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Proceedings 15th Annual IEEE Conference on Computational Complexity (2000)
Florence, Italy
July 4, 2000 to July 7, 2000
ISSN: 1093-0159
ISBN: 0-7695-0674-7
pp: 138
Nikolai K. Vereshchagin , Moscow State University
Michael V. Vyugin , Moscow State University
ABSTRACT
A string p is called a program to compute y given x if U(p; x) =y, where U denotes universal programming language. Kolmogorov complexity K(y\x) of y relative to x is defined as minimum length of a program to compute y given x. Let K(x) denote K(x\empty string) (Kolmogorov complexity of x) and let I(x : y) = K(x) +K(y) - K({x; y}) (the amount of mutual information in x; y). In the present paper we answer in negative the following question posed in [1]: Is it true that for any strings x; y there are independent minimum length programs p; q to translate between x; y, that is, is it true that for any x; y there are p; q such that U(p; x) =y, U(q; y) =x, the length of p is K(y\x), the length of q is K(x\y), and I(p : q) = 0(where the last three equalities hold up to an additive O(log(K(x\y)+K(y\x))) term)?
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CITATION

N. K. Vereshchagin and M. V. Vyugin, "Independent Minimum Length Programs to Translate between Given Strings," Proceedings 15th Annual IEEE Conference on Computational Complexity(CCC), Florence, Italy, 2000, pp. 138.
doi:10.1109/CCC.2000.856744
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