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.
