{"title":"Lower bounds for integer greatest common divisor computations","authors":"Y. Mansour, B. Schieber, Prasoon Tiwari","doi":"10.1145/103516.103522","DOIUrl":null,"url":null,"abstract":"An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, <or=) that computes the greatest common divisor (GCD) of all pairs of n-bit integers. A novel technique for handling the truncation operation is implicit in the proof. Also proved is a Theta (n) bound on the depth of any algebraic computation trees with operations (+, -, *, /, <or=) (where \"/\" stands for exact division) that solve many simple problems, e.g. testing if an n-bit integer is odd or computing the GCD of two n-bit integers.<<ETX>>","PeriodicalId":113255,"journal":{"name":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","volume":"2 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1988-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"34","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/103516.103522","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 34
Abstract
An Omega (log log n) lower bound is proved on the depth of any computation tree with operations (+, -, /, mod, >
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