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arXiv · 2505.09772

Characterization and Decidability of FC-Definable Regular Languages

Sam M. Thompson·Nicole Schweikardt·Dominik D. Freydenberger
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Abstract

FC is a first-order logic that reasons over all factors of a finite word using concatenation, and can define non-regular languages like that of all squares (ww). In this paper, we establish that there are regular languages that are not FC-definable. Moreover, we give a decidable characterization of the FC-definable regular languages in terms of algebra, automata, and regular expressions. The latter of which is natural and concise: Star-free generalized regular expressions extended with the Kleene star of terminal words.

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Sam M. Thompson, Nicole Schweikardt, Dominik D. Freydenberger. 2025-05-14. Characterization and Decidability of FC-Definable Regular Languages. https://arxiv.org/abs/2505.09772

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