代数公式的大小深度权衡

[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science Pub Date : 1991-09-01 DOI:10.1109/SFCS.1991.185387

N. Bshouty, Richard Cleve, Wayne Eberly

{"title":"代数公式的大小深度权衡","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":"{\"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}","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

摘要

证明了代数公式的大小和深度之间的一些权衡。结果表明，对于任意大于0的定值，任意大小为S的代数公式都可以转化为深度为O(log S)，大小为O(S/sup 1+ in /)的等效公式。这个结果是对先前已知结果的改进，其中，为了获得相同的深度边界，公式大小为Omega (S/sup alpha /)， alpha >或=2。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Size-depth tradeoffs for algebraic formulae

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.<>

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science

自引率

0.00%

发文量