On bounds for complexity of circuits of multi-input functional elements

In this paper we suggest a method to find lower bounds for complexity of circuits of functional elements. The essence of the method consists of replacing the initial, maybe quite complex, basis containing multi-input elements by a more simple basis, say, of two-input elements, with subsequent use of known lower bounds for complexity of circuits in the simple basis. The efficiency of this method is illustrated on particular examples of finding the asymptotics and even precise values of complexities of realisation of special Boolean functions, monotone Boolean functions and functions with small number of ones.