{"title":"Better bounds for threshold formulas","authors":"J. Radhakrishnan","doi":"10.1109/SFCS.1991.185384","DOIUrl":null,"url":null,"abstract":"The computation of threshold functions using formulas over the basis (AND, OR, NOT) is considered. It is shown that every monotone formula that computes the threshold function T/sub k//sup n/2<or=k<or=n/2, has size Omega (nk log (n/(k-1))). The same lower bound is shown to hold even in the stronger monotone contact networks model. Nearly optimal bounds on the size of Sigma Pi Sigma formulas computing T/sub k//sup n/ for small k are also shown.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"41 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"19","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1109/SFCS.1991.185384","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 19
Abstract
The computation of threshold functions using formulas over the basis (AND, OR, NOT) is considered. It is shown that every monotone formula that computes the threshold function T/sub k//sup n/2>
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