Normalized information distance and the oscillation hierarchy

We study the complexity of computing the normalized information distance. We introduce a hierarchy of limit-computable functions by considering the number of oscillations. This is a function version of the difference hierarchy for sets. We show that the normalized information distance is not in any...

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Bibliographic Details
Published in:Journal of computer and system sciences 2022-03, Vol.124, p.65-76
Main Authors: Ambos-Spies, Klaus, Merkle, Wolfgang, Terwijn, Sebastiaan A.
Format: Article
Language:English
Subjects:
Independence
Information distance
Kolmogorov complexity
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Summary:We study the complexity of computing the normalized information distance. We introduce a hierarchy of limit-computable functions by considering the number of oscillations. This is a function version of the difference hierarchy for sets. We show that the normalized information distance is not in any level of this hierarchy, strengthening previous nonapproximability results. As an ingredient to the proof, we demonstrate a conditional undecidability result about the independence of pairs of random strings.
ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2021.08.006