Abstract
We give a method for specifying ultrafilter equations and identify their projections on the set of profinite words. Let \(\mathcal{B}\) be the set of languages captured by first-order sentences using unary predicates for each letter, arbitrary uniform unary numerical predicates and a predicate for the length of a word. We illustrate our methods by giving profinite equations characterizing \(\mathcal{B} \cap \operatorname{Reg}\) via ultrafilter equations satisfied by \(\mathcal{B}\). This suffices to establish the decidability of the membership problem for \(\mathcal{B} \cap \operatorname{Reg}\).
Work supported by the project ANR 2010 BLAN 0202 02 FREC.
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Gehrke, M., Krebs, A., Pin, JÉ. (2014). From Ultrafilters on Words to the Expressive Power of a Fragment of Logic. In: Jürgensen, H., Karhumäki, J., Okhotin, A. (eds) Descriptional Complexity of Formal Systems. DCFS 2014. Lecture Notes in Computer Science, vol 8614. Springer, Cham. https://doi.org/10.1007/978-3-319-09704-6_13
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DOI: https://doi.org/10.1007/978-3-319-09704-6_13
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