Normalized Information Distance and the Oscillation Hierarchy
Logic
2019-11-15 v3 Computational Complexity
Information Theory
math.IT
Abstract
We study the complexity of approximations to the normalized information distance. We introduce a hierarchy of computable approximations 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 also prove a conditional undecidability result about independence.
Cite
@article{arxiv.1708.03583,
title = {Normalized Information Distance and the Oscillation Hierarchy},
author = {Klaus Ambos-Spies and Wolfgang Merkle and Sebastiaan A. Terwijn},
journal= {arXiv preprint arXiv:1708.03583},
year = {2019}
}
Comments
revised version of 2017 paper