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Two sources are better than one for increasing the Kolmogorov complexity of infinite sequences. (English) Zbl 1143.68020
Hirsch, Edward A. (ed.) et al., Computer science – theory and applications. Third international computer science symposium in Russia, CSR 2008 Moscow, Russia, June 7–12, 2008. Proceedings. Berlin: Springer (ISBN 978-3-540-79708-1/pbk). Lecture Notes in Computer Science 5010, 326-338 (2008).
Summary: 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.
For the entire collection see [Zbl 1136.68005].

MSC:
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
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