Equivalent characterizations of partial randomness for a recursively enumerable real

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dc.creatorTadaki, Kohtaro
dc.date2008-05-17
dc.date.accessioned2026-07-07T09:39:37Z
dc.date.available2026-07-07T09:39:37Z
dc.descriptionA real number αis called recursively enumerable if there exists a computable, increasing sequence of rational numbers which converges to α. The randomness of a recursively enumerable real αcan be characterized in various ways using each of the notions; program-size complexity, Martin-Löf test, Chaitin's Ωnumber, the domination and Ω-likeness of α, the universality of a computable, increasing sequence of rational numbers which converges to α, and universal probability. In this paper, we generalize these characterizations of randomness over the notion of partial randomness by parameterizing each of the notions above by a real number T\in(0,1]. We thus present several equivalent characterizations of partial randomness for a recursively enumerable real number.
dc.description19 pages, LaTeX2e, no figures
dc.identifierhttps://arxiv.org/abs/0805.2691
dc.identifierhttp://arxiv.org/abs/0805.2691
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/161238
dc.subjectInformation Theory
dc.subjectComputational Complexity
dc.subjectLogic
dc.titleEquivalent characterizations of partial randomness for a recursively enumerable real
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