Determinization of Parity automata

A central result in the theory of ω-automata is McNaughton's Theorem which states that every Buchi automaton is equivalent to a deterministic Muller automaton. The complexity of McNaughton's algorithm is huge. Safra provided an optimal construction. Safra's algorithm converts a Buchi automaton with n states to a deterministic Rabin automaton with n states. Much e orts have been invested to reduce constants in Safra's determinization procedure and to highlight and improve many ideas incorporated in it, such as: naming mechanism, acceptance mechanism, etc. Still, the procedure has an operational de nition which makes it di cult to teach. Muller and Schupp provided another determinization algorithm. It can be explained more easily and has the same asymptotic complexity. They also proved that every parity automaton with n states and m priorities is equivalent to a deterministic automaton with n states. We use a variant of Muller-Schupp's algorithm and prove that every parity automaton with n states and m priorities is equivalent to a deterministic parity automaton with n states and O(n) priorities. Our determinization procedure is declarative and thus is easy to explain.