on the number of infinite sequences with trivial initial segment complexity
文献类型：期刊论文
| 作者 | George Barmpalias ; T.F. Sterkenburg |
| 刊名 | Theoretical Computer Science
 |
| 出版日期 | 2011 |
| 卷号 | 412期号:52页码:7133-7146 |
| 关键词 | Kolmogorov complexity K-trivial sets Arithmetical complexity Trees |
| ISSN号 | 0304-3975 |
| 中文摘要 | 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. |
| 英文摘要 | 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. |
| 收录类别 | SCIENCEDIRECT ; EI |
| 语种 | 英语 |
| WOS记录号 | WOS:000298024600005 |
| 公开日期 | 2013-10-08 |
| 源URL | [http://ir.iscas.ac.cn/handle/311060/16020]  |
| 专题 | 软件研究所_软件所图书馆_期刊论文 |
| 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. |
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来源：软件研究所
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