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Based on a detailed graph theoretical analysis, Wagner's fundamentalresults of 1979 are turned into efficient algorithms to computethe Wadge degree, the Lifschitz degree, and the Rabin index of a regular!-language: the two former can be computed in time O(f2qb + k log k)and the latter in time O(f2qb) if the language is represented by a deterministicMuller automaton over an alphabet of cardinality b, with faccepting sets, q states, and k strongly connected components.Formal...

Computing the Wadge degree, the Lifschitz degree, and the Rabin index of a regular language of infinite words in polynomial time