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, ... more >>>

In this paper we give a direct proof of N_0=N_0^\prime, i.e., the equivalence of
uniform NC^1 based on different recursion principles: one is OR-AND complete
binary tree (in depth \log n) and the other is the recursion on notation with value
bounded in [0,k] and |x|(=n) many ... more >>>