Determinizing Asynchronous Automata on Infinite Inputs

Asynchronous automata are a natural distributed machine model for recognizing trace languages—languages defined over an alphabet equipped with an independence relation. To handle infinite traces, Gastin and Petit introduced Büchi asynchronous automata, which accept precisely the class of ω-regular trace languages. Like their sequential counterparts, these automata need to be non-deterministic in order to capture all ω-regular languages. Thus complementation of these automata is non-trivial. Complementation is an important operation because it is fundamental for treating the logical connective “not” in decision procedures for monadic secondorder logics. Subsequently, Diekert and Muscholl solved the complementation problem by showing that with a Muller acceptance condition, deterministic automata suffice for recognizing ω-regular trace languages. However, a direct determinization procedure, extending the classical subset construction, has proved elusive. In this paper, we present a direct determinization procedure for Büchi asynchronous automata, which generalizes Safra’s construction for sequential Büchi automata. As in the sequential case, the blow-up in the state space is essentially that of the underlying subset construc-