Logical Operations and Kolmogorov Complexity II
نویسندگان
چکیده
We investigate Kolmogorov complexity of the problem (a ! c) ^ (b ! d), deened as the minimum length of a program that given a outputs c and given b outputs d. We prove that unlike all known problems of this kind its complexity is not expressible in terms of Kolmogorov complexity of a, b, c, and d, their pairs, triples etc. This solves the problem posed in 9]. In the second part we consider the following theorem: there are two strings, whose mutual information is large but which have no common information in a strong sense. This theorem was proven in 7] via a non-constructive argument. We present a constructive proof, thus solving a problem posed in 7].
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Logical operations and Kolmogorov complexity
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