On the optimisation of Reed-Muller expressions

Abstract

The choice of a set of basis functions with which to represent Reed-Muller canonical forms makes less and less difference, on average, to the efficiency, as measured by the number of non-zero terms, in which they can be expressed, as the number of variables in the function increases. This is because the possible efficiency gain itself declines exponentially in the general case, independently of the basis used. We explain why this is so, and using an integrated set of software tools, including a genetic algorithm, we provide supporting evidence of the phenomenon.