The Constrained-Input Problem

Given a combinational output function f and an input constraint φ = 0, there is a set G( f, φ) of output functions equivalent to f with respect to φ. A function belongs to G( f, φ), that is, provided its evaluations agree with those of f for all argument combinations satisfying the constraint φ = 0. We define the constrained-input problem as that of generating G( f, φ), given f and φ. A general solution for this problem is developed. Applications to the "don't-care" problem and to translator synthesis are discussed.