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Author Mansour, Yishay ♦ Schieber, Baruch ♦ Tiwari, Prasoon
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1991
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Floor operation ♦ Greatest common devisor ♦ Lower bound ♦ Mod operation ♦ Truncation
Abstract It is proved that no finite computation tree with operations { +, -, *, /, mod, < } can decide whether the greatest common divisor (gcd) of $\textit{a}$ and $\textit{b}$ is one, for all pairs of integers $\textit{a}$ and $\textit{b}.$ This settles a problem posed by Gro¨tschel et al. Moreover, if the constants explicitly involved in any operation performed in the tree are restricted to be “0” and “1” (and any other constant must be computed), then we prove an &OHgr;(log log $\textit{n})$ lower bound on the depth of any computation tree with operations { +, -, *, /, mod, < } that decides whether the gcd of $\textit{a}$ and $\textit{b}$ is one, for all pairs of $\textit{n}-bit$ integers $\textit{a}$ and $\textit{b}.A$ novel technique for handling the truncation operation is implicit in the proof of this lower bound. In a companion paper, other lower bounds for a large class of problems are proved using a similar technique.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 1991-04-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 38
Issue Number 2
Page Count 19
Starting Page 453
Ending Page 471

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Source: ACM Digital Library