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Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity

  • Laurent Bienvenu
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

Merkle et al. [11] 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 \(\mathcal{H}({1\over2}+\delta)\) (\(\mathcal{H}\) being the Shannon entropy function) one can extract by a selection rule a biased subsequence with bias at least δ. We also prove an analogous result for finite strings.

Keywords

Selection Rule Binary Sequence Initial Capital Kolmogorov Complexity Empty Word 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Laurent Bienvenu
    • 1
  1. 1.Laboratoire d’Informatique Fondamentale, 39 rue Joliot-Curie, 13453 Marseille Cedex 13France

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