{"title":"One quantifier alternation in first-order logic with modular predicates","authors":"Manfred Kufleitner, Tobias Walter","doi":"10.1051/ita/2014024","DOIUrl":null,"url":null,"abstract":"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 $x \\equiv i \\mod n$ has been investigated by Barrington, Compton, Straubing and Therien. The study of FO[<,MOD]-fragments was initiated by Chaubard, Pin and Straubing. More recently, Dartois and Paperman showed that definability in the two-variable fragment FO2[<,MOD] is decidable. In this paper we continue this line of work. \r\nWe give an effective algebraic characterization of the word languages in Sigma2[<,MOD]. The fragment Sigma2 consists of first-order formulas in prenex normal form with two blocks of quantifiers starting with an existential block. In addition we show that Delta2[<,MOD], the largest subclass of Sigma2[<,MOD] which is closed under negation, has the same expressive power as two-variable logic FO2[<,MOD]. This generalizes the result FO2[<] = Delta2[<] of Therien and Wilke to modular predicates. As a byproduct, we obtain another decidable characterization of FO2[<,MOD].","PeriodicalId":438841,"journal":{"name":"RAIRO Theor. Informatics Appl.","volume":"64 4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2013-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"6","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"RAIRO Theor. Informatics Appl.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/ita/2014024","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 6
Abstract
Adding modular predicates yields a generalization of first-order logic FO over words. The expressive power of FO[<,MOD] with order comparison $x
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