论文标题
近似方法的可靠性
Localizability of the approximation method
论文作者
论文摘要
我们使用Razborov的近似方法来分析源于对复杂性的硬度放大量方法的研究，这引起了局部性障碍。调整Razborov获得的近似方法的局限性，我们表明，在许多情况下，不可能将近似方法与典型（可定位的）硬度放大度定理相结合以得出强路下限。特别是，人们不能使用近似方法来得出一个极其强的恒定深度电路下限，然后将其放大到$ NC^1 $的显式函数的下限。 为了证明这一点，我们表明，通过近似方法获得的下限在许多情况下是可以定位的，因为它们意味着电路的下限，这些电路被允许使用带有小型风扇的任意强大的甲壳。
We use the approximation method of Razborov to analyze the locality barrier which arose from the investigation of the hardness magnification approach to complexity lower bounds. Adapting a limitation of the approximation method obtained by Razborov, we show that in many cases it is not possible to combine the approximation method with typical (localizable) hardness magnification theorems to derive strong circuit lower bounds. In particular, one cannot use the approximation method to derive an extremely strong constant-depth circuit lower bound and then magnify it to an $NC^1$ lower bound for an explicit function. To prove this we show that lower bounds obtained by the approximation method are in many cases localizable in the sense that they imply lower bounds for circuits which are allowed to use arbitrarily powerful oracles with small fan-in.
