p-时间算法普适理论中的小电路和对偶弱PHP
Small circuits and dual weak PHP in the universal theory of p-time algorithms
摘要：
我们证明，在计算复杂性的假设下，它是一致的p-时间算法的真正的通用理论，一个特定的p-时间函数扩展$n$位$m \geq n^2$位违反了对偶弱鸽子洞原则：每个字符串$y$的长度$m$等于一些$x$的长度$n$的功能的值。该函数是真值表函数，将它计算的函数表分配给电路，假设P中的每种语言都有固定多项式大小的电路$n^d$。
英文摘要：
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 $n^d$.
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。
