Abstract
Let β be a real number with 1 < β < 2. We prove that the language of the β-shift is Δ\(^{\rm 0}_{n}\) iff β is a Δ n -real. The special case where n is 1 is the independently interesting result that the language of the β-shift is decidable iff β is a computable real. The “if” part of the proof is non-constructive; we show that for Walters’ version of the β-shift, no constructive proof exists.
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Simonsen, J.G. (2005). On Beta-Shifts Having Arithmetical Languages. In: Jȩdrzejowicz, J., Szepietowski, A. (eds) Mathematical Foundations of Computer Science 2005. MFCS 2005. Lecture Notes in Computer Science, vol 3618. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11549345_65
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DOI: https://doi.org/10.1007/11549345_65
Publisher Name: Springer, Berlin, Heidelberg
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