Email this article The Computational Power of Infinite Time Blum–Shub–Smale Machines
- Authors: Koepke P.1, Morozov A.S.2,3
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Affiliations:
- Math. Inst., Rheinische Friedrich–Wilhelms–Univ. Bonn
- Sobolev Institute of Mathematics
- Novosibirsk State University
- Issue: Vol 56, No 1 (2017)
- Pages: 37-62
- Section: Article
- URL: https://journal-vniispk.ru/0002-5232/article/view/234020
- DOI: https://doi.org/10.1007/s10469-017-9425-x
- ID: 234020
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Abstract
Functions that are computable on infinite time Blum–Shub–Smale machines (ITBM) are characterized via iterated Turing jumps, and we propose a normal form for these functions. It is also proved that the set of ITBM computable reals coincides with ℝ∩Lωω.
About the authors
P. Koepke
Math. Inst., Rheinische Friedrich–Wilhelms–Univ. Bonn
Author for correspondence.
Email: Koepke@math.uni-bonn.de
Germany, Endenicher Allee 60, Bonn, 53115
A. S. Morozov
Sobolev Institute of Mathematics; Novosibirsk State University
Email: Koepke@math.uni-bonn.de
Russian Federation, pr. Akad. Koptyuga 4, Novosibirsk, 630090; ul. Pirogova 1, Novosibirsk, 630090
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