Information Distance Revisited
Information Theory
2019-10-03 v2 math.IT
Abstract
We consider the notion of information distance between two objects x and y introduced by Bennett, G\'acs, Li, Vitanyi, and Zurek [1] as the minimal length of a program that computes x from y as well as computing y from x, and study different versions of this notion. It was claimed by Mahmud [11] that the prefix version of information distance equals max(K(x|y), K(y|) + O(1) (this equality with logarithmic precision was one of the main results of the paper by Bennett, G\'acs, Li, Vitanyi, and Zurek). We show that this claim is false, but does hold if the information distance is at least super logarithmic.
Cite
@article{arxiv.1807.11087,
title = {Information Distance Revisited},
author = {Bruno Bauwens and Alexander Shen},
journal= {arXiv preprint arXiv:1807.11087},
year = {2019}
}
Comments
Preliminary version, published for reference purposes