Baumslag-Gersten群中词搜索问题的参数化复杂度

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation Pub Date : 2020-07-20 DOI:10.1145/3373207.3404042

A. Myasnikov, Andrey Nikolaev

{"title":"Baumslag-Gersten群中词搜索问题的参数化复杂度","authors":"A. Myasnikov, Andrey Nikolaev","doi":"10.1145/3373207.3404042","DOIUrl":null,"url":null,"abstract":"We consider the word search problem in the Baumslag-Gersten group GB. We show that the parameterized complexity of this problem, where the area of van Kampen diagram serves as a parameter, is polynomial in the length of the input and the parameter. This contrasts the well-known result that the Dehn function and the time complexity of the word search problem in GB are non-elementary.","PeriodicalId":186699,"journal":{"name":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","volume":"13 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2020-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"1","resultStr":"{\"title\":\"On parameterized complexity of the word search problem in the Baumslag-Gersten group\",\"authors\":\"A. Myasnikov, Andrey Nikolaev\",\"doi\":\"10.1145/3373207.3404042\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the word search problem in the Baumslag-Gersten group GB. We show that the parameterized complexity of this problem, where the area of van Kampen diagram serves as a parameter, is polynomial in the length of the input and the parameter. This contrasts the well-known result that the Dehn function and the time complexity of the word search problem in GB are non-elementary.\",\"PeriodicalId\":186699,\"journal\":{\"name\":\"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation\",\"volume\":\"13 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2020-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/3373207.3404042\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/3373207.3404042","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

我们考虑Baumslag-Gersten组GB中的词搜索问题。我们证明了该问题的参数化复杂度，其中van Kampen图的面积作为参数，是输入长度和参数的多项式。这对比了众所周知的结果，即Dehn函数和GB中单词搜索问题的时间复杂度是非初等的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

On parameterized complexity of the word search problem in the Baumslag-Gersten group

We consider the word search problem in the Baumslag-Gersten group GB. We show that the parameterized complexity of this problem, where the area of van Kampen diagram serves as a parameter, is polynomial in the length of the input and the parameter. This contrasts the well-known result that the Dehn function and the time complexity of the word search problem in GB are non-elementary.

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

Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation

自引率

0.00%

发文量