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Algebra i logika, 2020, Volume 59, Number 6, Pages 627–648
DOI: https://doi.org/10.33048/alglog.2020.59.602 (Mi al2640) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Characterizations of ITBM-computability. I

P. Koepkea, A. S. Morozovb

a Math. Inst., Rheinische Friedrich-Wilhelms-Univ. Bonn, Bonn, GERMANY
b Sobolev Institute of Mathematics, Siberian Branch of the Russian Academy of Sciences, Novosibirsk
Full-text PDF (293 kB) Citations (4)
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DOI: https://doi.org/10.33048/alglog.2020.59.602
Abstract: We examine whether some well-known properties of partial recursive functions are valid for ITBM-computable functions, i.e., functions which can be computed with infinite time Blum–Shub–Smale machines. It is shown that properties of graphs of ITBM-computable functions differ from the usual properties of graphs of partial recursive functions. All possible ranges of ITBM-computable functions are described, and we consider the existence problem for ITBM-computable bijections between ITBM-computable sets of the same cardinality.
Keywords: Blum–Shub–Smale machine, ITBM-computable functions, partial recursive functions, graph of function.
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 2017.
Received: 05.06.2020
Revised: 05.03.2021
English version:
Algebra and Logic, 2021, Volume 59, Issue 6, Pages 423–436
DOI: https://doi.org/10.1007/s10469-021-09622-2
Bibliographic databases:
Document Type: Article
UDC: 510.5
Language: Russian
Citation: P. Koepke, A. S. Morozov, “Characterizations of ITBM-computability. I”, Algebra Logika, 59:6 (2020), 627–648; Algebra and Logic, 59:6 (2021), 423–436
Citation in format AMSBIB
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    		Алгебра и логика Algebra and Logic
     
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