SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Information distance from a question to an answer
Proceedings of the 13th ACM SIGKDD international conference on Knowledge discovery and data mining
Information shared by many objects
Proceedings of the 17th ACM conference on Information and knowledge management
New information distance measure and its application in question answering system
Journal of Computer Science and Technology
Nonapproximability of the normalized information distance
Journal of Computer and System Sciences
Information distance and its applications
CIAA'06 Proceedings of the 11th international conference on Implementation and Application of Automata
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Abstract: We investigate Kolmogorov complexity of the problem (a \rightarrow c) \wedge (b \rightarrow d), defined 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]. We give also an interpretation of both results in terms of Shannon entropy.