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.2019.23
URN: urn:nbn:de:0030-drops-102624
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/10262/
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Destombes, Julien ; Romashchenko, Andrei

Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts

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LIPIcs-STACS-2019-23.pdf (0.5 MB)

Abstract

We suggest necessary conditions of soficness of multidimensional shifts formulated in terms of resource-bounded Kolmogorov complexity. Using this technique we provide examples of effective and non-sofic shifts on Z^2 with very low block complexity: the number of globally admissible patterns of size n x n grows only as a polynomial in n.

BibTeX - Entry

@InProceedings{destombes_et_al:LIPIcs:2019:10262,
  author =	{Julien Destombes and Andrei Romashchenko},
  title =	{{Resource-Bounded Kolmogorov Complexity Provides an Obstacle to Soficness of Multidimensional Shifts}},
  booktitle =	{36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)},
  pages =	{23:1--23:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-100-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{126},
  editor =	{Rolf Niedermeier and Christophe Paul},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/10262},
  doi =		{10.4230/LIPIcs.STACS.2019.23},
  annote =	{Keywords: Sofic shifts, Block complexity, Kolmogorov complexity}
}

Keywords: Sofic shifts, Block complexity, Kolmogorov complexity
Collection: 36th International Symposium on Theoretical Aspects of Computer Science (STACS 2019)
Issue Date: 2019
Date of publication: 12.03.2019

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