Normalized information distance and the oscillation hierarchy
نویسندگان
چکیده
We study the complexity of computing normalized information distance. introduce a hierarchy limit-computable functions by considering number oscillations. This is function version difference for sets. show that distance not in any level this hierarchy, strengthening previous nonapproximability results. As an ingredient to proof, we demonstrate conditional undecidability result about independence pairs random strings.
منابع مشابه
Normalized Information Distance and the Oscillation Hierarchy
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 ingredie...
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Article history: Received 23 October 2009 Received in revised form 11 June 2010 Accepted 28 June 2010 Available online 3 July 2010
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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 comp...
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ژورنال
عنوان ژورنال: Journal of Computer and System Sciences
سال: 2022
ISSN: ['1090-2724', '0022-0000']
DOI: https://doi.org/10.1016/j.jcss.2021.08.006