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Author Beame, Paul ♦ Hastad, Johan
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©1989
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Abstract Optimal &OHgr;(log $\textit{n}/log$ log $\textit{n})$ lower bounds on the time for CRCW PRAMS with polynomially bounded numbers of processors or memory cells to compute parity and a number of related problems are proven. A strict time hierarchy of explicit Boolean functions of $\textit{n}$ bits on such machines that holds up to &Ogr;(log $\textit{n}/log$ log $\textit{n})$ time is also exhibited. That is, for every time bound $\textit{T}$ within this range a function is exhibited that can be easily computed using polynomial resources in time $\textit{T}$ but requires more than polynomial resources to be computed in time $\textit{T}$ - 1. Finally, it is shown that almost all Boolean functions of $\textit{n}$ bits require log $\textit{n}$ - log log $\textit{n}$ + &OHgr;(1) time when the number of processors is at most polynomial in $\textit{n}.$ The bounds do not place restrictions on the uniformity of the algorithms nor on the instruction sets of the machines.
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 1989-07-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 36
Issue Number 3
Page Count 28
Starting Page 643
Ending Page 670


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Source: ACM Digital Library