### Optimal bounds for decision problems on the CRCW PRAMOptimal bounds for decision problems on the CRCW PRAM

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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