Abstract
This paper shows the equivalence between the family of recognizable languages over infinite traces and deterministic asynchronous cellular Muller automata. We thus give a proper generalization of McNaughton's Theorem from infinite words to infinite traces. Thereby we solve one of the main open problems in this field. As a special case we obtain that every closed (w.r.t. the independence relation) word language is accepted by some I-diamond deterministic Muller automaton. We also determine the complexity of deciding whether a deterministic I-diamond Muller automaton accepts a closed language.
This research has been supported by the ESPRIT Basic Research Action No. 6317 ASMICS 2.
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Diekert, V., Muscholl, A. (1993). Deterministic asynchronous automata for infinite traces. In: Enjalbert, P., Finkel, A., Wagner, K.W. (eds) STACS 93. STACS 1993. Lecture Notes in Computer Science, vol 665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-56503-5_61
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DOI: https://doi.org/10.1007/3-540-56503-5_61
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