{'fraction_non_alphanumeric': 0.023520485584218515, 'fraction_numerical': 0.0, 'mean_word_length': 5.942105263157894, 'pattern_counts': {'":': 0, '<': 0, '<?xml version=': 0, '>': 0, 'https://': 0, 'lorem ipsum': 0, 'www.': 0, 'xml': 0}, 'pii_count': 0, 'substrings_counts': 0, 'word_list_counts': {'cursed_substrings.json': 0, 'profanity_word_list.json': 0, 'sexual_word_list.json': 0, 'zh_pornsignals.json': 0}}
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 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.