The upper estimate of the volumetric power consumption of the circuits that implement boolean operators

In this work volume schemes which are generalization of plane schemes in space are considered. The class of the schemes implementing boolean operators was considered. For this class upper assessment of potential — a measure of the power equal to quantity of the circuit elements giving unit on this input pattern is received. It is shown that any operator of $n$ variables can be realized with a volume scheme whose potential does not exceed $\mathcal{O}(m \cdot 2^{n/3})$ if $m \leq n$ and $\mathcal{O}(\frac{m}{n} \cdot \sqrt[3]{n} \cdot 2^{n/3})$ if $m > n$.