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Title: Lowness properties and approximations of the jump
Authors: Figueira, S.
Nies, A.
Stephan, F. 
Keywords: ω-r.e.
Kolmogorov complexity
Issue Date: 6-Jan-2006
Source: 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.
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
ISSN: 15710661
DOI: 10.1016/j.entcs.2005.05.025
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