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Conference on Computability in Europe

CiE 2013: The Nature of Computation. Logic, Algorithms, Applications pp 231–240Cite as

Cardinal-Recognizing Infinite Time Turing Machines

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7921))

Abstract

We introduce a model of infinitary computation which enhances the infinite time Turing machine model slightly but in a natural way by giving the machines the capability of detecting cardinal stages of computation. The computational strength with respect to ITTMs is determined to be precisely that of the strong halting problem and the nature of the new characteristic ordinals (clockable, writable, etc.) is explored.

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References

  1. Hamkins, J.D., Lewis, A.: Infinite time Turing machines. Journal of Symbolic Logic 65(2), 567–604 (2000)

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  2. Koepke, P.: Turing computations on ordinals. Bulletin of Symbolic Logic 11(3), 377–397 (2005)

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  3. Welch, P.: The length of infinite time Turing computations. Bulletin of the London Mathematical Society 32(2), 129–136 (2000)

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Author information

Authors and Affiliations

  1. Mathematics Program, The Graduate Center of the City University of New York, 365 Fifth Avenue, New York, NY, 10016, USA

    Miha E. Habič

Authors
  1. Miha E. Habič
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Editors and Affiliations

  1. Dipartimento die Informatica, Sistemistica e Comunicazione, Università degli Studi di Milano-Bicocca, Piazza dell’Ateneo Nuovo 1, 20126, Milan, Italy

    Paola Bonizzoni

  2. Institute for Theoretical Computer Science, Mathematics and Operations Research, Faculty of Computer Science, Universität der Bundeswehr München, Werner-Heisenberg-Weg 39, 85577, Neubiberg, Germany

    Vasco Brattka

  3. Institute for Logic, Language and Computation, University of Amsterdam, Postbus 94242, 1090 GE, Amsterdam, The Netherlands

    Benedikt Löwe

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© 2013 Springer-Verlag Berlin Heidelberg

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Habič, M.E. (2013). Cardinal-Recognizing Infinite Time Turing Machines. In: Bonizzoni, P., Brattka, V., Löwe, B. (eds) The Nature of Computation. Logic, Algorithms, Applications. CiE 2013. Lecture Notes in Computer Science, vol 7921. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39053-1_27

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  • DOI: https://doi.org/10.1007/978-3-642-39053-1_27

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39052-4

  • Online ISBN: 978-3-642-39053-1

  • eBook Packages: Computer ScienceComputer Science (R0)

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