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Counting in uniform TC0

机译:TC0计数

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摘要

In this paper we first give a uniform AC0 algorithm which uses partial sums to compute multiple addition. Then we use it to show that multiple addition is computable in uniform TC0 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 TC0 (by using count k+1 times sequentially when the product has size O((logn)k)). We also prove that multiple product with sharply bounded size is computable in uniform AC0.
机译:在本文中,我们首先给出一个统一的AC0算法,该算法使用部分和计算多重加法。然后,我们使用它来证明仅通过顺序使用一次计数就可以在统一TC0中计算出多个加法。通过构造用于多次加法的位矩阵,我们证明了具有对数大小的多个乘积可以在统一的TC0中进行计算(当乘积的大小为O((logn)k)时,按顺序使用k + 1次)。我们还证明,在统一的AC0中,可以计算出大小明显受限的多个乘积。

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