Division in logspace-uniform ${\text{NC}}^{1}$
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 3, pp. 259-275.

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

Classification: 68Q05,  68Q10,  68Q15,  68Q17
Keywords: parallel complexity, NC, integer division, uniformity
@article{ITA_2001__35_3_259_0,
author = {Chiu, Andrew and Davida, George and Litow, Bruce},
title = {Division in logspace-uniform $\mbox{NC}^1$},
journal = {RAIRO - Theoretical Informatics and Applications - Informatique Th\'eorique et Applications},
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Chiu, Andrew; Davida, George; Litow, Bruce. Division in logspace-uniform $\mbox{NC}^1$. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Volume 35 (2001) no. 3, pp. 259-275. http://archive.numdam.org/item/ITA_2001__35_3_259_0/

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