid systems. The method extends a finite‑state refinement approach by constructing a new abstraction that eliminates counterexamples, which involves computing reachable sets in the continuous state space. Reachability‑based refinement of varying complexity yields efficient abstraction improvements, as shown by examples and prototype experiments that outperform existing methods.

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 hybrid systems. Following an approach originally developed for finite-state systems [11, 25], 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. Experimental results for a prototype implementation indicate significant advantages over existing methods.