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The Computational Power of Infinite Time Blum–Shub–Smale Machines

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Algebra and Logic Aims and scope

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∩L ωω.

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Authors and Affiliations

  1. Math. Inst., Rheinische Friedrich–Wilhelms–Univ. Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    P. Koepke

  2. Sobolev Institute of Mathematics, pr. Akad. Koptyuga 4, Novosibirsk, 630090, Russia

    A. S. Morozov

  3. Novosibirsk State University, ul. Pirogova 1, Novosibirsk, 630090, Russia

    A. S. Morozov

Authors
  1. P. Koepke
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  2. A. S. Morozov
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Corresponding author

Correspondence to P. Koepke.

Additional information

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.

Translated from Algebra i Logika, Vol. 56, No. 1, pp. 55-92, January-February, 2017.

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Koepke, P., Morozov, A.S. The Computational Power of Infinite Time Blum–Shub–Smale Machines. Algebra Logic 56, 37–62 (2017). https://doi.org/10.1007/s10469-017-9425-x

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  • DOI: https://doi.org/10.1007/s10469-017-9425-x

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