{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2023,10,27]],"date-time":"2023-10-27T05:40:31Z","timestamp":1698385231865},"reference-count":8,"publisher":"Wiley","issue":"4","license":[{"start":{"date-parts":[[2006,10,11]],"date-time":"2006-10-11T00:00:00Z","timestamp":1160524800000},"content-version":"vor","delay-in-days":3967,"URL":"http:\/\/onlinelibrary.wiley.com\/termsAndConditions#vor"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Random Struct Algorithms"],"published-print":{"date-parts":[[1995,12]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>In this paper we prove improved lower and upper bounds on the size of sample spaces which which are required to be independent on specified neighborhoods. Our new constructions yield sample spaces whose size is smaller than previous constructions due to Schulman. Our lower bounds generalize the known lower bounds of Alon et al. and Chor et al. In obtaining these bounds we examine the possibilities and limitations of amplifying limited independence by fixed functions. We show that in general independence cannot be amplified from <jats:italic>k<\/jats:italic>\u2010wise independence to (<jats:italic>k<\/jats:italic> + 1)\u2010wise independence. Finally, we enumerate all possible logical consequences of pairwise independence random bits, i.e., events whose probabilities are a consequence of pairwise independence.<\/jats:p>","DOI":"10.1002\/rsa.3240070404","type":"journal-article","created":{"date-parts":[[2007,6,2]],"date-time":"2007-06-02T00:56:33Z","timestamp":1180745793000},"page":"301-310","source":"Crossref","is-referenced-by-count":0,"title":["On the impossibility of amplifying the independence of random variables"],"prefix":"10.1002","volume":"7","author":[{"given":"Jin\u2010Yi","family":"Cai","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Suresh","family":"Chari","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2006,10,11]]},"reference":[{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1016\/0196-6774(86)90019-2"},{"key":"e_1_2_1_3_2","volume-title":"The Probabilistic Method","author":"Alon N.","year":"1992"},{"key":"e_1_2_1_4_2","doi-asserted-by":"crossref","unstructured":"B.Chor O.Goldreich J.H\u00e5stad J.Friedman S.Rudich andR.Smolensky The bit extraction problem ort\u2010resilient functions Proc. IEEE Symposium on Foundations of Computer Science Portland Oregon 1985 pp.396\u2013407.","DOI":"10.1109\/SFCS.1985.55"},{"key":"e_1_2_1_5_2","doi-asserted-by":"publisher","DOI":"10.1007\/BF02579457"},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1214\/aop\/1176996762"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.1979.1055985"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1137\/0215074"},{"key":"e_1_2_1_9_2","doi-asserted-by":"crossref","unstructured":"L. J.Schulman Sample spaces uniform on neighborhoods Proc. ACM Symposium on Theory of Computing 1992 Vancouver British Columbia pp.17\u201325.","DOI":"10.1145\/129712.129715"}],"container-title":["Random Structures &amp; Algorithms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.wiley.com\/onlinelibrary\/tdm\/v1\/articles\/10.1002%2Frsa.3240070404","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/pdf\/10.1002\/rsa.3240070404","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2023,10,26]],"date-time":"2023-10-26T18:10:43Z","timestamp":1698343843000},"score":1,"resource":{"primary":{"URL":"https:\/\/onlinelibrary.wiley.com\/doi\/10.1002\/rsa.3240070404"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1995,12]]},"references-count":8,"journal-issue":{"issue":"4","published-print":{"date-parts":[[1995,12]]}},"alternative-id":["10.1002\/rsa.3240070404"],"URL":"https:\/\/doi.org\/10.1002\/rsa.3240070404","archive":["Portico"],"relation":{},"ISSN":["1042-9832","1098-2418"],"issn-type":[{"value":"1042-9832","type":"print"},{"value":"1098-2418","type":"electronic"}],"subject":[],"published":{"date-parts":[[1995,12]]}}}