深度，高度和DNR度

IF 0.7 4区数学

Discrete Mathematics and Theoretical Computer Science Pub Date : 2015-08-17 DOI:10.23638/DMTCS-19-4-2

Philippe Moser, F. Stephan

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引用次数: 10

摘要

我们在递归理论的背景下研究了Bennett深度序列;我们特别研究了\(O(1)\text {-deep}_K\)、\(O(1)\text {-deep}_C\)、有序\(\text {-deep}_K\)和有序\(\text {-deep}_C\)序列的概念。我们的主要结果是Martin-Lof随机集不是有序的\(\text {-deep}_C\)，每个多一度包含一个不是\(O(1)\text {-deep}_C\)的集，\(O(1)\text {-deep}_C\)集和有序的\(\text {-deep}_K\)集具有高或DNR图灵度，没有K-trival集是\(O(1)\text {-deep}_K\)。

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Depth, Highness and DNR degrees

We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of \(O(1)\text {-deep}_K\), \(O(1)\text {-deep}_C\), order\(\text {-deep}_K\) and order\(\text {-deep}_C\) sequences. Our main results are that Martin-Lof random sets are not order\(\text {-deep}_C\), that every many-one degree contains a set which is not \(O(1)\text {-deep}_C\), that \(O(1)\text {-deep}_C\) sets and order\(\text {-deep}_K\) sets have high or DNR Turing degree and that no K-trival set is \(O(1)\text {-deep}_K\).

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来源期刊

Discrete Mathematics and Theoretical Computer Science 数学-计算机：软件工程

自引率

14.30%

发文量

期刊介绍： DMTCS is a open access scientic journal that is online since 1998. We are member of the Free Journal Network. Sections of DMTCS Analysis of Algorithms Automata, Logic and Semantics Combinatorics Discrete Algorithms Distributed Computing and Networking Graph Theory.