{"title":"二次映射很难采样","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":"{\"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}","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}
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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