{"title":"Quadratic Maps Are Hard to Sample","authors":"Emanuele Viola","doi":"10.1145/2934308","DOIUrl":null,"url":null,"abstract":"This note proves the existence of a quadratic GF(2) map p: {0, 1}n → {0, 1} such that no constant-depth circuit of size poly(n) can sample the distribution (u, p(u)) for uniform u.","PeriodicalId":198744,"journal":{"name":"ACM Transactions on Computation Theory (TOCT)","volume":"42 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2016-06-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"9","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"ACM Transactions on Computation Theory (TOCT)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2934308","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 9
Abstract
This note proves the existence of a quadratic GF(2) map p: {0, 1}n → {0, 1} such that no constant-depth circuit of size poly(n) can sample the distribution (u, p(u)) for uniform u.
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