2026-07-26T04:14:54Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:3945 2024-03-06T10:34:41Z ddc:004 open_access

Two-variable first order logic with modular predicates over words Dartois, Luc Paperman, Charles First order logic automata theory semigroup modular predicates We consider first order formulae over the signature consisting of the symbols of the alphabet, the symbol < (interpreted as a linear order) and the set MOD of modular numerical predicates. We study the expressive power of FO^2[<,MOD], the two-variable first order logic over this signature, interpreted over finite words. We give an algebraic characterization of the corresponding regular languages in terms of their syntactic morphisms and we also give simple unambiguous regular expressions for them. It follows that one can decide whether a given regular language is captured by FO^2[<,MOD]. Our proofs rely on a combination of arguments from semigroup theory (stamps), model theory (Ehrenfeucht-Fraïssé games) and combinatorics. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Luc Dartois and Charles Paperman 2013 Is Part Of LIPIcs, Volume 20, 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2013.329 urn:nbn:de:0030-drops-39450 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2013.329 eng https://creativecommons.org/licenses/by-nd/3.0/legalcode