Superlinear lower bounds for bounded-width branching programs

D. M. Barrington, Howard Straubing
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引用次数: 45

Abstract

The authors use algebraic techniques to obtain superlinear lower bounds on the size of bounded-width branching programs to solve a number of problems. In particular, they show that any bounded-width branching program computing a nonconstant threshold function has length Omega (n log log n), improving on the previous lower bounds known to apply to all such threshold functions. They also show that any program over a finite solvable monoid computing products in a nonsolvable group has length Omega (n log log n). This result is a step toward proving the conjecture that the circuit complexity class ACC/sup 0/ is properly contained in NC/sup 1/.<>
有界宽度分支规划的超线性下界
作者利用代数方法得到了有界宽度分支规划大小的超线性下界,从而解决了一系列问题。特别是,他们表明,任何计算非常数阈值函数的有界宽度分支程序的长度为Omega (n log log n),改进了先前已知的适用于所有此类阈值函数的下界。他们还表明,在不可解群中的有限可解单类计算产品上的任何程序都具有Omega (n log log n)的长度。这一结果向证明电路复杂度类ACC/sup 0/正确包含在NC/sup 1/中的猜想又迈进了一步。
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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