An Efficient Interpolation-Based Projected Sum of Product Decomposition via Genetic Algorithm

Projected Sum of Products (P-SOP) is a bounded multi-level representation. The synthesis of P-SOP representation is based on decomposing the input space with respect to the orthogonal basis x(i)'circle plus p(X-(i)) and x(i)circle plus p(X-(i)) where x(i) is an input variable and p(X-(i)) is a function of all variables except x(i). Different p(X-(i)) may result in different areas after synthesis. Therefore, to obtain a minimal P-SOP circuit, it is important to select an appropriate variable xi and function p((X(i))). In this paper, we propose a Genetic Algorithm to efficiently determine x(i) and p(X-(i)). Experimental results show that the proposed approach saves 81% CPU time in searching such a pair as compared to an exhaustive method without sacrificing the optimality.