License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.STACS.2017.58
URN: urn:nbn:de:0030-drops-70347
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Zimand, Marius

List Approximation for Increasing Kolmogorov Complexity

LIPIcs-STACS-2017-58.pdf (0.5 MB)


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.

BibTeX - Entry

  author =	{Marius Zimand},
  title =	{{List Approximation for Increasing Kolmogorov Complexity}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{58:1--58:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Heribert Vollmer and Brigitte ValleĢe},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-70347},
  doi =		{10.4230/LIPIcs.STACS.2017.58},
  annote =	{Keywords: Kolmogorov complexity, list approximation, randomness extractor}

Keywords: Kolmogorov complexity, list approximation, randomness extractor
Collection: 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)
Issue Date: 2017
Date of publication: 06.03.2017

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