Remark on minimization of depth of Boolean circuits

It is shown that Lozhkin’s method (1981) for minimization of the depth of formulas with a bounded number of changing types of elements in paths from input to output and Hoover-Klawe-Pippenger’s method (technical report in 1981, journal publication in 1984) for minimization of the depth of circuits with unbounded branching by insertion of trees from buffers with bounded branching of outputs for each buffer are dual to each other and can be proved by one and the same method.