有意义的信息

单个有限对象（如二进制字符串）中的信息通常通过其柯克莫尔复杂度来度量。可以将该信息分为两个部分：解释对象中有用规律性所包含的信息，以及解释剩余偶然信息所包含的信息。规律可以在几种不同的模型类中表达。柯克莫尔提出了有限集合的模型类，后续推广为可计算概率质量函数。 resulting theory, known as Algorithmic Statistics, analyzes the algorithmic sufficient statistic when the statistic is restricted to the given model class. However, the most general way to proceed is perhaps to express the useful information as a recursive function. The resulting measure has been called the ``sophistication'' of the object. We develop the theory of recursive functions statistic, the maximum and minimum value, the existence of absolutely nonstochastic objects (that have maximal sophistication--all the information in them is meaningful and there is no residual randomness), determine its relation with the more restricted model classes of finite sets, and computable probability distributions, in particular with respect to the algorithmic (Kolmogorov) minimal sufficient statistic, the relation to the halting problem and further algorithmic properties.