E. Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen
{"title":"On the complexity of numerical analysis","authors":"E. Allender, Peter Bürgisser, Johan Kjeldgaard-Pedersen, Peter Bro Miltersen","doi":"10.1109/CCC.2006.30","DOIUrl":null,"url":null,"abstract":"We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSLP; given a division-free straight-line program producing an integer N, decide whether N > 0. We show that PosSLP lies in the counting hierarchy, and combining our results with work of Tiwari, we show that the Euclidean traveling salesman problem lies in the counting hierarchy - the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE","PeriodicalId":325664,"journal":{"name":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","volume":"25 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2006-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"181","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"21st Annual IEEE Conference on Computational Complexity (CCC'06)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/CCC.2006.30","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 181
Abstract
We study two quite different approaches to understanding the complexity of fundamental problems in numerical analysis. We show that both hinge on the question of understanding the complexity of the following problem, which we call PosSLP; given a division-free straight-line program producing an integer N, decide whether N > 0. We show that PosSLP lies in the counting hierarchy, and combining our results with work of Tiwari, we show that the Euclidean traveling salesman problem lies in the counting hierarchy - the previous best upper bound for this important problem (in terms of classical complexity classes) being PSPACE
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
