A Functional Canonical Form

In the field of switching theory the important problem of designing switching circmts economically has been attacked from many different points of view. Thus far, no solution has been completely satisfactory. These solutions have been effected primarily by the use of properties of Boolean algebra or of switching elements. In the opinion of this author the probability of achieving a satisfactory solution would be increased by an approach which rches on more fundamental and intrinsic properties, the structural properties of the switching functions representing the final networks desired. Except for references [ll and [2] in which it is shown that economical switching networks exist when the associated switching function possesses the structural property of decomposability, this viewpoint has been overlooked. In this paper, this viewpoint is investigated further, and as a result a functional canonical form is established. The utility of this canonical form in practice and theory should be comparable to that of the tree or pyramid circuit.