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Towards a Theory of Infinite Time Blum-Shub-Smale Machines

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Book cover How the World Computes (CiE 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7318))

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Abstract

We introduce a generalization of Blum-Shub-Smale machines on the standard real numbers ℝ that is allowed to run for a transfinite ordinal number of steps before terminating. At limit times, register contents are set to the ordinary limit of previous register contents in ℝ. It is shown that each such machine halts before time ω ω or diverges. We undertake first steps towards estimating the computational strength of these new machines.

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References

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Authors and Affiliations

  1. Mathematisches Institut, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Peter Koepke & Benjamin Seyfferth

Authors
  1. Peter Koepke
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  2. Benjamin Seyfferth
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Editor information

Editors and Affiliations

  1. School of Mathematics, University of Leeds, LS2 9JT, Leeds, UK

    S. Barry Cooper

  2. Computer Laboratory, University of Cambridge, Willialm Gates Building, J.J. Thomson Avenue, CB3 0FD, Cambridge, UK

    Anuj Dawar

  3. Institute for Logic, Language and Computation, University of Amsterdam, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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© 2012 Springer-Verlag Berlin Heidelberg

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Koepke, P., Seyfferth, B. (2012). Towards a Theory of Infinite Time Blum-Shub-Smale Machines. In: Cooper, S.B., Dawar, A., Löwe, B. (eds) How the World Computes. CiE 2012. Lecture Notes in Computer Science, vol 7318. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30870-3_41

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  • DOI: https://doi.org/10.1007/978-3-642-30870-3_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-30869-7

  • Online ISBN: 978-3-642-30870-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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