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Hardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type

Authors Emmanuel Jeandel, Pascal Vanier



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LIPIcs.STACS.2013.490.pdf
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Emmanuel Jeandel
Pascal Vanier

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Emmanuel Jeandel and Pascal Vanier. Hardness of Conjugacy, Embedding and Factorization of multidimensional Subshifts of Finite Type. In 30th International Symposium on Theoretical Aspects of Computer Science (STACS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 20, pp. 490-501, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)
https://doi.org/10.4230/LIPIcs.STACS.2013.490

Abstract

Subshifts of finite type are sets of colorings of the plane defined by local constraints. They can be seen as a discretization of continuous dynamical systems. We investigate here the hardness of deciding factorization, conjugacy and embedding of subshifts of finite type (SFTs) in dimension d > 1. In particular, we prove that the factorization problem is Sigma^0_3-complete and that the conjugacy and embedding problems are Sigma^0_1-complete in the arithmetical hierarchy.
Keywords
  • Subshifts
  • Computability
  • Factorization
  • Embedding
  • Conjugacy

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