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.
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Bienvenu, L. (2007). Kolmogorov-Loveland Stochasticity and Kolmogorov Complexity. In: Thomas, W., Weil, P. (eds) STACS 2007. STACS 2007. Lecture Notes in Computer Science, vol 4393. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70918-3_23
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DOI: https://doi.org/10.1007/978-3-540-70918-3_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70917-6
Online ISBN: 978-3-540-70918-3
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