Theory of Computing Systems

, Volume 51, Issue 3, pp 352–371 | Cite as

Computability of Countable Subshifts in One Dimension

  • Douglas CenzerEmail author
  • Ali Dashti
  • Ferit Toska
  • Sebastian Wyman


We investigate the computability of countable subshifts in one dimension, and their members. Subshifts of Cantor–Bendixson rank two contain only eventually periodic elements. Any rank two subshift in 2 is decidable. Subshifts of rank three may contain members of arbitrary Turing degree. In contrast, effectively closed (\(\Pi^{0}_{1}\)) subshifts of rank three contain only computable elements, but \(\Pi^{0}_{1}\) subshifts of rank four may contain members of arbitrary \(\Delta^{0}_{2}\) degree. There is no subshift of rank ω+1.


Computability Symbolic dynamics \(\Pi^{0}_{1}\) classes 


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Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  • Douglas Cenzer
    • 1
    Email author
  • Ali Dashti
    • 1
  • Ferit Toska
    • 1
  • Sebastian Wyman
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesvilleUSA

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