Extracting Kolmogorov complexity with applications to dimension zero-one laws

We apply results on extracting randomness from independent sources to ''extract'' Kolmogorov complexity. For any @a,@e>0, given a string x with K(x)>@a|x|, we show how to use a constant number of advice bits to efficiently compute another string y, |y|=@W(|x|), with K(y)>(1-@e)|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.

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