Bottom-up disjoint-support decomposition based on cofactor and boolean difference analysis

This paper presents a new approach for Boolean decomposition based on the Boolean difference and cofactor analysis. Two simple tests provide sufficient and necessary conditions to identify AND and exclusive-OR (XOR) decompositions. The proposed method can decompose an n-input function in O(n . log n) cofactor and O(n) equivalence test operations. Recently, 2-to-1 multiplexers (MUX) have also been used to perform such decomposition. However, MUX with more inputs has been neglected. We provide sufficient and necessary conditions to obtain MUX decompositions of functions with an arbitrary number of inputs.