{"title":"关于四维酉角矩阵的恒等问题","authors":"Rui-Tao Dong","doi":"10.4230/LIPIcs.MFCS.2022.43","DOIUrl":null,"url":null,"abstract":"We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\\mathsf{UT}(4, \\mathbb{Z})$ of $4 \\times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in $\\mathsf{UT}(4, \\mathbb{Z})$.","PeriodicalId":369104,"journal":{"name":"International Symposium on Mathematical Foundations of Computer Science","volume":"32 3 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2022-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"4","resultStr":"{\"title\":\"On the Identity Problem for Unitriangular Matrices of Dimension Four\",\"authors\":\"Rui-Tao Dong\",\"doi\":\"10.4230/LIPIcs.MFCS.2022.43\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\\\\mathsf{UT}(4, \\\\mathbb{Z})$ of $4 \\\\times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in $\\\\mathsf{UT}(4, \\\\mathbb{Z})$.\",\"PeriodicalId\":369104,\"journal\":{\"name\":\"International Symposium on Mathematical Foundations of Computer Science\",\"volume\":\"32 3 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-02-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"4\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"International Symposium on Mathematical Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.4230/LIPIcs.MFCS.2022.43\",\"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/10.4230/LIPIcs.MFCS.2022.43","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
On the Identity Problem for Unitriangular Matrices of Dimension Four
We show that the Identity Problem is decidable in polynomial time for finitely generated sub-semigroups of the group $\mathsf{UT}(4, \mathbb{Z})$ of $4 \times 4$ unitriangular integer matrices. As a byproduct of our proof, we also show the polynomial-time decidability of several subset reachability problems in $\mathsf{UT}(4, \mathbb{Z})$.
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