Information disclosure in the framework of Kolmogorov complexity

Abstract: We consider the network consisting of three nodes $1, 2, 3$ connected by two open channels $1\rightarrow 2$ and $1\rightarrow 3$. 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.