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Title:
Kolmogorov complexity and computably enumerable sets
Author: Barmpalias, George ; Li, Angsheng
Keyword: Computably enumerable sets ; Kolmogorov complexity ; Relativization
Source: ANNALS OF PURE AND APPLIED LOGIC
Issued Date: 2013
Volume: 164, Issue:12, Pages:1187-1200
Indexed Type: SCI
Department: [Barmpalias, George; Li, Angsheng] Chinese Acad Sci, Inst Software, State Key Lab Comp Sci, Beijing 100190, Peoples R China.
Abstract: We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing research on this topic, along with recent developments and open problems. Besides this survey, our main original result is the following characterization of the computably enumerable sets with trivial initial segment prefix-free complexity. A computably enumerable set A is K-trivial if and only if the family of sets with complexity bounded by the complexity of A is uniformly computable from the halting problem. (C) 2013 Elsevier B.V. All rights reserved.
English Abstract: We study the computably enumerable sets in terms of the: (a) Kolmogorov complexity of their initial segments; (b) Kolmogorov complexity of finite programs when they are used as oracles. We present an extended discussion of the existing research on this topic, along with recent developments and open problems. Besides this survey, our main original result is the following characterization of the computably enumerable sets with trivial initial segment prefix-free complexity. A computably enumerable set A is K-trivial if and only if the family of sets with complexity bounded by the complexity of A is uniformly computable from the halting problem. (C) 2013 Elsevier B.V. All rights reserved.
Language: 英语
WOS ID: WOS:000324715300003
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Content Type: 期刊论文
URI: http://ir.iscas.ac.cn/handle/311060/16900
Appears in Collections:软件所图书馆_期刊论文

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Recommended Citation:
Barmpalias, George,Li, Angsheng. Kolmogorov complexity and computably enumerable sets[J]. ANNALS OF PURE AND APPLIED LOGIC,2013-01-01,164(12):1187-1200.
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