{"title":"通用Skolem集","authors":"F. Luca, J. Ouaknine, J. Worrell","doi":"10.1109/LICS52264.2021.9470513","DOIUrl":null,"url":null,"abstract":"It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subset $\\mathcal{S}$ of the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n))n ≥ 0 and decides whether u(n) = 0 for some $n \\in \\mathcal{S}$. The main technical contribution of the paper is to exhibit such a set.","PeriodicalId":174663,"journal":{"name":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":"49 4 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2021-06-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"Universal Skolem Sets\",\"authors\":\"F. Luca, J. Ouaknine, J. Worrell\",\"doi\":\"10.1109/LICS52264.2021.9470513\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subset $\\\\mathcal{S}$ of the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n))n ≥ 0 and decides whether u(n) = 0 for some $n \\\\in \\\\mathcal{S}$. The main technical contribution of the paper is to exhibit such a set.\",\"PeriodicalId\":174663,\"journal\":{\"name\":\"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"volume\":\"49 4 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2021-06-29\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/LICS52264.2021.9470513\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/LICS52264.2021.9470513","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
It is a longstanding open problem whether there is an algorithm to decide the Skolem Problem for linear recurrence sequences, namely whether a given such sequence has a zero term. In this paper we introduce the notion of a Universal Skolem Set: an infinite subset $\mathcal{S}$ of the positive integers such that there is an effective procedure that inputs a linear recurrence sequence u = (u(n))n ≥ 0 and decides whether u(n) = 0 for some $n \in \mathcal{S}$. The main technical contribution of the paper is to exhibit such a set.
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