Logic Synthesis of EXOR Projected Sum of Products

Abstract

We define a new algebraic form for Boolean function representation, called EXOR-Projected Sum of Products(EP-SOP), consisting in a four level network that can be easily implemented in practice. Deriving an optimal EP-SOP from an optimal SOP form is a NPNP-hard problem; nevertheless we propose a very efficient approximation algorithm, which returns, in polynomial time, an EP-SOP form whose cost is guaranteed to be near the optimum. Experimental evidence shows that for about 35% of the classical synthesis benchmarks, EP-SOP networks have a smaller area and delay with respect to the optimal SOPs (sometimes gaining even 40-50% of the area). Since the computational times required are extremely short, we recommend the use of the proposed approach as a post-processing step after SOP minimization