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Information Processing Letters
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Extracting Randomness Using Few Independent Sources
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Constructive dimension equals Kolmogorov complexity
Information Processing Letters
Extracting kolmogorov complexity with applications to dimension zero-one laws
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Increasing kolmogorov complexity
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
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Information Processing Letters
Algorithmically Independent Sequences
DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
On Generating Independent Random Strings
CiE '09 Proceedings of the 5th Conference on Computability in Europe: Mathematical Theory and Computational Practice
Algorithmically independent sequences
Information and Computation
Counting dependent and independent strings
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Impossibility of independence amplification in Kolmogorov complexity theory
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Randomness, computation and mathematics
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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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 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.