Restructuring logic representations with simple disjunctive decompositions

Simple disjunctive decomposition is a special case of logic function decompositions, where variables are divided into two disjoint sets and there is only one newly introduced variable. It offers an optimal structure for a singleoutput function. This paper presents two techniques that enable us to apply simple disjunctive decompositions with little overhead. Firstly, we propose a method to find simple disjunctive decomposition forms efficiently by limiting decomposition types to be found to two: a decomposition where the bound set is a set of symmetric variables and a decomposition where the output function is a 2-input function. Secondly, we propose an algorithm that constructs a new logic representation for a simple disjunctive decomposition just by assigning constant values to variables in the original representation. The algorithm enables us to apply the decomposition with keeping good structures of the original representation. We performed experiments for decomposing functions and confirmed the efficiency of our method. We also performed experiments for restructuring fanout free cones of multi-level logic circuits, and obtained better results than when not restructuring them.