Uniformity of systems of monotone functions (Q1878547)

Let \(\mathfrak U\) be a finite system of functions from \(P_k\), \(k\geq 2\), and \(\Phi\) be a formula over \(\mathfrak U\). For precomplete classes of monotone functions of \(k\)-valued logic for \(k\leq 7\) it is shown that for any finite system of functions \(A\) generating one of the classes, constants \(c\) and \(d\) are found so that for any function \(f\) from \([A]\) the depth \(D(f)\) and complexity \(L(f)\) of the function \(f\) in the class of formulas over \(A\) are correlated as \(D(f)\leq c\log_2L(f)+d\).