Certain properties of nondegenerate superpositions in $P_k$

We investigate the possibility of obtaining a function which depends essentially on an arbitrary number of arguments from the functions of some finite system in $P_k$. We introduce a characteristic of the initial finite system, by means of which we express the complexity of obtaining the simplest function of the given number of variables. The estimate obtained below, for the Shannon function for the realization of functions in $P_k$ by formulas, is higher than the one known earlier.