{"title":"毫不含糊的奇偶校验查询复杂度","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":"{\"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}","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}
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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