Determinizing Asynchronous Automata on Infinite Inputs
Asynchrono us 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 -regular trace languages. Like their sequential counterparts, these automata need to be non-deterministic in order to capture all -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 -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 construction.