Normalized information distance and the oscillation hierarchy

• Verfasst von: Ambos-Spies, Klaus [VerfasserIn]
• Verfasst von: Merkle, Wolfgang [VerfasserIn]
• Verfasst von: Terwijn, Sebastiaan A. [VerfasserIn]
• Titel: Normalized information distance and the oscillation hierarchy
• Verf.angabe: Klaus Ambos-Spies, Wolfgang Merkle, Sebastiaan A. Terwijn
• Jahr: 2022
• Umfang: 12 S.
• Fussnoten: Available online 24 September 2021 ; Gesehen am 19.11.2021
• Titel Quelle: Enthalten in: Journal of computer and system sciences
• Ort Quelle: San Diego, Calif. [u.a.] : Elsevier, 1967
• Jahr Quelle: 2022
• Band/Heft Quelle: 124(2022) vom: März, Seite 65-76
• ISSN Quelle: 1090-2724
• DOI: doi:10.1016/j.jcss.2021.08.006
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: Independence
• Sach-SW: Information distance
• Sach-SW: Kolmogorov complexity
• K10plus-PPN: 1778007929

Abstract

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.