Nonuniform Kolmogorov extractors

We establish tight bounds on the amount on nonuniformity that is necessary for extracting a string with randomness rate 1 from a single source of randomness with lower randomness rate. More precisely, as instantiations of more general results, we show that while O(1) amount of advice regarding the source is not enough for extracting a string with randomness rate 1 from a source string with constant subunitary random rate, \omega(1) amount of advice is.
Comment: This is a part of the conference paper from CCC 2011. It corrects an erroneus result from there, namely Theorem 4.8 (the new version has weaker parameters)