An improved complexity hierarchy on the depth of Boolean functions

Summary

Circuit depth is an important complexity measure for a Boolean function. Let some Boolean function of n variables have depth k according to an arbitrary binary basis Ω. For each j where [log n]≦j≦k we prove the existence of a Boolean function f with the following properties. f depends essentially on n variables and the depth of f according to Ω is exactly j Thus we state the best possible hierarchy result on the depth of all nondegenerate Boolean functions.