Determinizing Asynchronous Automata on Infinite Inputs - Klarlund, Nils; Mukund, Madhavan; Sohoni, Milind (BRICS Report Series, 1995)
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 Buchi asynchronous automata, which accept precisely the class of omega-regular trace languages. Like their sequential counterparts, these automata need to be non-deterministic in order to capture all omega-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 second-order logics. Subsequently, Diekert and Muscholl solved the complementation problem by showing that with a Muller acceptance condition, deterministic automata suffice for recognizing omega-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 Buchi asynchronous automata, which generalizes Safra’s construction for sequential Buchi automata. As in the sequential case, the blow-up in the state space is essentially that of the underlying subset construction.