{"title":"布尔函数单调性测试需要(几乎)n 1/2非自适应查询","authors":"Xi Chen, Anindya De, R. Servedio, Li-Yang Tan","doi":"10.1145/2746539.2746570","DOIUrl":null,"url":null,"abstract":"We prove a lower bound of Ω(n1/2-c), for all c> 0, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an n-variable Boolean function is monotone versus constant-far from monotone. This improves a ~Ω(n1/5) lower bound for the same problem that was obtained in [6], and is very close to the recent upper bound of ~O(n1/2/ε2) by Khot et al. [13].","PeriodicalId":20566,"journal":{"name":"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing","volume":"17 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2014-12-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"53","resultStr":"{\"title\":\"Boolean Function Monotonicity Testing Requires (Almost) n 1/2 Non-adaptive Queries\",\"authors\":\"Xi Chen, Anindya De, R. Servedio, Li-Yang Tan\",\"doi\":\"10.1145/2746539.2746570\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove a lower bound of Ω(n1/2-c), for all c> 0, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an n-variable Boolean function is monotone versus constant-far from monotone. This improves a ~Ω(n1/5) lower bound for the same problem that was obtained in [6], and is very close to the recent upper bound of ~O(n1/2/ε2) by Khot et al. [13].\",\"PeriodicalId\":20566,\"journal\":{\"name\":\"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing\",\"volume\":\"17 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2014-12-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"53\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Proceedings of the forty-seventh annual ACM symposium on Theory of Computing\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/2746539.2746570\",\"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 forty-seventh annual ACM symposium on Theory of Computing","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2746539.2746570","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Boolean Function Monotonicity Testing Requires (Almost) n 1/2 Non-adaptive Queries
We prove a lower bound of Ω(n1/2-c), for all c> 0, on the query complexity of (two-sided error) non-adaptive algorithms for testing whether an n-variable Boolean function is monotone versus constant-far from monotone. This improves a ~Ω(n1/5) lower bound for the same problem that was obtained in [6], and is very close to the recent upper bound of ~O(n1/2/ε2) by Khot et al. [13].
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