在众多Oracle中识别诚实的${\rm EXP}^{\rm NP}$ Oracle
Identifying an Honest ${\rm EXP}^{\rm NP}$ Oracle Among Many
摘要：
我们提供了一个通用的框架，通过制定以下计算任务的功能$f$，以消除短的建议：给定两个预言，其中至少有一个是诚实的（即正确计算$f$的所有输入）以及一个输入，任务是计算$f$的输入与预言的帮助下，由一个概率多项式时间机器，我们称之为选择器。我们描述的语言，短的建议可以删除的概念选择器：一个paddable语言有一个选择器，当且仅当短的建议的概率机器，接受语言可以删除任何相对化的世界。以前，实例检查器是一个有用的工具，可以删除概率计算的简短建议。我们指出实例检查器的存在性是一个比删除短通知更强的属性：尽管${\rm EXP}^{\rm NP}$ -完全语言的实例检查器不存在，除非${\rm EXP}^{\rm NP} = {\rm NEXP}$，我们证明了存在任何${\rm EXP}^{\rm NP}$ -完全语言的选择器，通过Babai，Fortnow和Lund（1991）对${\rm MIP} = {\rm NEXP}$的证明。
英文摘要：
We provide a general framework to remove short advice by formulating the following computational task for a function $f$: given two oracles at least one of which is honest (i.e. correctly computes $f$ on all inputs) as well as an input, the task is to compute $f$ on the input with the help of the oracles by a probabilistic polynomial-time machine, which we shall call a selector. We characterize the languages for which short advice can be removed by the notion of selector: a paddable language has a selector if and only if short advice of a probabilistic machine that accepts the language can be removed under any relativized world. Previously, instance checkers have served as a useful tool to remove short advice of probabilistic computation. We indicate that existence of instance checkers is a property stronger than that of removing short advice: although no instance checker for ${\rm EXP}^{\rm NP}$-complete languages exists unless ${\rm EXP}^{\rm NP} = {\rm NEXP}$, we prove that there exists a selector for any ${\rm EXP}^{\rm NP}$-complete language, by building on the proof of ${\rm MIP} = {\rm NEXP}$ by Babai, Fortnow, and Lund (1991).
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