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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| Main Authors: | , , |
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| Format: | Article (Journal) |
| Language: | English |
| Published: |
2022
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| In: |
Journal of computer and system sciences
Year: 2022, Volume: 124, Pages: 65-76 |
| ISSN: | 1090-2724 |
| DOI: | 10.1016/j.jcss.2021.08.006 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: https://doi.org/10.1016/j.jcss.2021.08.006 Verlag, lizenzpflichtig, Volltext: https://www.sciencedirect.com/science/article/pii/S0022000021000866 
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| Author Notes: | Klaus Ambos-Spies, Wolfgang Merkle, Sebastiaan A. Terwijn |
| 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. |
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| Item Description: | Available online 24 September 2021 Gesehen am 19.11.2021 |
| Physical Description: | Online Resource |
| ISSN: | 1090-2724 |
| DOI: | 10.1016/j.jcss.2021.08.006 |