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Paper:

TR97-034 | 3rd September 1997 00:00

Counting in uniform $TC^0$

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TR97-034
Authors: Jui-Lin Lee
Publication: 10th September 1997 21:25
Downloads: 1247
Keywords: 


Abstract:

In this paper we first give a uniform $AC^0$ algorithm which uses
partial sums to compute multiple addition. Then we use it to show
that multiple addition is computable in uniform $TC^0$ by using
$count$ only once sequentially. By constructing bit matrix for
multiple addition, we prove that multiple product with
poly-logarithmic size is computable in uniform $TC^0$
(by using $count$ $k+1$ times sequentially when the product
has size $O((\log n)^k)$). We also prove that multiple product
with sharply bounded size is computable in uniform $AC^0$.



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