Abstract. Predicate abstraction frameworks are a powerful means of combating the state explosion problem in model checking as they automatically synthesize abstract models that either verify compliance with a property, give rise to a genuine counter-example or produce a spurious counter-example that drives refinement of the abstract model. Prominent tools for safety (e.g. Blast) and termination (e.g. Terminator) checking rely on this approach. This paper presents such an abstraction framework for all properties of the modal µ-calculus based on ranked predicate abstraction. We show that our framework is incremental and confluent and should therefore allow good refinement heuristics. Moreover, ranked predicate abstractions are proved to be precise (i.e. optimal as abstractions) and also complete in that all properties true in a model are also true in a finite-state, ranked predicate abstraction of that model. This completeness relates to known characterizations of relative completeness for predicate abstraction with branching time.
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