Normalized Information Distance is Not Semicomputable

Details Normalized Information Distance is Not Semicomputable Normalized Information Distance is Not Semicomputable

2010-06-16

arxiv.org/abs/1006.3275v1

Computer Science

Computational Complexity

9 pages, LaTeX, No figures, To appear in J. Comput. Syst. Sci

Scientific paper

Normalized information distance (NID) uses the theoretical notion of Kolmogorov complexity, which for practical purposes is approximated by the length of the compressed version of the file involved, using a real-world compression program. This practical application is called 'normalized compression distance' and it is trivially computable. It is a parameter-free similarity measure based on compression, and is used in pattern recognition, data mining, phylogeny, clustering, and classification. The complexity properties of its theoretical precursor, the NID, have been open. We show that the NID is neither upper semicomputable nor lower semicomputable.

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