Two-variable first order logic with modular predicates over words
نویسندگان
چکیده
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 FO2[<,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 FO2[<,MOD]. Our proofs rely on a combination of arguments from semigroup theory (stamps), model theory (Ehrenfeucht-Fräıssé games) and combinatorics. 1998 ACM Subject Classification F.4.3 Formal Languages
منابع مشابه
One quantifier alternation in first-order logic with modular predicates
Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison x < y and predicates for x ≡ i mod n has been investigated by Barrington, Compton, Straubing and Thérien. The study of FO[<,MOD]fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two...
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