CAS II: Symmetric Partitions as Kolmogorov Models

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CAS II: Symmetric Partitions as Kolmogorov Models

In algorithmic statistics a string x is explained by a finite set containing it, and Kolmogorov's structure function records the smallest such model at each level of complexity. Vereshchagin's strong models, those computable from the data by a total algorithm, are essentially the cells of simple partitions. We read a partition of binary strings as a hypothesis, with the cell containing x as its model, and develop algorithmic statistics over symmetric partitions: the orbit partitions of groups ac

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