{"title":"Unambiguous parity-query complexity","authors":"Dmytro Gavinsky","doi":"10.48550/arXiv.2401.11274","DOIUrl":null,"url":null,"abstract":"We give a lower bound of $\\Omega(\\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\\{0,1\\}^n$ whose value is\"0\"if the Hamming weight of the input is at most n/3, is\"1\"if the weight is at least 2n/3, and may be arbitrary otherwise.","PeriodicalId":11639,"journal":{"name":"Electron. Colloquium Comput. Complex.","volume":"46 3","pages":"TR24-009"},"PeriodicalIF":0.0000,"publicationDate":"2024-01-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Electron. Colloquium Comput. Complex.","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.48550/arXiv.2401.11274","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
Abstract
We give a lower bound of $\Omega(\sqrt n)$ on the unambiguous randomised parity-query complexity of the approximate majority problem -- that is, on the lowest randomised parity-query complexity of any function over $\{0,1\}^n$ whose value is"0"if the Hamming weight of the input is at most n/3, is"1"if the weight is at least 2n/3, and may be arbitrary otherwise.
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