License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2021.122
URN: urn:nbn:de:0030-drops-141914
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14191/
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Callard, Antonin ; Vanier, Pascal

Computational Characterization of Surface Entropies for ℤ² Subshifts of Finite Type

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Abstract

Subshifts of finite type (SFTs) are sets of colorings of the plane that avoid a finite family of forbidden patterns. In this article, we are interested in the behavior of the growth of the number of valid patterns in SFTs. While entropy h corresponds to growths that are squared exponential 2^{hn²}, surface entropy (introduced in Pace’s thesis in 2018) corresponds to the eventual linear term in exponential growths. We give here a characterization of the possible surface entropies of SFTs as the Π₃ real numbers of [0,+∞].

BibTeX - Entry

@InProceedings{callard_et_al:LIPIcs.ICALP.2021.122,
  author =	{Callard, Antonin and Vanier, Pascal},
  title =	{{Computational Characterization of Surface Entropies for \mathbb{Z}² Subshifts of Finite Type}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{122:1--122:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14191},
  URN =		{urn:nbn:de:0030-drops-141914},
  doi =		{10.4230/LIPIcs.ICALP.2021.122},
  annote =	{Keywords: surface entropy, arithmetical hierarchy of real numbers, 2D subshifts, symbolic dynamics}
}

Keywords: surface entropy, arithmetical hierarchy of real numbers, 2D subshifts, symbolic dynamics
Collection: 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)
Issue Date: 2021
Date of publication: 02.07.2021

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