近似方法的局部化

摘要：

我们使用Razborov的近似方法来分析的局部性障碍所产生的硬度放大方法的复杂性下界的调查。适应Razborov得到的近似方法的限制，我们表明，在许多情况下，它是不可能结合的近似方法与典型的（本地化）硬度放大定理，以获得强大的电路下界。特别是，不能使用近似方法来导出一个非常强的恒定深度电路下限，然后将其放大到一个显式函数的$NC^1$下限。为了证明这一点，我们表明，由近似方法得到的下界在许多情况下是本地化的意义上说，他们意味着电路允许使用任意强大的预言与小扇入的下界。

英文摘要：

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.

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