Finding all simple disjunctive decompositions using irredundant sum-of-products forms

Finding disjunctive decompositions is an important technique to realize compact logic networks. Simple disjunctive decomposition is a basic and useful concept, that extracts a single output subblock function whose input variable set is disjunctive from the other part. The paper presents a method for finding simple disjunctive decompositions by generating irredundant sum-of-products forms and applying factorization. We prove that all simple disjunctive decompositions can be extracted in our method, namely all possible decompositions are included in the factored logic networks. Experimental results show that our method can efficiently extract all the simple disjunctive decompositions of the large scale functions. Our result clarifies the relationship between the functional decomposition method and the two-level logic factorization method.