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Algebra i logika, 2017, Volume 56, Number 1, Pages 55–92
DOI: https://doi.org/10.17377/alglog.2017.56.103 (Mi al778) 		 
This article is cited in 8 scientific papers (total in 8 papers)

The computational power of infinite time Blum–Shub–Smale machines

P. Koepkea, A. S. Morozovbc

a Math. Inst., Rheinische Friedrich-Wilhelms-Univ. Bonn, Endenicher Allee 60, Bonn, 53115 Germany
b Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090 Russia
c Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090 Russia
Full-text PDF (313 kB) Citations (8)
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DOI: https://doi.org/10.17377/alglog.2017.56.103
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 $\mathbb R\cap L_{\omega^\omega}$.
Keywords: infinite time Blum–Shub–Smale machines, infinite computations, iterated jump, ITBM, BSS-machines, computable reals.
Funding agency Grant number
Alexander von Humboldt-Stiftung
Supported by the Alexander von Humboldt Foundation. The results were obtained during the second author's visit to the University of Bonn in spring 2012.
Received: 18.08.2015
Revised: 24.02.2016
English version:
Algebra and Logic, 2017, Volume 56, Issue 1, Pages 37–62
DOI: https://doi.org/10.1007/s10469-017-9425-x
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: P. Koepke, A. S. Morozov, “The computational power of infinite time Blum–Shub–Smale machines”, Algebra Logika, 56:1 (2017), 55–92; Algebra and Logic, 56:1 (2017), 37–62
Citation in format AMSBIB
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\by P.~Koepke, A.~S.~Morozov
\paper The computational power of infinite time Blum--Shub--Smale machines
\jour Algebra Logika
\yr 2017
\vol 56
\issue 1
\pages 55--92
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\crossref{https://doi.org/10.17377/alglog.2017.56.103}
\transl
\jour Algebra and Logic
\yr 2017
\vol 56
\issue 1
\pages 37--62
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    • This publication is cited in the following 8 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Алгебра и логика Algebra and Logic
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