EXOR Projected Sum of Products

Bernasconi, Anna and Ciriani, Valentina and Cordone, Roberto (2006) EXOR Projected Sum of Products. Technical Report del Dipartimento di Informatica . Università di Pisa, Pisa, IT.

In this paper we introduce a new algebraic form for Boolean function representation, called \emph{EXOR-Projected Sum of Products} (\emph{EP-SOP}), resulting in a four level network that can be easily implemented in practice. We prove that deriving an optimal EP-SOP from an optimal SOP form is a hard problem ($NP^{NP}$-hard); 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 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, we recommend the use of the proposed approach as a post-processing step after SOP minimization.