We propose a refinement approach to symbolic SCC analysis, which performs large parts of the computation on abstracted systems, and on small subsets of the state space. For language-emptiness checking, it quickly discards uninteresting parts of the state space; for the remaining states, it adapts the model checking computation to the strength of the SCCs at hand. We present a general framework for SCC refinement, which uses a compositional approach to generate and refine overapproximations. We

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... how that our algorithm significantly outperforms the one of Emerson and Lei.