Relativizing computations of Turing machines to an oracle is a central concept in the theory of computation, both in complexity theory and in computability theory(!). Inspired by lowness notions from computability theory, Allender introduced the concept of “low for speed” oracles. An oracle A is low for speed if relativizing to A has essentially no effect on computational complexity, meaning that if a decidable language can be decided in time $f(n)$ with access to oracle A, then it can be decided in time $poly(f(n))$ without any oracle. The existence of non-computable such A's was later proven by Bayer and Slaman, who even constructed a computably enumerable one, and exhibited a number of properties of these oracles. In this paper, we pursue this line of research, answering the questions left by Bayer and Slaman and give further evidence that the class of low for speed oracles is a very rich one.

在复杂性理论和可计算性理论中，将图灵机的计算相对于Oracle都是计算理论的中心概念。受可计算性理论中低度概念的启发，Allender引入了“低速”预言的概念。一个oracle一个较低速度，如果相对化，以一对计算的复杂性基本没有影响，也就是说，如果一个可判定语言可以及时决定$F（ñ）$可以访问oracle A，那么就可以及时确定$pØ升ÿ（F（ñ））$没有任何预言。后来，Bayer和Slaman证明了不可计算的此类A的存在，他们甚至构造了一个可计算的可枚举A，并展示了这些先知的许多特性。在本文中，我们继续进行这一研究，回答了拜耳和斯拉曼留下的问题，并进一步证明了低速神谕者是一个非常丰富的人。