{"title":"Size-depth tradeoffs for algebraic formulae","authors":"N. Bshouty, Richard Cleve, Wayne Eberly","doi":"10.1109/SFCS.1991.185387","DOIUrl":null,"url":null,"abstract":"Some tradeoffs between the size and depth of algebraic formulas are proved. It is shown that, for any fixed in >0, any algebraic formula of size S can be converted into an equivalent formula of depth O(log S) and size O(S/sup 1+ in /). This result is an improvement over previously known results where, to obtain the same depth bound, the formula size is Omega (S/sup alpha /), with alpha >or=2.<<ETX>>","PeriodicalId":320781,"journal":{"name":"[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science","volume":"50 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1991-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","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.1991.185387","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 5
Abstract
Some tradeoffs between the size and depth of algebraic formulas are proved. It is shown that, for any fixed in >0, any algebraic formula of size S can be converted into an equivalent formula of depth O(log S) and size O(S/sup 1+ in /). This result is an improvement over previously known results where, to obtain the same depth bound, the formula size is Omega (S/sup alpha /), with alpha >or=2.<>
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