Functions with Small C-Measures

Abstract

Recall that the C-measure of a function is the maximum column multiplicity among a set of functional decompositions f(X ₁, X ₂), where X ₁ = (x ₁, x ₂, …, x _k ) and ${X}_{2} = ({x}_{k+1},{x}_{k+2},\ldots, {x}_{n}).$ The C-measure tends to increase exponentially with the number of input variables, n. However, many practical functions have small C-measures. This chapter considers classes of functions whose C-measures are small. Such functions can be efficiently realized by LUT cascades.