EXOR Projected Sum of Products

In this paper, the authors introduce a new algebraic form for Boolean function representation, called EXOR-projected sum of products (EP-SOP), resulting in a four level network that can be easily implemented in practice. The authors prove that deriving an optimal EP-SOP from an optimal sum of products (SOP) form is a hard problem (NP ^NP-hard); nevertheless the authors 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 the 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, the authors recommend the use of the proposed approach as a postprocessing step after SOP minimization