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Analogues of Chaitinʼs Omega in the computably enumerable sets

Barmpalias, G., Hölzl, R., Lewis-Pye, Andrew and Merkle, W. (2013) Analogues of Chaitinʼs Omega in the computably enumerable sets. Information Processing Letters, 113 (5-6). pp. 171-178. ISSN 0020-0190

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Identification Number: 10.1016/j.ipl.2013.01.007


We show that there are computably enumerable (c.e.) sets with maximum initial segment Kolmogorov complexity amongst all c.e. sets (with respect to both the plain and the prefix-free version of Kolmogorov complexity). These c.e. sets belong to the weak truth table degree of the halting problem, but not every weak truth table complete c.e. set has maximum initial segment Kolmogorov complexity. Moreover, every c.e. set with maximum initial segment prefix-free complexity is the disjoint union of two c.e. sets with the same property; and is also the disjoint union of two c.e. sets of lesser initial segment complexity.

Item Type: Article
Official URL:
Additional Information: © 2013 Elsevier B.V.
Divisions: Mathematics
Subjects: Q Science > QA Mathematics
Date Deposited: 06 Aug 2013 11:51
Last Modified: 20 Jul 2021 00:58
Projects: 611501-10168, 2010-Y2GB03, ISCAS2010-01, D002-258/18.12.08
Funders: Research Fund for International Young Scientists, International Young Scientist Fellowship, Network Algorithms and Digital Information, Bulgarian National Science

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