A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf
.
Extracting Kolmogorov Complexity with Applications to Dimension Zero-One Laws
[chapter]
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
doi:10.1007/11786986_30
fatcat:y2yfcqfdufgr5fxde6fygl5kua