Synthesis on switching lattices of Dimension-reducible Boolean functions

In this paper we study the switching lattice synthesis of a special class of regular Boolean functions called D-reducible functions. D-reducible functions are functions whose points are completely contained in an affine space A strictly smaller than the whole Boolean cube {0, 1}ⁿ. The D-reducibility of a function f can be exploited in the lattice synthesis process: the idea is to independently find lattice implementations for the characteristic function of the subspace A and for the projection of f onto A, and to compose them in order to construct the lattice for f. The overall lattice area can be further reduced exploiting the peculiar structure of the affine subspaces of {0, 1}ⁿ. To this aim, we propose a method for implementing compact lattice representations of affine subspaces whose characteristic function is represented by the product of single literals and EXOR factors of two literals. The experimental results validate the proposed approach.