Computable symbolic dynamics

Mathematical Logic Quarterly 54 (5):460-469 (2008)

Abstract
We investigate computable subshifts and the connection with effective symbolic dynamics. It is shown that a decidable Π01 class P is a subshift if and only if there exists a computable function F mapping 2ℕ to 2ℕ such that P is the set of itineraries of elements of 2ℕ. Π01 subshifts are constructed in 2ℕ and in 2ℤ which have no computable elements. We also consider the symbolic dynamics of maps on the unit interval
Keywords symbolic dynamics  Π01 classes  Computability
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DOI 10.1002/malq.200710066
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On the Computability of Fractal Dimensions and Hausdorff Measure.Ker-I. Ko - 1998 - Annals of Pure and Applied Logic 93 (1-3):195-216.

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