A map approach to the solution of a class of boolean functional equations

Abstract

Typically, simultaneous Boolean equations are expressed by a set of relations Fi = fi, i = 1,2 ?, where the Fi and fi are switching functions of N binary variables. In many logical design problems, a special type of Boolean equation is often encountered; namely, F(A0, A1 ?, An?1, X0, X1 ?, Xm?1) = f(a1, a2 ?, ak, X0, X1 ?, Xm?1), in which the arguments Ai's and Xi's are binary variables and the a1's are implicit functions of the Ai's only. This paper presents a somewhat new approach to solving such special types of Boolean functional equations. The solution function (see reference 1) can be formulated and mapped on a Veitch chart, especially tailored to the present problem, and all possible sets of solutions of the implicit functions ai's which satisfy the original functional equation are obtained simultaneously. Other possible applications and extensions of this method are discussed also.