| | |
Summary: LIPIcs Leibniz International Proceedings in Informatics
Kolmogorov Complexity in
Randomness Extraction
John M. Hitchcock1
, A. Pavan2
, N. V. Vinodchandran3
1Department of Computer Science, University of Wyoming
jhitchco@cs.uwyo.edu
2Department of Computer Science, Iowa State University
pavan@cs.iastate.edu
3Department of Computer Science and Engineering, University of Nebraska-Lincoln
vinod@cse.unl.edu
ABSTRACT.
We clarify the role of Kolmogorov complexity in the area of randomness extraction. We show that a
computable function is an almost randomness extractor if and only if it is a Kolmogorov complexity
extractor, thus establishing a fundamental equivalence between two forms of extraction studied in
the literature: Kolmogorov extraction and randomness extraction. We present a distribution Mk
based on Kolmogorov complexity that is complete for randomness extraction in the sense that a
computable function is an almost randomness extractor if and only if it extracts randomness from
Mk.
|
