Slopes of 3-Dimensional Subshifts of Finite Type

  • Etienne Moutot
  • Pascal VanierEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10846)


In this paper we study the directions of periodicity of three-dimensional subshifts of finite type (SFTs) and in particular their slopes. A configuration of a subshift has a slope of periodicity if it is periodic in exactly one direction, the slope being the angles of the periodicity vector. In this paper, we prove that any \(\varSigma ^0_2\) set may be realized as a a set of slopes of an SFT.



The authors would like to thank anonymous reviewers who pointed out a mistake in a previous version of the paper.

This work was supported by grant TARMAC ANR 12 BS02 007 01.


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Authors and Affiliations

  1. 1.LIP, ENS de Lyon – CNRS – INRIA – UCBL – Université de LyonLyon CedexFrance
  2. 2.Laboratoire d’Algorithmique, Complexité et Logique Université de Paris-Est, LACL, UPECParisFrance

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