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An Explicit Solution to Post’s Problem over the Reals

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Fundamentals of Computation Theory (FCT 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3623))

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Abstract

In the BSS model of real number computations we prove a concrete and explicit semi-decidable language to be undecidable yet not reducible from (and thus strictly easier than) the real Halting Language. This solution to Post’s Problem over the reals significantly differs from its classical, discrete variant where advanced diagonalization techniques are only known to yield the existence of such intermediate Turing degrees.

Then we strengthen the above result and show as well the existence of an uncountable number of incomparable semi-decidable Turing degrees below the real Halting problem in the BSS model. Again, our proof will give concrete such problems representing these different degrees.

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Authors and Affiliations

  1. Department of Mathematics and Computer Science, Syddansk Universitet, Campusvej 55, 5230, Odense M, Denmark

    Klaus Meer & Martin Ziegler

Authors
  1. Klaus Meer
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  2. Martin Ziegler
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Editors and Affiliations

  1. Institut für Theoretische Informatik, Universität zu Lübeck, Germany

    Maciej Liśkiewicz

  2. Institut für Theoretische Informatik, Universität zu Lübeck, Ratzeburger Allee 160, 23538, Lübeck, Germany

    Rüdiger Reischuk

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© 2005 Springer-Verlag Berlin Heidelberg

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Meer, K., Ziegler, M. (2005). An Explicit Solution to Post’s Problem over the Reals. In: Liśkiewicz, M., Reischuk, R. (eds) Fundamentals of Computation Theory. FCT 2005. Lecture Notes in Computer Science, vol 3623. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11537311_41

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  • DOI: https://doi.org/10.1007/11537311_41

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-28193-1

  • Online ISBN: 978-3-540-31873-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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