最低速度集

摘要：

如果Oracle $A$不能加速已经可计算的集合的计算，则它是低速的：如果可判定语言可以使用$A$作为Oracle在时间$t(n)$中判定，则它可以在没有Oracle的情况下在时间$p(t(n))$中判定某个多项式$p$。低速集合的存在性首先由Bayer和Slaman证明，他们构造了一个低速的不可计算可计算集合。在本文中，我们回答了以前提出的问题Bienvenu和唐尼，谁问是否有一个最小的程度，这是低的速度。通过强迫构造最小度集合的标准方法与使集合低速不相容;但是我们能够使用强迫和完全近似的有趣的新组合来构造一个既具有最小度又具有低速的集合。

英文摘要：

An oracle $A$ is low-for-speed if it is unable to speed up the computation of a set which is already computable: if a decidable language can be decided in time $t(n)$ using $A$ as an oracle, then it can be decided without an oracle in time $p(t(n))$ for some polynomial $p$. The existence of a set which is low-for-speed was first shown by Bayer and Slaman who constructed a non-computable computably enumerable set which is low-for-speed. In this paper we answer a question previously raised by Bienvenu and Downey, who asked whether there is a minimal degree which is low-for-speed. The standard method of constructing a set of minimal degree via forcing is incompatible with making the set low-for-speed; but we are able to use an interesting new combination of forcing and full approximation to construct a set which is both of minimal degree and low-for-speed.

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。