Expected Algorithmic Complexity and
Informational Measures of Randomness, Predictability, and Structure

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Algorithmic Complexity and Informational Measures of Randomness

The provided text, excerpts from the paper "Expected Algorithmic Complexity and Informational Measures of Randomness, Predictability, and Structure," explores the relationship between Kolmogorov-Chaitin (KC) complexity and various measures from information theory concerning randomness, prediction, and structure in stochastic processes, particularly time series. The authors address the uncomputability of KC complexity by focusing on its expected value, which scales linearly with the sequence length at the Shannon entropy rate (h_μ). Crucially, the paper distinguishes between two types of KC complexity—generative (gKC) and predictive (pKC)—depending on the underlying Turing machine encoding model used. The offset in the complexity's linear growth is identified as either the past-future mutual information (E) for generative models or the statistical complexity (C_μ) for optimally predictive models, thus providing an informational decomposition of algorithmic complexity. Ultimately, the work clarifies how these informational measures provide structure-based interpretations for the components of the Turing machine programs underlying KC complexity.

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