#5471. Normalized information distance and the oscillation hierarchy

August 2026publication date
Proposal available till 19-05-2025
4 total number of authors per manuscript0 $

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Journal’s subject area:
Applied Mathematics;
Computational Theory and Mathematics;
Theoretical Computer Science;
Computer Networks and Communications;
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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.
Keywords:
Independence; Information distance; Kolmogorov complexity

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