Two-variable first order logic with modular predicates over words

LIPICS - Leibniz International Proceedings in Informatics, Feb 2013

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-Fra�ss� games) and combinatorics.

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Luc Dartois, Charles Paperman. Two-variable first order logic with modular predicates over words, LIPICS - Leibniz International Proceedings in Informatics, 2013, 329-340, DOI: 10.4230/LIPIcs.STACS.2013.329