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|Title:||Lowness properties and approximations of the jump||Authors:||Figueira, S.
|Issue Date:||6-Jan-2006||Citation:||Figueira, S., Nies, A., Stephan, F. (2006-01-06). Lowness properties and approximations of the jump. Electronic Notes in Theoretical Computer Science 143 (SPEC. ISS.) : 45-57. ScholarBank@NUS Repository. https://doi.org/10.1016/j.entcs.2005.05.025||Abstract:||We study and compare two combinatorial lowness notions: strong jump-traceability and well-approximability of the jump, by strengthening the notion of jump-traceability and ω-r.e. for sets of natural numbers. We prove that there is a strongly jump-traceable set which is not computable, and that if A′ is well-approximable then A is strongly jump-traceable. For r.e. sets, the converse holds as well. We characterize jump-traceability and the corresponding strong variant in terms of Kolmogorov complexity, and we investigate other properties of these lowness notions. © 2005 Elsevier B.V. All rights reserved.||Source Title:||Electronic Notes in Theoretical Computer Science||URI:||http://scholarbank.nus.edu.sg/handle/10635/104663||ISSN:||15710661||DOI:||10.1016/j.entcs.2005.05.025|
|Appears in Collections:||Staff Publications|
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