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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 eective procedure that transforms one input sequence into another sequence with higher randomness rate. By contrast, we display such a uniform eective 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.

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