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Division in logspace-uniform NC1

Published online by Cambridge University Press:  15 April 2002

Andrew Chiu ,
George Davida  and
Bruce Litow
Andrew Chiu
Affiliation:
EECS Department, University of Wisconsin-Milwaukee, Milwaukee, WI, U.S.A.
George Davida
Affiliation:
EECS Department, University of Wisconsin-Milwaukee, Milwaukee, WI, U.S.A.; e-mail: davida@cs.uwm.edu
Bruce Litow
Affiliation:
School of Information Technology, James Cook University, Townsville, Qld. 4811, Australia; e-mail: bruce@cs.jcu.edu.au
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Abstract

Beame, Cook and Hoover were the first to exhibit a log-depth, polynomial size circuit family for integer division. However, the family was not logspace-uniform. In this paper we describe log-depth, polynomial size, logspace-uniform, i.e., NC1 circuit family for integer division. In particular, by a well-known result this shows that division is in logspace. We also refine the method of the paper to show that division is in dlogtime-uniform NC1.

Keywords

Parallel complexityNCinteger divisionuniformity.
Type
Research Article
Information
RAIRO - Theoretical Informatics and Applications , Volume 35 , Issue 3 , May 2001 , pp. 259 - 275
Copyright
© EDP Sciences, 2001

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