List Approximation for Increasing Kolmogorov Complexity

Zimand, Marius

doi:10.4230/LIPIcs.STACS.2017.58

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List Approximation for Increasing Kolmogorov Complexity

Author Marius Zimand

Part of: Volume: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Part of: Series: Leibniz International Proceedings in Informatics (LIPIcs)
Part of: Conference: Symposium on Theoretical Aspects of Computer Science (STACS)
License: Creative Commons Attribution 3.0 Unported license
Publication Date: 2017-03-06

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Document Identifiers

DOI: 10.4230/LIPIcs.STACS.2017.58
URN: urn:nbn:de:0030-drops-70347

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Keywords

Kolmogorov complexity
list approximation
randomness extractor

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Abstract

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.

Cite As Get BibTex

Marius Zimand. List Approximation for Increasing Kolmogorov Complexity. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 58:1-58:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.STACS.2017.58

Author Details

Marius Zimand

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