Publikation: Randomness and Degree Theory for Infinite Time Register Machines
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2016
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Computability. 2016, 5(2), pp. 181-196. ISSN 2211-3568. eISSN 2211-3576. Available under: doi: 10.3233/COM-160055
Zusammenfassung
A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of van Lambalgen's theorem holds. This is then applied to obtain results on the structure of ITRM-degrees. Finally, we consider autoreducibility for ITRMs and show that randomness implies non-autoreducibility.
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CARL, Merlin, 2016. Randomness and Degree Theory for Infinite Time Register Machines. In: Computability. 2016, 5(2), pp. 181-196. ISSN 2211-3568. eISSN 2211-3576. Available under: doi: 10.3233/COM-160055BibTex
@article{Carl2016Rando-32737,
year={2016},
doi={10.3233/COM-160055},
title={Randomness and Degree Theory for Infinite Time Register Machines},
number={2},
volume={5},
issn={2211-3568},
journal={Computability},
pages={181--196},
author={Carl, Merlin}
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<dcterms:abstract xml:lang="eng">A concept of randomness for infinite time register machines (ITRMs) is defined and studied. In particular, we show that for this notion of randomness, computability from mutually random reals implies computability and that an analogue of van Lambalgen's theorem holds. This is then applied to obtain results on the structure of ITRM-degrees. Finally, we consider autoreducibility for ITRMs and show that randomness implies non-autoreducibility.</dcterms:abstract>
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