发表机构
Faculty of Mathematics; Computer Science University of Bucharest Bucharest, Romania（; ）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出“罕见或错误”方法，证明相对于随机谕示，多项式层级各层级以免疫语言实现强分离，扩展了 Bennett-Gill 与 Vereshchagin 的经典结果。
AI 中文摘要
Rossman、Servedio 和 Tan 证明了多项式层级相对于随机谕示是无限的。本文通过考虑由免疫语言见证的强分离，加强了这一著名结果。本文的主要结果表明，相对于随机谕示，多项式层级的各层级以免疫方式分离。具体而言，对于随机谕示 $A$，以概率 1 成立：对每个 $k\geq 1$，存在一个属于 $\Sigma_{k}^{P,A}$ 的语言，该语言对 $\Pi_{k}^{P,A}$ 免疫；对称地，存在一个属于 $\Pi_{k}^{P,A}$ 的语言，该语言对 $\Sigma_{k}^{P,A}$ 免疫。我们因此扩展了 Bennett 和 Gill 以及 Vereshchagin 的经典结果。我们通过发展一种“罕见或错误”的强分离方法来实现这一目标。我们通过加强计算复杂度文献中相对于随机谕示的其他分离，凸显了该方法的灵活性。
英文摘要
Rossman, Servedio, and Tan proved that the polynomial hierarchy is infinite relative to a random oracle. This paper strengthens this celebrated result by considering \emph{strong separations}, witnessed by immune languages. The main result of the paper shows that with respect to a random oracle the levels of the polynomial hierarchy separate with immunity. Specifically, with probability one over a random oracle $A$, for every $k\geq 1$ there is a language in $Σ_{k}^{P,A}$ that is immune to $Π_{k}^{P,A}$, and, symmetrically, a language in $Π_{k}^{P,A}$ that is immune to $Σ_{k}^{P,A}$. We thus extend classical results due to Bennett and Gill and Vereshchagin. We accomplish this by developing a "rare-or-wrong" approach to strong separations. We highlight the flexibility of the approach by strengthening other separations with respect to a random oracle from the complexity-theoretic literature.
