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The Recognizability Strength of Infinite Time Turing Machines with Ordinal Parameters

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2017

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Schlicht, Philipp

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https://doi.org/10.1007/978-3-319-58741-7_20
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KARI, Jarkko, ed. and others. Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, proceedings. Cham: Springer, 2017, pp. 198-209. Lecture Notes in Computer Science. 10307. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-58740-0. Available under: doi: 10.1007/978-3-319-58741-7_20

Zusammenfassung

We study infinite time Turing machines that attain a special state at a given class of ordinals during the computation. We prove results about sets that can be recognized by these machines. For instance, the recognizable sets of natural numbers with respect to the cardinal-detecting infinite time Turing machines introduced in [Hab13] are contained in a countable level of the constructible hierarchy, and the recognizable sets of natural numbers with respect to finitely many ordinal parameters are constructible.

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510 Mathematik

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13th Conference on Computability in Europe, CiE 2017, 12. Juni 2017 - 16. Juni 2017, Turku, Finland
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ISO 690CARL, Merlin, Philipp SCHLICHT, 2017. The Recognizability Strength of Infinite Time Turing Machines with Ordinal Parameters. 13th Conference on Computability in Europe, CiE 2017. Turku, Finland, 12. Juni 2017 - 16. Juni 2017. In: KARI, Jarkko, ed. and others. Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, proceedings. Cham: Springer, 2017, pp. 198-209. Lecture Notes in Computer Science. 10307. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-58740-0. Available under: doi: 10.1007/978-3-319-58741-7_20
BibTex
@inproceedings{Carl2017-05-12Recog-43665,
  year={2017},
  doi={10.1007/978-3-319-58741-7_20},
  title={The Recognizability Strength of Infinite Time Turing Machines with Ordinal Parameters},
  number={10307},
  isbn={978-3-319-58740-0},
  issn={0302-9743},
  publisher={Springer},
  address={Cham},
  series={Lecture Notes in Computer Science},
  booktitle={Unveiling Dynamics and Complexity : 13th Conference on Computability in Europe, CiE 2017, Turku, Finland, June 12-16, 2017, proceedings},
  pages={198--209},
  editor={Kari, Jarkko},
  author={Carl, Merlin and Schlicht, Philipp}
}
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