Deterministic asynchronous automata for infinite traces
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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
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.
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