Theory of Computing Systems

, Volume 46, Issue 4, pp 707–722

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

Article

DOI: 10.1007/s00224-009-9214-6

Cite this article as:
Zimand, M. Theory Comput Syst (2010) 46: 707. doi:10.1007/s00224-009-9214-6
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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.

Keywords

Kolmogorov complexity Hausdorff dimension 

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Department of Computer and Information SciencesTowson UniversityTowsonUSA

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