{"title":"子序列和上序列逻辑中的可判定性","authors":"Prateek Karandikar, P. Schnoebelen","doi":"10.4230/LIPIcs.FSTTCS.2015.84","DOIUrl":null,"url":null,"abstract":"We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \\Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable.","PeriodicalId":175000,"journal":{"name":"Foundations of Software Technology and Theoretical Computer Science","volume":"33 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2015-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"17","resultStr":"{\"title\":\"Decidability in the Logic of Subsequences and Supersequences\",\"authors\":\"Prateek Karandikar, P. Schnoebelen\",\"doi\":\"10.4230/LIPIcs.FSTTCS.2015.84\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \\\\Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable.\",\"PeriodicalId\":175000,\"journal\":{\"name\":\"Foundations of Software Technology and Theoretical Computer Science\",\"volume\":\"33 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-10-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"17\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Foundations of Software Technology and Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.FSTTCS.2015.84\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Foundations of Software Technology and Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.4230/LIPIcs.FSTTCS.2015.84","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Decidability in the Logic of Subsequences and Supersequences
We consider first-order logics of sequences ordered by the subsequence ordering, aka sequence embedding. We show that the \Sigma_2 theory is undecidable, answering a question left open by Kuske. Regarding fragments with a bounded number of variables, we show that the FO2 theory is decidable while the FO3 theory is undecidable.
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