eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2017-03-06
58:1
58:12
10.4230/LIPIcs.STACS.2017.58
article
List Approximation for Increasing Kolmogorov Complexity
Zimand, Marius
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol066-stacs2017/LIPIcs.STACS.2017.58/LIPIcs.STACS.2017.58.pdf
Kolmogorov complexity
list approximation
randomness extractor