Computability of Countable Subshifts

We investigate the computability of countable subshifts in one dimension, and their members. Subshifts of Cantor-Bendixson rank one contain only eventually periodic elements. Any rank one subshift in 2Z is is decidable. Subshifts of rank two may contain members of arbitrary Turing degree. In contrast, effectively closed (Π0 1 ) subshifts of rank two contain only computable elements, but Π0 1 subshifts of rank three may contain members of arbitrary ∆0 2 degree. There is no subshift of rank ω.

• Type: Journal
• Year: 2010
• Where: CIE
• Authors: Douglas A. Cenzer, S. Ali Dashti, Ferit Toska, Sebastian Wyman
• Keywords: Applied Computing, Arbitrary Turing Degree, CIE 2010, Countable Subshifts, Periodic Elements