{"title":"有界独立愚弄2度阈值函数","authors":"Ilias Diakonikolas, D. Kane, Jelani Nelson","doi":"10.1109/FOCS.2010.8","DOIUrl":null,"url":null,"abstract":"For an $n$-variate degree–$2$ real polynomial $p$, we prove that $\\E_{x\\sim \\mathcal{D}}[\\sgn(p(x))]$ is determined up to an additive $\\eps$ as long as $\\mathcal{D}$ is a $k$-wise independent distribution over $\\bits^n$ for $k = \\poly(1/\\eps)$. This gives a broad class of explicit pseudorandom generators against degree-$2$ boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).","PeriodicalId":228365,"journal":{"name":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","volume":"80 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2009-11-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"102","resultStr":"{\"title\":\"Bounded Independence Fools Degree-2 Threshold Functions\",\"authors\":\"Ilias Diakonikolas, D. Kane, Jelani Nelson\",\"doi\":\"10.1109/FOCS.2010.8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For an $n$-variate degree–$2$ real polynomial $p$, we prove that $\\\\E_{x\\\\sim \\\\mathcal{D}}[\\\\sgn(p(x))]$ is determined up to an additive $\\\\eps$ as long as $\\\\mathcal{D}$ is a $k$-wise independent distribution over $\\\\bits^n$ for $k = \\\\poly(1/\\\\eps)$. This gives a broad class of explicit pseudorandom generators against degree-$2$ boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).\",\"PeriodicalId\":228365,\"journal\":{\"name\":\"2010 IEEE 51st Annual Symposium on Foundations of Computer Science\",\"volume\":\"80 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2009-11-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"102\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"2010 IEEE 51st Annual Symposium on Foundations of Computer Science\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1109/FOCS.2010.8\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"2010 IEEE 51st Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/FOCS.2010.8","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
For an $n$-variate degree–$2$ real polynomial $p$, we prove that $\E_{x\sim \mathcal{D}}[\sgn(p(x))]$ is determined up to an additive $\eps$ as long as $\mathcal{D}$ is a $k$-wise independent distribution over $\bits^n$ for $k = \poly(1/\eps)$. This gives a broad class of explicit pseudorandom generators against degree-$2$ boolean threshold functions, and answers an open question of Diakonikolas et al. (FOCS 2009).
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