论文标题
小电路和双重弱PHP在P时间算法的通用理论中
Small circuits and dual weak PHP in the universal theory of p-time algorithms
论文作者
论文摘要
我们证明，根据计算复杂性假设，它与真正的P时间算法的真实通用理论是一致的，即将$ n $位扩展到$ m \ geq n^2 $ bits的特定p时函数违反了双弱的pigeonhole原理：每个长度$ m $ m $ y等于$ x $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n等于该函数是分配给电路的真实表函数，其计算的函数表，假设是P中的每种语言都有固定多项式大小$ n^d $的电路。
We prove, under a computational complexity hypothesis, that it is consistent with the true universal theory of p-time algorithms that a specific p-time function extending $n$ bits to $m \geq n^2$ bits violates the dual weak pigeonhole principle: every string $y$ of length $m$ equals the value of the function for some $x$ of length $n$. The function is the truth-table function assigning to a circuit the table of the function it computes and the hypothesis is that every language in P has circuits of a fixed polynomial size $n^d$.
