Read-polarity-once Boolean functions

Abstract

Efficient exact factoring algorithms are limited to read-once (RO) functions, where each variable appears once in the final Boolean expression. However, these algorithms present two important constraints: (1) they do not consider incompletely specified Boolean functions (ISF); and (2) they are not suitable for binate functions. To overcome the first drawback, an algorithm that finds RO expressions for ISF, whenever possible, is proposed. With respect to the second limitation, we propose a domain transformation that splits existing binate variables into two independent unate variables. Such domain transformation leads to ISF, which can be efficiently factored by applying the proposed algorithm. The combination of both contributions gives optimal results for a novel broader class of Boolean functions called read-polarity-once (RPO) functions, where each polarity (positive and negative) of a variable appears at most once in the factored form. Experimental results carried out over ISCAS'85 benchmark circuits have shown that RPO functions are significantly more frequent than RO functions.