一个构造性证明：提出 $\Sigma_2^P$ 中无法被大小为 $n^k$ 的电路族判定的语言
计算复杂性
2014-09-18 v2
摘要
据我所知，在我最初得出这一结果时（1998 年），这是首个构造性证明，表明对于任意整数 ， 中都存在一种无法被大小为 的逻辑电路族模拟的语言。然而，该结果此前已被非构造性地证明；有关此问题的历史详见 Cai 和 Watanabe [CW08]。本构造性证明基于构建一个源自可满足性问题（satisfiability problem）的语言 ，以及一个由交替图灵机定义的语言 。我们证明了 与 的并集无法被大小为 的电路模拟。
引用
@article{arxiv.1408.6334,
title = {A constructive proof presenting languages in $\Sigma_2^P$ that cannot be decided by circuit families of size $n^k$},
author = {Sunny Daniels},
journal= {arXiv preprint arXiv:1408.6334},
year = {2014}
}
备注
This is a corrected version of my previous article (of the same name) which attracted the attention of Professor Lance Fortnow at Georgia Institute of Technology ("Sixteen Years in the Making" in his Complexity Theory Blog). The original had a missing closing bracket in a footnote and a reference to the wrong step in the machine for $\Lambda_k$