{"title":"更好的阈值公式边界","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":"{\"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}","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}
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>