Characterization and Decidability of FC-Definable Regular Languages
Logic in Computer Science
2025-12-23 v2 Formal Languages and Automata Theory
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.
Keywords
Cite
@article{arxiv.2505.09772,
title = {Characterization and Decidability of FC-Definable Regular Languages},
author = {Sam M. Thompson and Nicole Schweikardt and Dominik D. Freydenberger},
journal= {arXiv preprint arXiv:2505.09772},
year = {2025}
}