Uniformity of a certain systems of functions of many-valued logic

Abstract

For any finite system A of functions of many-valued logic taking values in the set {0,1} such that a projection of A generates the class of all monotone boolean functions, it is proved that there exists constants c and d such that for an arbitrary function f e [A] the depth D(f) and the complexity L(f) of f in the class of formulas over A satisfy the relation D(f) ≤ clog2L(f) + d.