关于各种随机串集合的多项式深度
On the polynomial depth of various sets of random strings
摘要：
本文提出了新的概念的多项式深度（称为单调多深度），基于多项式版本的单调Kolmogorov复杂性。我们表明，单调多深度满足深度概念的所有理想的属性，即，平凡序列和随机序列都不是单调多深的，单调多深满足慢增长定律，即，没有简单的过程可以将非深序列转换为深序列，并且单调多深序列（无条件地）存在。我们给出了两个自然的深集的例子，通过证明莱文随机字符串的集合和柯尔莫哥洛夫随机字符串的集合都是单调多深的。
英文摘要：
This paper proposes new notions of polynomial depth (called monotone poly depth), based on a polynomial version of monotone Kolmogorov complexity. We show that monotone poly depth satisfies all desirable properties of depth notions i.e., both trivial and random sequences are not monotone poly deep, monotone poly depth satisfies the slow growth law i.e., no simple process can transform a non deep sequence into a deep one, and monotone poly deep sequences exist (unconditionally). We give two natural examples of deep sets, by showing that both the set of Levin-random strings and the set of Kolmogorov random strings are monotone poly deep.
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。
