The fine approach to measure information dependence is based on the total conditional complexity CT(y|x), which is defined as the minimal length of a total program that outputs y on the input x. It is known that the total conditional complexity can be much larger than than the plain conditional complexity. Such strings x, y are defined by means of a diagonal argument and are not otherwise interesting. In this paper we investigate whether this happens also for some natural objects. More specifically, we consider the following objects: the number of strings of complexity less than n and the lex first string of length n and complexity at least n. It is known that they have negligible mutual conditional complexities. In this paper we prove that their mutual total conditional complexities may be large. This is the first example of natural objects whose plain conditional complexity is much less than the total one.

翻译：精细衡量信息依赖性的方法基于总条件复杂度CT(y|x)，其定义为从输入x输出y的总程序的最小长度。已知总条件复杂度可能远大于普通条件复杂度。此类字符串x,y通过对角论证定义，且本身并无特殊意义。本文探讨这种现象是否也会出现在某些自然对象中，具体研究以下对象：复杂度小于n的字符串数量，以及长度为n且复杂度至少为n的字典序第一字符串。已知它们具有可忽略的互条件复杂度，但本文证明其互总条件复杂度可能较大。这是首个表明自然对象普通条件复杂度远小于总条件复杂度的实例。