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2009 The K-Degrees, Low for K Degrees,and Weakly Low for K Sets
Joseph S. Miller
Notre Dame J. Formal Logic 50(4): 381-391 (2009). DOI: 10.1215/00294527-2009-017


We call A weakly low for K if there is a c such that K A ( σ ) K ( σ ) c for infinitely many σ; in other words, there are infinitely many strings that A does not help compress. We prove that A is weakly low for K if and only if Chaitin's Ω is A-random. This has consequences in the K-degrees and the low for K (i.e., low for random) degrees. Furthermore, we prove that the initial segment prefix-free complexity of 2-random reals is infinitely often maximal. This had previously been proved for plain Kolmogorov complexity.


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Joseph S. Miller . "The K-Degrees, Low for K Degrees,and Weakly Low for K Sets." Notre Dame J. Formal Logic 50 (4) 381 - 391, 2009.


Published: 2009
First available in Project Euclid: 11 February 2010

zbMATH: 1213.03053
MathSciNet: MR2598870
Digital Object Identifier: 10.1215/00294527-2009-017

Primary: 68Q30
Secondary: 03D30 , 03D80

Keywords: Martin-Lof randomness , prefix-free Kolmogorov complexity

Rights: Copyright © 2009 University of Notre Dame


Vol.50 • No. 4 • 2009
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