Extracting Kolmogorov Complexity with Applications to Dimension Zero-One Laws [chapter]

Lance Fortnow, John M. Hitchcock, A. Pavan, N. V. Vinodchandran, Fengming Wang
2006 Lecture Notes in Computer Science  
We apply recent results on extracting randomness from independent sources to "extract" Kolmogorov complexity. For any α, > 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 − )|y|. This result holds for both classical and space-bounded Kolmogorov complexity. We use the extraction procedure for space-bounded complexity to establish zero-one laws for polynomial-space strong dimension. Our
more » ... results include: In other words, from a dimension standpoint and with respect to a small amount of advice, the exponential-time class E is either minimally complex (dimension 0) or maximally complex (dimension 1) within ESPACE. Classification: Computational and Structural Complexity.
doi:10.1007/11786986_30 fatcat:y2yfcqfdufgr5fxde6fygl5kua