真实性是指数据集中自我描述信息的数量
Facticity as the amount of self-descriptive information in a data set
摘要：
使用柯尔莫哥洛夫复杂性理论，字符串的真实性定义为它包含的自描述信息的量。证明了（在合理的假设下：空机器的存在和忠实指标的可用性）真实性是确定的，即随机串的真实性为0，并且对于可压缩串0 <n（x）< 1/2 |x| + O（1）.因此，真实性客观地衡量了数据集中结构信息和特定信息之间的张力。对于二进制字符串，有一个所谓的真实性阈值，它取决于它们的熵。具有高于此阈值的facticty的字符串没有最佳随机模型，并且本质上是计算性的。事实与熵的关系曲线的形状与在复杂系统中观察到的著名的熵曲线相吻合。讨论了事实过程的概念。这种方法克服了早期建议使用两部分代码来定义数据集的意义或有用性的问题。
英文摘要：
Using the theory of Kolmogorov complexity the notion of facticity ϕ(x) of a string is defined as the amount of self-descriptive information it contains. It is proved that (under reasonable assumptions: the existence of an empty machine and the availability of a faithful index) facticity is definite, i.e. random strings have facticity 0 and for compressible strings 0 < ϕ(x) < 1/2 |x| + O(1). Consequently facticity measures the tension in a data set between structural and ad-hoc information objectively. For binary strings there is a so-called facticity threshold that is dependent on their entropy. Strings with facticty above this threshold have no optimal stochastic model and are essentially computational. The shape of the facticty versus entropy plot coincides with the well-known sawtooth curves observed in complex systems. The notion of factic processes is discussed. This approach overcomes problems with earlier proposals to use two-part code to define the meaningfulness or usefulness of a data set.
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