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Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity

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Abstract

Merkle et al. (Ann. Pure Appl. Logic 138(1–3):183–210, 2006) showed that all Kolmogorov-Loveland stochastic infinite binary sequences have constructive Hausdorff dimension 1. In this paper, we go even further, showing that from an infinite sequence of dimension less than \(\mathcal {H}(\frac {1}{2}+\delta)\) (ℋ being the Shannon entropy function) one can extract by an effective selection rule a biased subsequence with bias at least δ. We also prove an analogous result for finite strings.

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  1. Laboratoire d’Informatique Fondamentale, Université de Provence & CNRS, 39 rue Joliot-Curie, 13453, Marseille Cedex 13, France

    Laurent Bienvenu

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  1. Laurent Bienvenu
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Correspondence to Laurent Bienvenu.

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Bienvenu, L. Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity. Theory Comput Syst 46, 598–617 (2010). https://doi.org/10.1007/s00224-009-9232-4

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  • DOI: https://doi.org/10.1007/s00224-009-9232-4

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