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Extracting Kolmogorov complexity with applications to dimension zero-one laws

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Abstract

We apply results on extracting randomness from independent sources to "extract" Kolmogorov complexity. For any α,ε >0, given a string x with K(x) > α|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y| =Ω(|x|), with K(y)> (1-ε)|y|. This result holds for both unbounded and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for the strong dimensions of complexity classes within ESPACE. The unbounded extraction procedure yields a zero-one law for the constructive strong dimensions of Turing degrees. © 2010 Elsevier Inc. All rights reserved.

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APA

Fortnow, L., Hitchcock, J. M., Pavan, A., Vinodchandran, N. V., & Wang, F. (2011). Extracting Kolmogorov complexity with applications to dimension zero-one laws. Information and Computation, 209(4), 627–636. https://doi.org/10.1016/j.ic.2010.09.006

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