Computability of Countable Subshifts

  • Douglas Cenzer
  • Ali Dashti
  • Ferit Toska
  • Sebastian Wyman
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6158)

Abstract

The computability of countable subshifts and their members is examined. Results include the following. Subshifts of Cantor-Bendixson rank one contain only eventually periodic elements. Any rank one subshift, in which every limit point is periodic, is decidable. Subshifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (\(\Pi^0_1\)) subshifts of rank two contain only computable elements, but \(\Pi^0_1\) subshifts of rank three may contain members of arbitrary c. e. degree. There is no subshift of rank ω.

Keywords

Computability Symbolic Dynamics \(\Pi^0_1\) Classes 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Douglas Cenzer
    • 1
  • Ali Dashti
    • 1
  • Ferit Toska
    • 1
  • Sebastian Wyman
    • 1
  1. 1.Department of MathematicsUniversity of FloridaGainesville

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