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

  • Marius Zimand
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5010)

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 uniform 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.

Keywords

Kolmogorov complexity Hausdorff dimension 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • Marius Zimand
    • 1
  1. 1.Department of Computer and Information SciencesTowson UniversityBaltimoreUSA

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