Abstract and Model Check while you Prove
In Proceedings of the eleventh International Conference on Computer-Aided Verification (CAV99), Trento, Italy, Jul 7-10, 1999. This paper is © Springer-Verlag. See the LNCS series Homepage
The construction of abstractions is essential for reducing large or infinite state systems to small or finite state systems. Boolean abstractions, where boolean variables replace concrete predicates, are an important class that subsume several abstraction schemes. We show how boolean abstractions can be constructed simply, efficiently, and precisely for infinite state systems while preserving properties in the full $\mu$-calculus. We also propose an automatic refinement algorithm which refines the abstraction until the property is verified or a counterexample is found. Our algorithm is implemented as a proof rule in the PVS verification system. With the abstraction proof rule, proof strategies combining deductive proof construction, model checking, and abstraction can be defined entirely within the PVS framework.
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