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DOI: 10.4230/LIPIcs.ICALP.2016.110

Algorithmic Complexity for the Realization of an Effective Subshift By a Sofic

Authors: Mathieu Sablik and Michael Schraudner

Published in: LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

Abstract

Realization of d-dimensional effective subshifts as projective sub-actions of d + d'-dimensional sofic subshifts for d' >= 1 is now well known [Hochman, 2009; Durand/Romashchenko/Shen, 2012; Aubrun/Sablik, 2013]. In this paper we are interested in qualitative aspects of this realization. We introduce a new topological conjugacy invariant for effective subshifts, the speed of convergence, in view to exhibit algorithmic properties of these subshifts in contrast to the usual framework that focuses on undecidable properties.

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Mathieu Sablik and Michael Schraudner. Algorithmic Complexity for the Realization of an Effective Subshift By a Sofic. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 110:1-110:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{sablik_et_al:LIPIcs.ICALP.2016.110,
  author =	{Sablik, Mathieu and Schraudner, Michael},
  title =	{{Algorithmic Complexity for the Realization of an Effective Subshift By a Sofic}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{110:1--110:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-013-2},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{55},
  editor =	{Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.110},
  URN =		{urn:nbn:de:0030-drops-62454},
  doi =		{10.4230/LIPIcs.ICALP.2016.110},
  annote =	{Keywords: Subshift, computability, time complexity, space complexity, tilings}
}

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Algorithmic Complexity for the Realization of an Effective Subshift By a Sofic

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