伪周期词与舍夫列夫问题

IF 0.7 4区数学 Discrete Mathematics and Theoretical Computer Science Pub Date : 2023-10-16 DOI:10.46298/dmtcs.9919

Joseph Meleshko, Pascal Ochem, Jeffrey Shallit, Sonja Linghui Shan

{"title":"伪周期词与舍夫列夫问题","authors":"Joseph Meleshko, Pascal Ochem, Jeffrey Shallit, Sonja Linghui Shan","doi":"10.46298/dmtcs.9919","DOIUrl":null,"url":null,"abstract":"We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete.","PeriodicalId":55175,"journal":{"name":"Discrete Mathematics and Theoretical Computer Science","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Pseudoperiodic Words and a Question of Shevelev\",\"authors\":\"Joseph Meleshko, Pascal Ochem, Jeffrey Shallit, Sonja Linghui Shan\",\"doi\":\"10.46298/dmtcs.9919\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete.\",\"PeriodicalId\":55175,\"journal\":{\"name\":\"Discrete Mathematics and Theoretical Computer Science\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.7000,\"publicationDate\":\"2023-10-16\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Discrete Mathematics and Theoretical Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.46298/dmtcs.9919\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics and Theoretical Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.46298/dmtcs.9919","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}

引用次数: 0

摘要

将序列中周期的概念推广为一类新的伪周期，并证明了它的一些基本结果。我们重新审视了舍夫列夫2012年的一篇论文的结果，并以一种更简单、更统一的方式对他的结果进行了修正，并为他之前未解决的一个问题提供了一个完整的答案。我们考虑寻找具有特定伪周期并具有最小可能临界指数的词。最后，我们考虑了确定一个有限字是否是给定大小的伪周期的问题，并证明了它是np完全的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Pseudoperiodic Words and a Question of Shevelev

We generalize the familiar notion of periodicity in sequences to a new kind of pseudoperiodicity, and we prove some basic results about it. We revisit the results of a 2012 paper of Shevelev and reprove his results in a simpler and more unified manner, and provide a complete answer to one of his previously unresolved questions. We consider finding words with specific pseudoperiod and having the smallest possible critical exponent. Finally, we consider the problem of determining whether a finite word is pseudoperiodic of a given size, and show that it is NP-complete.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Discrete Mathematics and Theoretical Computer Science 数学-计算机：软件工程

自引率

14.30%

发文量

期刊介绍： DMTCS is a open access scientic journal that is online since 1998. We are member of the Free Journal Network. Sections of DMTCS Analysis of Algorithms Automata, Logic and Semantics Combinatorics Discrete Algorithms Distributed Computing and Networking Graph Theory.

期刊最新文献

Bears with Hats and Independence Polynomials Pseudoperiodic Words and a Question of Shevelev Gossiping with interference in radio ring networks Dissecting power of intersection of two context-free languages Embedding phylogenetic trees in networks of low treewidth