Exponential Determinization for ω-Automata with Strong-Fairness Acceptance Condition

In [Saf88] an exponential determinization procedure for Büchi automata was shown, yielding tight bounds for decision procedures of some logics ([EJ88, Saf88, SV89, KT89]). In [SV89] the complexity of determinization and complementation of ω-automata was further investigated, leaving as an open question the complexity of the determinization of a single class of ω-automata. For this class of ω-automata with strong fairness as acceptance condition (Streett automata), [SV89] managed to show an exponential complementation procedure, however the blow-up of translating these automata, to any of the classes known to admit exponential determinization, is inherently exponential. This might suggest that the blow-up of the determinization of Streett automata is inherently doubly exponential. This paper shows an exponential determinization construction for Streett automata. In fact, the complexity of our construction is roughly the same as the complexity achieved in [Saf88] for Büchi automata. Moreover, a simple observation extends this upper bound to the complementation problem. Since any ω-automaton that admits exponential determinization can be easily converted into a Streett automaton, we have obtained a single procedure that can be used for all of these conversions. Furthermore, this construction is optimal (up to a constant factor in the exponent) for all of these conversions. Our results imply that Streett automata (with strong fairness as acceptance condition) can be used instead of Büchi automata (with the weaker acceptance condition) without any loss of efficiency. ∗Part of this work was carried out while the author was at M.I.T. supported in part by a Weizmann Fellowship and NSF grant CCR-8912586. Another part of this work was carried out while the author was at IBM Almaden & Stanford University