The class of finitely locally threshold testable ω-languages is proved to be decidable relatively to the class of all regular ω-languages. We apply this to the monadic second order theory of infinite word structures with successor function: it is decidable whether for a given monadic second-order formula there exists a first-order formula with the same set of infinite word models.
CITATION STYLE
Wilke, T. (1993). Locally threshold testable languages of infinite words. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 665 LNCS, pp. 607–616). Springer Verlag. https://doi.org/10.1007/3-540-56503-5_60
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