On Beta-Shifts Having Arithmetical Languages | Zendy

Jakob Grue Simonsen | Zendy

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On Beta-Shifts Having Arithmetical Languages

Author(s) -

Jakob Grue Simonsen

Publication year - 2005

Publication title -

lecture notes in computer science

Language(s) - English

Resource type - Book series

SCImago Journal Rank - 0.249

H-Index - 400

eISSN - 1611-3349

pISSN - 0302-9743

ISBN - 3-540-28702-7

DOI - 10.1007/11549345_65

Subject(s) - arithmetic function , constructive , decidability , mathematics , constructive proof , beta (programming language) , discrete mathematics , combinatorics , arithmetic , computer science , programming language , process (computing)

Let β be a real number with 1 β β-shift is Δ$^{\rm 0}_{n}$ iff β is a Δn-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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