电路下限、帮助函数和远程点问题
Circuit Lower Bounds, Help Functions, and the Remote Point Problem
摘要：
我们调查的权力代数分支程序（ABP）增强帮助多项式，和恒定深度的布尔电路增强帮助功能。我们将这两个模型中证明显式下界的问题与远程点问题（由Alon、Panigrahy和Yekhanin（RANDOM '09）引入）联系起来。更确切地说，证明下界的ABP与帮助多项式有关的远程点问题w.r.t.的秩度量，并为帮助功能的恒定深度电路，它是有关的远程点问题w.r.t.海明度量。对于代数分支程序的帮助多项式与一定程度的限制，我们显示指数大小的下界显式多项式。
英文摘要：
We investigate the power of Algebraic Branching Programs (ABPs) augmented with help polynomials, and constant-depth Boolean circuits augmented with help functions. We relate the problem of proving explicit lower bounds in both these models to the Remote Point Problem (introduced by Alon, Panigrahy, and Yekhanin (RANDOM '09)). More precisely, proving lower bounds for ABPs with help polynomials is related to the Remote Point Problem w.r.t. the rank metric, and for constant-depth circuits with help functions it is related to the Remote Point Problem w.r.t. the Hamming metric. For algebraic branching programs with help polynomials with some degree restrictions we show exponential size lower bounds for explicit polynomials.
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