Automatic Abstraction Techniques for Propositional µ-calculus Model Checking

An abstraction/refinement paradigm for the full propositional μ-calculus is presented. No distinction is made between universal or existential fragments. Necessary conditions for conservative verification are provided, along with a fully automatic symbolic model checking abstraction algorithm. The algorithm begins with conservative verification of an initial abstraction. If the conclusion is negative, it derives a “goal set” of states which require further resolution. It then successively refines, with respect to this goal set, the approximations made in the subformulas, until the given formula is verified or computational resources are exhausted.

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