on the number of infinite sequences with trivial initial segment complexity

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	on the number of infinite sequences with trivial initial segment complexity
	George Barmpalias; T.F. Sterkenburg
	2011
发表期刊	Theoretical Computer Science
ISSN	0304-3975
卷号	412 期号:52 页码:7133-7146
摘要	The sequences which have trivial prefix-free initial segment complexity are known as K -trivial sets, and form a cumulative hierarchy of length ω . We show that the problem of finding the number of K -trivial sets in the various levels of the hierarchy is Δ 3 0 . This answers a question of Downey/Miller/Yu (see Downey (2010)?[7,?Section 10.1.4]) which also appears in Nies (2009)?[17,?Problem 5.2.16]. We also show the same for the hierarchy of the low for K sequences, which are the ones that (when used as oracles) do not give a shorter initial segment complexity compared to the computable oracles. In both cases the classification Δ 3 0 is sharp.; The sequences which have trivial prefix-free initial segment complexity are known as K -trivial sets, and form a cumulative hierarchy of length ω . We show that the problem of finding the number of K -trivial sets in the various levels of the hierarchy is Δ 3 0 . This answers a question of Downey/Miller/Yu (see Downey (2010)?[7,?Section 10.1.4]) which also appears in Nies (2009)?[17,?Problem 5.2.16]. We also show the same for the hierarchy of the low for K sequences, which are the ones that (when used as oracles) do not give a shorter initial segment complexity compared to the computable oracles. In both cases the classification Δ 3 0 is sharp.
收录类别	SCIENCEDIRECT ; EI
关键词	Kolmogorov Complexity K-trivial Sets Arithmetical Complexity Trees
部门归属	aState Key Laboratory of Computer Science Institute of Software ChineseAcademy of Sciences Beijing 100190 P.O. Box 8718 China; bInstitute for Logic Language and Computation Universiteit van Amsterdam P.O. Box 94242 1090 GE Amsterdam The Netherlands
语种	英语
WOS记录号	WOS:000298024600005
引用统计
内容类型	期刊论文
URI标识	http://ir.iscas.ac.cn/handle/311060/16020
专题	中国科学院软件研究所
推荐引用方式 GB/T 7714	George Barmpalias,T.F. Sterkenburg. on the number of infinite sequences with trivial initial segment complexity[J]. Theoretical Computer Science,2011,412(52):7133-7146.
APA	George Barmpalias,&T.F. Sterkenburg.(2011).on the number of infinite sequences with trivial initial segment complexity.Theoretical Computer Science,412(52),7133-7146.
MLA	George Barmpalias,et al."on the number of infinite sequences with trivial initial segment complexity".Theoretical Computer Science 412.52(2011):7133-7146.