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)-[deep.sub.K], O(1)-[deep.sub.C], order-[deep.sub.K] and order-[deep.sub.C] sequences. Our main results are that Martin-Lof random sets are not order-[deep.sub.C], that every many-one...

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Vydáno v:Discrete Mathematics and Theoretical Computer Science Ročník 19; číslo 4; s. 1
Hlavní autoři: Moser, Philippe, Stephan, Frank
Médium: Journal Article
Jazyk:angličtina
Vydáno: Nancy DMTCS 01.12.2017
Témata:
Algorithms
Computation
Fuzzy sets
Logic
Mathematical research
Numbers, Random
Sequences
Set theory
Singapore
ISSN:1462-7264, 1365-8050
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Shrnutí:We study Bennett deep sequences in the context of recursion theory; in particular we investigate the notions of O(1)-[deep.sub.K], O(1)-[deep.sub.C], order-[deep.sub.K] and order-[deep.sub.C] sequences. Our main results are that Martin-Lof random sets are not order-[deep.sub.C], that every many-one degree contains a set which is not O(1)-[deep.sub.C], that O(1)-[deep.sub.C] sets and order-[deep.sub.K] sets have high or DNR Turing degree and that no K-trival set is O(1)-[deep.sub.K]. Keywords: Bennett logical depth, Kolmogorov complexity, algorithmic randomness theory, computability and randomness.
Bibliografie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
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ISSN:1462-7264
1365-8050