# Division in logspace-uniform ${\text{NC}}^{1}$

Andrew Chiu; George Davida; Bruce Litow

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications (2001)

- Volume: 35, Issue: 3, page 259-275
- ISSN: 0988-3754

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topChiu, Andrew, Davida, George, and Litow, Bruce. "Division in logspace-uniform $\mbox{NC}^1$." RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications 35.3 (2001): 259-275. <http://eudml.org/doc/92665>.

@article{Chiu2001,

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., $\mbox\{NC\}^1$ 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 $\mbox\{NC\}^1$.},

author = {Chiu, Andrew, Davida, George, Litow, Bruce},

journal = {RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications},

keywords = {parallel complexity; NC; integer division; uniformity; polynomial size circuit family},

language = {eng},

number = {3},

pages = {259-275},

publisher = {EDP-Sciences},

title = {Division in logspace-uniform $\mbox\{NC\}^1$},

url = {http://eudml.org/doc/92665},

volume = {35},

year = {2001},

}

TY - JOUR

AU - Chiu, Andrew

AU - Davida, George

AU - Litow, Bruce

TI - Division in logspace-uniform $\mbox{NC}^1$

JO - RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

PY - 2001

PB - EDP-Sciences

VL - 35

IS - 3

SP - 259

EP - 275

AB - 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., $\mbox{NC}^1$ 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 $\mbox{NC}^1$.

LA - eng

KW - parallel complexity; NC; integer division; uniformity; polynomial size circuit family

UR - http://eudml.org/doc/92665

ER -

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