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| on the number of infinite sequences with trivial initial segment complexity | |
| George Barmpalias; T.F. Sterkenburg | |
| 2011 | |
| Source | Theoretical Computer Science
 |
| ISSN | 0304-3975 |
| Volume | 412Issue:52Pages:7133-7146 |
| English Abstract | 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. |
| Indexed Type | SCIENCEDIRECT ; EI |
| Keyword | Kolmogorov Complexity K-trivial Sets Arithmetical Complexity Trees |
| Department | 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 |
| Language | 英语 |
| WOS ID | WOS:000298024600005 |
| Citation statistics | |
| Content Type | 期刊论文 |
| URI | http://ir.iscas.ac.cn/handle/311060/16020 |
| Collection | 中国科学院软件研究所 |
| Recommended Citation 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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