{"title":"带模谓词的一阶逻辑中的一个量词交替","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":"{\"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}","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}