List Approximation for Increasing Kolmogorov Complexity
It is impossible to effectively modify a string in order to increase its Kolmogorov complexity. But is it possible to construct a few strings, not longer than the input string, so that most of them have larger complexity? We show that the answer is yes. We present an algorithm that on input a string x of length n returns a list with O(n^2) many strings, all of length n, such that 99% of them are more complex than x, provided the complexity of x is less than n. We obtain similar results for other parameters, including a polynomial-time construction.
Kolmogorov complexity
list approximation
randomness extractor
58:1-58:12
Regular Paper
Marius
Zimand
Marius Zimand
10.4230/LIPIcs.STACS.2017.58
Creative Commons Attribution 3.0 Unported license
https://creativecommons.org/licenses/by/3.0/legalcode