Dimension-reducible Boolean Functions based on Affine Spaces

We define and study a new class of regular Boolean functions called D-reducible. A D-reducible function, depending on all its n input variables, can be studied and synthesized in a space of dimension strictly smaller than n. We show that the D-reducibility property can be efficiently tested, in time polynomial in the representation of f, that is, an initial SOP form of f. A D-reducible function can be efficiently decomposed, giving rise to a new logic form, that we have called DredSOP. This form is shown here to be generally smaller than the corresponding minimum SOP form. Our experiments have also shown that a great number of functions of practical importance are indeed D-reducible, thus validating the overall interest of our approach.