文章基本信息

标题：Two-variable first order logic with modular predicates over words
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作者：Luc Dartois ; Charles Paperman
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2013
卷号：20
页码：329-340
DOI：10.4230/LIPIcs.STACS.2013.329
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：First order logic; automata theory; semigroup; modular predicates