Geodesic
Characterizations of ITBM-computability. I
Algebra i logika, Tome 59 (2020) no. 6, pp. 627-648

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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. 
@article{AL_2020_59_6_a1,
     author = {P. Koepke and A. S. Morozov},
     title = {Characterizations of {ITBM-computability.~I}},
     journal = {Algebra i logika},
     pages = {627--648},
     publisher = {mathdoc},
     volume = {59},
     number = {6},
     year = {2020},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/AL_2020_59_6_a1/}
}
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P. Koepke; A. S. Morozov. Characterizations of ITBM-computability. I. Algebra i logika, Tome 59 (2020) no. 6, pp. 627-648. http://geodesic.mathdoc.fr/item/AL_2020_59_6_a1/