{"title":"关于可逆序列的Skolem问题","authors":"George Kenison","doi":"10.48550/arXiv.2203.07061","DOIUrl":null,"url":null,"abstract":"Given an integer linear recurrence sequence h X n i ∞ n =0 , the Skolem Problem asks to determine whether there is an n ∈ N 0 such that X n = 0. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"11 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-03-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On the Skolem Problem for Reversible Sequences\",\"authors\":\"George Kenison\",\"doi\":\"10.48550/arXiv.2203.07061\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Given an integer linear recurrence sequence h X n i ∞ n =0 , the Skolem Problem asks to determine whether there is an n ∈ N 0 such that X n = 0. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.\",\"PeriodicalId\":369104,\"journal\":{\"name\":\"International Symposium on Mathematical Foundations of Computer Science\",\"volume\":\"11 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-14\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Mathematical Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.48550/arXiv.2203.07061\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"International Symposium on Mathematical Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2203.07061","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 1
摘要
给定一个整数线性递归序列h X n i∞n =0, Skolem问题要求确定是否存在一个n∈n0使得X n =0。Lipton, Luca, Nieuwveld, Ouaknine, Purser和Worrell最近的工作证明了Skolem问题对于一类最多为7阶的可逆序列是可决定的。这里我们给出了他们的结果的另一种证明。我们的新方法采用了由Dubickas和Smyth引起的位于两个同心圆上的伽罗瓦共轭的一个强有力的结果。
Given an integer linear recurrence sequence h X n i ∞ n =0 , the Skolem Problem asks to determine whether there is an n ∈ N 0 such that X n = 0. Recent work by Lipton, Luca, Nieuwveld, Ouaknine, Purser, and Worrell proved that the Skolem Problem is decidable for a class of reversible sequences of order at most seven. Here we give an alternative proof of their result. Our novel approach employs a powerful result for Galois conjugates that lie on two concentric circles due to Dubickas and Smyth.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
