{"title":"多对数独立性愚AC^0电路","authors":"M. Braverman","doi":"10.1145/1754399.1754401","DOIUrl":null,"url":null,"abstract":"We prove that poly-sized AC^0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazzi’s theorem.","PeriodicalId":158572,"journal":{"name":"2009 24th Annual IEEE Conference on Computational Complexity","volume":"83 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"105","resultStr":"{\"title\":\"Poly-logarithmic Independence Fools AC^0 Circuits\",\"authors\":\"M. Braverman\",\"doi\":\"10.1145/1754399.1754401\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We prove that poly-sized AC^0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazzi’s theorem.\",\"PeriodicalId\":158572,\"journal\":{\"name\":\"2009 24th Annual IEEE Conference on Computational Complexity\",\"volume\":\"83 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-07-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"105\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2009 24th Annual IEEE Conference on Computational Complexity\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1145/1754399.1754401\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2009 24th Annual IEEE Conference on Computational Complexity","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/1754399.1754401","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
We prove that poly-sized AC^0 circuits cannot distinguish a poly-logarithmically independent distribution from the uniform one. This settles the 1990 conjecture by Linial and Nisan [LN90]. The only prior progress on the problem was by Bazzi [Baz07], who showed that O(log^2 n)-independent distributions fool poly-size DNF formulas. Razborov [Raz08] has later given a much simpler proof for Bazzi’s theorem.
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