Barmpalias, G., Hölzl, R., Lewis, A. E. M. 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
Abstract
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: | http://www.journals.elsevier.com/information-proce... |
| Additional Information: | © 2013 Elsevier B.V. |
| Library of Congress subject classification: | Q Science > QA Mathematics |
| Sets: | Departments > Mathematics |
| Funders: | Research Fund for International Young Scientists, International Young Scientist Fellowship , Network Algorithms and Digital Information, Bulgarian National Science |
| Projects: | 611501-10168, 2010-Y2GB03, ISCAS2010-01, D002-258/18.12.08 |
| Date Deposited: | 06 Aug 2013 11:51 |
| URL: | http://eprints.lse.ac.uk/51461/ |
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