Increasing kolmogorov complexity

Authors:
Harry Buhrman;Lance Fortnow;Ilan Newman;Nikolai Vereshchagin
Affiliations:
,CWI, Amsterdam, the Netherlands;Dept. of Computer Science, University of Chicago;Dept. of Computer Science, Haifa University, Israel;Moscow State University
Venue:
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Year:
2005

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Abstract

How much do we have to change a string to increase its Kolmogorov complexity? We show that we can increase the complexity of any non-random string of length n by flipping $O(\sqrt{n})$ bits and some strings require $\Omega(\sqrt{n})$ bit flips. For a given m, we also give bounds for increasing the complexity of a string by flipping m bits.