All strings with low mutual information with the halting sequence will have flat Kolmogorov Structure Functions, in the context of Algorithmic Statistics. Assuming the Independence Postulate, strings with non-negligible information with the halting sequence are purely mathematical constructions, and cannot be found in nature. Thus Algorithmic Statistics does not study strings in the physical world. This leads to the general thesis that two part codes require limitations as shown in the Minimum Description Length Principle. We also discuss issues with set-restricted Kolmogorov Structure Functions.

翻译：在算法统计学的框架下，所有与停机序列互信息较低的字符串都将具有平坦的柯尔莫哥洛夫结构函数。若假设独立性公设成立，则与停机序列具有不可忽略信息的字符串均为纯粹的数学构造，在自然界中不可能存在。因此算法统计学的研究对象并非物理世界中的字符串。这一结论引出一个普遍论点：如最小描述长度原理所示，两部分编码方案需要施加限制条件。本文亦讨论了集合受限柯尔莫哥洛夫结构函数的相关问题。