A lower bound for primality

Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317) Pub Date : 1999-05-04 DOI:10.1109/CCC.1999.766257

E. Allender, M. Saks, I. Shparlinski

引用次数: 22

Abstract

Recent work by Bernasconi, Damm and Shparlinski proved lower bounds on the circuit complexity of the square-free numbers, and raised as an open question if similar (or stronger) lower bounds could be proved for the set of prime numbers. In this short note, we answer this question affirmatively, by showing that the set of prime numbers (represented in the usual binary notation) is not contained in AC/sup 0/ [p] for any prime p. Similar lower bounds are presented for the set of square-free numbers, and for the problem of computing the greatest common divisor of two numbers.

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原数的下界

Bernasconi, Damm和Shparlinski最近的工作证明了无平方数的电路复杂度的下界，并提出了一个开放的问题，即是否可以为素数集证明类似(或更强)的下界。在这个简短的说明中，我们肯定地回答了这个问题，通过证明对于任何素数p, AC/sup 0/ [p]中都不包含素数集(用通常的二进制符号表示)。对于无平方数集，以及计算两个数的最大公约数的问题，也给出了类似的下界。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Proceedings. Fourteenth Annual IEEE Conference on Computational Complexity (Formerly: Structure in Complexity Theory Conference) (Cat.No.99CB36317)

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