关于逼近方法和P对NP问题
On the Approximation Method and the P versus NP Problem
摘要：
首先给出了“自然证明”并没有为P $\not=$ NP的布尔复杂性证明建立障碍的原因。然后，我们研究其扩展的近似方法，以证明NP中合适的布尔函数的非单调复杂性的超多项式下界，或者理解为什么这是不可能的。证明了仅用逼近方法不能证明任何函数$f \in {\cal B}_n$的超线性下界。此外，还对布尔函数的非单调复杂性和单调复杂性下界的证明方法进行了综述。最后，对如何研究P vs. NP问题以及如何证明NP中布尔函数的非单调复杂性的超线性下界给出了个人的看法。
英文摘要：
First of all we give some reasons that "natural proofs" built not a barrier to prove P $\not=$ NP using Boolean complexity. Then we investigate the approximation method for its extension to prove super-polynomial lower bounds for the non-monotone complexity of suitable Boolean functions in NP or to understand why this is not possible. It is given some evidence that the approximation method alone cannot be used to prove a super-linear lower bound for any function $f \in {\cal B}_n$. Additionally, an overview on the methods for proving lower bounds of the non-monotone and the monotone complexity of Boolean functions is given. Finally, a personal opinion how to proceed the research on the P versus NP problem and also on proving a super-linear lower bound for the non-monotone complexity of a Boolean function in NP is given.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
