Representation of boolean functions as arithmetic polynomials

The paper is concerned with representation of an ordered system (cortege) of Boolean functions by computing an arithmetic polynomial. By specifying operations of addition and multiplication on a set of corteges an algebra of corteges is introduced. The complexity of cortege implementation is estimated in terms of the number of polynomial addends. A class of polynomials is shown to exist for which the dependence between the implementation complexity and the cortege length is monotone. The complexity is in this case minimized through extended description of the specified system by additional functions.