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Characterization and Decidability of FC-Definable Regular Languages

Published: May 14, 2025 | arXiv ID: 2505.09772v1

By: Sam M. Thompson, Nicole Schweikardt, Dominik D. Freydenberger

Potential Business Impact:

Finds patterns in words computers can't.

Business Areas:
Charter Schools Education

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.

Country of Origin
🇩🇪 🇬🇧 United Kingdom, Germany

Page Count
18 pages

Category
Computer Science:
Logic in Computer Science