Area-driven Boolean bi-decomposition by function approximation

Bi-decomposition rewrites logic functions as the composition of simpler components. It is related to Boolean division, where a given function is rewritten as the product of a divisor and a quotient, but bi-decomposition can be defined for any Boolean operation of two operands. The key questions are how to find a good divisor and then how to compute the quotient. In this article, we select the divisor by approximation of the original function and then characterize by an incompletely specified function the full flexibility of the quotient for each binary operator. We target area-driven exact bi-decomposition, and we apply it to the bi-decomposition of Sum-of-Products (SOP) forms. We report experiments that exhibit significant gains in literals of SOP forms when rewritten as bi-decompositions with respect to the product operator. This suggests the application of this framework to other logic forms and binary operations, both for exact and approximate implementations.