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Determinization of B\"uchi automata is a long-known difficult problem andafter the seminal result of Safra, who developed the first asymptoticallyoptimal construction from B\"uchi into Rabin automata, much work went intoimproving, simplifying or avoiding Safra's construction. A different, lessknown determinization construction was derived by Muller and Schupp and appearsto be unrelated to Safra's construction on the first sight. In this paper wepropose a new meta-construction from nondeterministic B\"uchi to deterministicparity automata which strictly subsumes both the construction of Safra and theconstruction of Muller and Schupp. It is based on a correspondence betweenstructures that are encoded in the macrostates of the determinizationprocedures - Safra trees on one hand, and levels of the split-tree, whichunderlies the Muller and Schupp construction, on the other. Our constructionallows for combining the mentioned constructions and opens up new directionsfor the development of heuristics.

Determinization of B\"uchi Automata: Unifying the Approaches of Safra and Muller-Schupp