On the lower bound for the maximum potential of plain circuits with several outputs through the area

In this paper we consider the relationship between the area and the maximum potential of plain circuits realizing Boolean operators. The maximal potential is a complexity measure of plain circuits, reflecting the power consumption of the circuit in the worst case, it is also often called activity. It is equal to the maximum number of outputs of circuit elements equal to $1$, where the maximum is taken over all input sets of the circuit. It was porved that for arbitrary Boolean operator $f$, its maximal potential $\widehat{U}$ is greater or equal than $\sqrt{S}/4\sqrt{2}$ where $S$ is the area of the minimal plain circuit realizing $f$.