深度作为随机性缺陷
Depth as Randomness Deficiency
摘要：
对象的深度涉及计算时间和超过获得对象所需的最短程序长度的程序长度之间的权衡。它给出了一个无条件的下限的计算时间从一个给定的程序在没有辅助信息。称为逻辑深度和计算深度的变体在柯尔莫哥洛夫复杂性理论中表示。本文导出了逻辑深度和计算深度之间的定量关系，并通过将它们与A. Kolmogorov和L.莱文关于随机性不足的富有成效的概念。随后，我们重新审视无限弦的计算深度，引入超深序列的概念，并将其与其他方法联系起来。
英文摘要：
Depth of an object concerns a tradeoff between computation time and excess of program length over the shortest program length required to obtain the object. It gives an unconditional lower bound on the computation time from a given program in absence of auxiliary information. Variants known as logical depth and computational depth are expressed in Kolmogorov complexity theory. We derive quantitative relation between logical depth and computational depth and unify the different depth notions by relating them to A. Kolmogorov and L. Levin's fruitful notion of randomness deficiency. Subsequently, we revisit the computational depth of infinite strings, introducing the notion of super deep sequences and relate it with other approaches.
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。
