Denote by $H$ the Halting problem. Let $R_U: = \{ x | C_U(x) \ge |x|\}$, where $C_U(x)$ is the plain Kolmogorov complexity of $x$ under a universal decompressor $U$. We prove that there exists a universal $U$ such that $H \in P^{R_U}$, solving the problem posted by Eric Allender.
翻译:记$H$为停机问题。令$R_U: = \{ x | C_U(x) \ge |x|\}$,其中$C_U(x)$为通用解压器$U$下$x$的普通柯尔莫哥洛夫复杂度。我们证明存在一个通用$U$使得$H \in P^{R_U}$,从而解决了Eric Allender提出的问题。