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arXiv · 2311.04895

The Monadic Theory of Toric Words

Valérie Berthé·Toghrul Karimov·Joël Ouaknine·Mihir Vahanwala·James Worrell
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Abstract

For which unary predicates $P_1, \ldots, P_m$ is the MSO theory of the structure $\langle \mathbb{N}; <, P_1, \ldots, P_m \rangle$ decidable? We survey the state of the art, leading us to investigate combinatorial properties of almost-periodic, morphic, and toric words. In doing so, we show that if each $P_i$ can be generated by a toric dynamical system of a certain kind, then the attendant MSO theory is decidable.

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Valérie Berthé, Toghrul Karimov, Joël Ouaknine, Mihir Vahanwala, James Worrell. 2023-11-08. The Monadic Theory of Toric Words. https://arxiv.org/abs/2311.04895

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