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ITRM-recognizability from Random Oracles

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2015

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https://doi.org/10.1007/978-3-319-20028-6_14
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BECKMANN, Arnold, ed. and others. Evolving Computability : 11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29-July 3, 2015 ; Proceedings. Cham [u.a.]: Springer, 2015, pp. 137-144. Lecture Notes in Computer Science. 9136. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-20027-9. Available under: doi: 10.1007/978-3-319-20028-6_14

Zusammenfassung

By a theorem of Sacks, if a real x is recursive relative to all elements of a set of positive Lebesgue measure, x is recursive. This statement - and the analogous statement for non-meagerness instead of positive Lebesgue measure - has been shown to carry over to many models of transfinite computations in [7]. Here, we start exploring another analogue concerning recognizability rather than computability. We show that, for Infinite Time Register Machines (ITRMs), if a real x is recognizable relative to all elements of a non-meager Borel set Y, then x is recognizable.

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Fachgebiet (DDC)
510 Mathematik

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infinite time register machines, algorithmic randomness, recognizability,

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11th Conference on Computability in Europe, CiE 2015, 29. Juni 2015 - 3. Juli 2015, Bucharest
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ISO 690CARL, Merlin, 2015. ITRM-recognizability from Random Oracles. 11th Conference on Computability in Europe, CiE 2015. Bucharest, 29. Juni 2015 - 3. Juli 2015. In: BECKMANN, Arnold, ed. and others. Evolving Computability : 11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29-July 3, 2015 ; Proceedings. Cham [u.a.]: Springer, 2015, pp. 137-144. Lecture Notes in Computer Science. 9136. ISSN 0302-9743. eISSN 1611-3349. ISBN 978-3-319-20027-9. Available under: doi: 10.1007/978-3-319-20028-6_14
BibTex
@inproceedings{Carl2015ITRMr-32710,
  year={2015},
  doi={10.1007/978-3-319-20028-6_14},
  title={ITRM-recognizability from Random Oracles},
  number={9136},
  isbn={978-3-319-20027-9},
  issn={0302-9743},
  publisher={Springer},
  address={Cham [u.a.]},
  series={Lecture Notes in Computer Science},
  booktitle={Evolving Computability : 11th Conference on Computability in Europe, CiE 2015, Bucharest, Romania, June 29-July 3, 2015 ; Proceedings},
  pages={137--144},
  editor={Beckmann, Arnold},
  author={Carl, Merlin}
}
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