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Theory"],"published-print":{"date-parts":[[2016,7,26]]},"abstract":"<jats:p>\n                    This note proves the existence of a quadratic GF(2) map\n                    <jats:italic toggle=\"yes\">p<\/jats:italic>\n                    : {0, 1}\n                    <jats:sup>\n                      <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    <\/jats:sup>\n                    \u2192 {0, 1} such that no constant-depth circuit of size poly(\n                    <jats:italic toggle=\"yes\">n<\/jats:italic>\n                    ) can sample the distribution (\n                    <jats:italic toggle=\"yes\">u<\/jats:italic>\n                    ,\n                    <jats:italic toggle=\"yes\">p<\/jats:italic>\n                    (\n                    <jats:italic toggle=\"yes\">u<\/jats:italic>\n                    )) for uniform\n                    <jats:italic toggle=\"yes\">u<\/jats:italic>\n                    .\n                  <\/jats:p>","DOI":"10.1145\/2934308","type":"journal-article","created":{"date-parts":[[2016,6,15]],"date-time":"2016-06-15T15:32:01Z","timestamp":1466004721000},"page":"1-4","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":4,"title":["Quadratic Maps Are Hard to Sample"],"prefix":"10.1145","volume":"8","author":[{"given":"Emanuele","family":"Viola","sequence":"first","affiliation":[{"name":"Northeastern University, Boston, MA"}]}],"member":"320","published-online":{"date-parts":[[2016,6,14]]},"reference":[{"key":"e_1_2_1_1_1","doi-asserted-by":"publisher","DOI":"10.1016\/0020-0190(87)90036-6"},{"key":"e_1_2_1_2_1","first-page":"42","article-title":"Large deviation bounds for decision trees and sampling lower bounds for AC0-circuits","volume":"19","author":"Beck Chris","year":"2012","unstructured":"Chris Beck, Russell Impagliazzo, and Shachar Lovett. 2012. Large deviation bounds for decision trees and sampling lower bounds for AC0-circuits. Electron. Colloquium Computat. Complexity (ECCC) 19 (2012), 42.","journal-title":"Electron. Colloquium Computat. Complexity (ECCC)"},{"key":"e_1_2_1_3_1","doi-asserted-by":"publisher","DOI":"10.1109\/FOCS.2014.17"},{"key":"e_1_2_1_4_1","doi-asserted-by":"publisher","DOI":"10.1145\/2141938.2141941"},{"key":"e_1_2_1_5_1","doi-asserted-by":"publisher","DOI":"10.1007\/BF00189260"},{"key":"e_1_2_1_6_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00037-012-0039-3"},{"key":"e_1_2_1_7_1","doi-asserted-by":"publisher","DOI":"10.1137\/100814998"},{"key":"e_1_2_1_8_1","doi-asserted-by":"publisher","DOI":"10.1007\/978-3-642-32512-0_56"},{"key":"e_1_2_1_9_1","unstructured":"Emanuele Viola. 2014a. Is Nature a low complexity sampler? http:\/\/emanueleviola.wordpress.com\/2014\/11\/09\/is-nature-a-low-comple xity-sampler."},{"key":"e_1_2_1_10_1","doi-asserted-by":"publisher","DOI":"10.1137\/11085983X"}],"container-title":["ACM Transactions on Computation Theory"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2934308","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2934308","content-type":"application\/pdf","content-version":"vor","intended-application":"syndication"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/2934308","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,11,18]],"date-time":"2025-11-18T09:42:11Z","timestamp":1763458931000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/2934308"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2016,6,14]]},"references-count":10,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2016,7,26]]}},"alternative-id":["10.1145\/2934308"],"URL":"https:\/\/doi.org\/10.1145\/2934308","relation":{},"ISSN":["1942-3454","1942-3462"],"issn-type":[{"type":"print","value":"1942-3454"},{"type":"electronic","value":"1942-3462"}],"subject":[],"published":{"date-parts":[[2016,6,14]]},"assertion":[{"value":"2015-08-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-01-01","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2016-06-14","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}