Information disclosure in the framework of Kolmogorov complexity

08/03/2021

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by   Nikolay Vereshchagin, et al.

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We consider the network consisting of three nodes 1, 2, 3 connected by two open channels 1→ 2 and 1→ 3. The information present in the node 1 consists of four strings x,y,z,w. The nodes 2, 3 know x,w and need to know y,z, respectively. We want to arrange transmission of information over the channels so that both nodes 2 and 3 learn what they need and the disclosure of information is as small as possible. By information disclosure we mean the amount of information in the strings transmitted through channels about x,y,z,w (or about x,w). We are also interested in whether it is possible to minimize the disclosure of information and simultaneously minimize the length of words transferred through the channels.