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.2020.46
URN: urn:nbn:de:0030-drops-119071
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2020/11907/
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Bauwens, Bruno

Information Distance Revisited

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LIPIcs-STACS-2020-46.pdf (0.4 MB)

Abstract

We consider the notion of information distance between two objects x and y introduced by Bennett, Gács, Li, Vitanyi, and Zurek [C. H. Bennett et al., 1998] as the minimal length of a program that computes x from y as well as computing y from x, and study different versions of this notion. In the above paper, it was shown that the prefix version of information distance equals max (K(x|y),K(y|x)) up to additive logarithmic terms. It was claimed by Mahmud [Mahmud, 2009] that this equality holds up to additive O(1)-precision. We show that this claim is false, but does hold if the distance is at least logarithmic. This implies that the original definition provides a metric on strings that are at superlogarithmically separated.

BibTeX - Entry

@InProceedings{bauwens:LIPIcs:2020:11907,
  author =	{Bruno Bauwens},
  title =	{{Information Distance Revisited}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{46:1--46:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Christophe Paul and Markus Bl{\"a}ser},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2020/11907},
  URN =		{urn:nbn:de:0030-drops-119071},
  doi =		{10.4230/LIPIcs.STACS.2020.46},
  annote =	{Keywords: Kolmogorov complexity, algorithmic information distance}
}

Keywords: Kolmogorov complexity, algorithmic information distance
Collection: 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)
Issue Date: 2020
Date of publication: 04.03.2020

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