Application of Graph Theory Algorithms in Non-disjoint Functional Decomposition of Specific Boolean Functions

Abstract

Functional decomposition is a technique that allows to minimize Boolean functions that cannot be optimally minimized using other methods, such as variable reduction and linear decomposition. A heuristic method for finding nondisjoint decomposition has been proposed lately. In this paper, we examine how the usage of different graph theory techniques affects the computation time and the quality of the solution obtained. In total, six different approaches were analyzed. The results presented herein prove the advantages of the proposed approaches, showing that results obtained for standard benchmark M-out-of-20 functions are better than those presented in previous publication. Results obtained for randomly generated functions prove that time complexity and scalability are significantly better when using the heuristic graph coloring algorithm. However, quality of the solution is worse, in general