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Two Sources Are Better than One for Increasing the Kolmogorov Complexity of Infinite Sequences

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Abstract

The randomness rate of an infinite binary sequence is characterized by the sequence of ratios between the Kolmogorov complexity and the length of the initial segments of the sequence. It is known that there is no effective procedure that transforms one input sequence into another sequence with higher randomness rate. By contrast, we display such a uniform effective procedure having as input two independent sequences with positive but arbitrarily small constant randomness rate. Moreover the transformation is a truth-table reduction and the output has randomness rate arbitrarily close to 1.

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Authors and Affiliations

  1. Department of Computer and Information Sciences, Towson University, Towson, USA

    Marius Zimand

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  1. Marius Zimand
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Correspondence to Marius Zimand.

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The author is supported by NSF grant CCF 0634830. Part of this work was done while visiting University of Auckland, New Zealand.

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Zimand, M. Two Sources Are Better than One for Increasing the Kolmogorov Complexity of Infinite Sequences. Theory Comput Syst 46, 707–722 (2010). https://doi.org/10.1007/s00224-009-9214-6

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  • DOI: https://doi.org/10.1007/s00224-009-9214-6

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