Order of state functions and logic functions

Abstract

An n-variable state function is a function from {0, 1} n into R , where R is the set of real numbers. We have shown that there is a one to one correspondence between its minterm normal form and positive term normal form. This enables us to calculate the order of a state function by having its positive term normal form. We then define a logic function through a state function operated by the Heaviside function. Using the above-mentioned correspondence result, we devise its graphical expression and get a simple proof of the following celebrated result of Minsky and Papert: An n-variable parity function has order n.