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Regular version of the site

Book chapter

Information Distance Revisited

P. 46:1-46:14.

We consider the notion of information distance between two objects x and y introduced by Bennett, Gács, Li, Vitanyi, and Zurek [C. H. Bennett et al., 1998] 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. In the above paper, it was shown that the prefix version of information distance equals max (K(x|y),K(y|x)) up to additive logarithmic terms. It was claimed by Mahmud [Mahmud, 2009] that this equality holds up to additive O(1)-precision. We show that this claim is false, but does hold if the distance is at least logarithmic. This implies that the original definition provides a metric on strings that are at superlogarithmically separated.

In book

Vol. 154: Leibniz International Proceedings in Informatics (LIPIcs). Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik, 2020.