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

Authors:
Marius Zimand
Affiliations:
Towson University, Department of Computer and Information Sciences, Towson, USA
Venue:
Theory of Computing Systems - Special Issue: Symposium on Computer Science; Guest Editors: Sergei Artemov, Volker Diekert and Alexander Razborov
Year:
2010

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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.