Generalization of complexity estimates for flat circuits realizing partial Boolean operators

In this paper we consider the Shannon function of plain circuit activity for class of partial Boolean operators with restrictions on the number of different operator values. It is proved that for the class of partial operators with $m$ outputs, domain of cardinality $d$, and the number of different values not exceeding $r$ the mean and maximal orders of activity are equal to $(\sqrt{d}+m\sqrt{r}/\log r)\sqrt{\log r}$ by the order.