On the activity of cell circuits realising the system of all conjunctions

We investigate the activity of cell circuits, the measure of their complexity, which describes the functioning of such circuits from the energy point of view. For the system $K_n$ of all elementary conjunctions of $n$ variables we find the order of the minimal activity as $n\to\infty$. We prove that it is impossible to reach simultaneously the minimal in order activity and complexity of realising the system $K_n$ in the class of cell circuits.