Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity

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


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.


Selection Rule Binary Sequence Initial Capital Kolmogorov Complexity Empty Word 
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© 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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