SAT-based Abstraction Refinement for Real-time Systems

In this paper, we present an abstraction refinement approach for model checking safety properties of realtime systems using SAT-solving. We present a faithful embedding of bounded model checking for systems of timed automata into propositional logic with linear arithmetic and prove correctness. With this logical representation, we achieve a linear-size representation of parallel composition and introduce a quick abstraction technique that works uniformly for clocks, events, and states. When necessary, abstractions are refined by analysing spurious counterexamples using a promising extension of counterexample-guided abstraction refinement with syntactic information about Craig interpolants. To support generalisations, our overall approach identifies the algebraic and logical principles required for logic-based abstraction refinement.