Determinizing Asynchronous Automata on Infinite Inputs

Nils Klarlund, Madhavan Mukund, Milind Sohoni
1995 BRICS Report Series  
Asynchronous automata are a natural distributed machine model<br />for recognizing trace languages - languages defined over an alphabet<br />equipped with an independence relation.<br />To handle infinite traces, Gastin and Petit introduced Buchi asynchronous<br />automata, which accept precisely the class of omega-regular trace<br />languages. Like their sequential counterparts, these automata need to<br />be non-deterministic in order to capture all omega-regular languages. Thus<br
more » ... tation of these automata is non-trivial. Complementation<br />is an important operation because it is fundamental for treating the<br />logical connective "not" in decision procedures for monadic second-order<br />logics. Subsequently, Diekert and Muscholl solved the complementation<br />problem by showing that with a Muller acceptance condition, deterministic<br />automata suffice for recognizing omega-regular trace languages.<br />However, a direct determinization procedure, extending the classical<br />subset construction, has proved elusive.<br />In this paper, we present a direct determinization procedure for<br />Buchi asynchronous automata, which generalizes Safra's construction<br />for sequential Buchi automata. As in the sequential case, the blow-up<br />in the state space is essentially that of the underlying subset construction.
doi:10.7146/brics.v2i58.19959 fatcat:otfewrye5ra3da5eraiioqiome