Work

Characterization and Decidability of FC-Definable Regular Languages

Year: 2025

Type: conference-paper

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.

Source: Proceedings - Symposium on Logic in Computer Science

DOI: 10.1109/lics65433.2025.00033

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

Institutions: Loughborough University, Humboldt-Universität zu Berlin

Language: English

Topic: semigroups and automata theory

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funder: Engineering and Physical Sciences Research Council

Award: Foundations of the Finite Model Theory of Concatenation