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Ultrafilter and Non-standard Turing Machines

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Book cover Unconventional Computing (UC 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5204))

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Abstract

We consider several kinds of non-finitary computation, using ordinary Turing machines, as usual, as the reference case. The main problem which this short paper tries to address, is the problem of defining the output, or final message, of a machine which has run for a countably infinite number of steps. A modest scheme, using non-standard numbers, is proposed.

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Authors and Affiliations

  1. Department of Decision Sciences, University of South Africa (Pretoria), P.O. Box 392, Unisa, 0003,  

    Petrus H. Potgieter

  2. Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria, 0002

    Elemér E. Rosinger

Authors
  1. Petrus H. Potgieter
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  2. Elemér E. Rosinger
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Cristian S. Calude José Félix Costa Rudolf Freund Marion Oswald Grzegorz Rozenberg

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© 2008 Springer-Verlag Berlin Heidelberg

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Potgieter, P.H., Rosinger, E.E. (2008). Ultrafilter and Non-standard Turing Machines. In: Calude, C.S., Costa, J.F., Freund, R., Oswald, M., Rozenberg, G. (eds) Unconventional Computing. UC 2008. Lecture Notes in Computer Science, vol 5204. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85194-3_18

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  • DOI: https://doi.org/10.1007/978-3-540-85194-3_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-85193-6

  • Online ISBN: 978-3-540-85194-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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