On relation between non-disjoint decomposition and multiple-vertex dominators

Abstract

This paper addresses the problem of non-disjoint decomposition of Boolean functions. Decomposition has multiple applications in logic synthesis, testing and formal verification. First, we show that the problem of computing non-disjoint decompositions of Boolean functions can be reduced to the problem of finding multiple-vertex dominators of circuit graphs. Then, we prove that there exists an algorithm for computing all multiple-vertex dominators of a fixed size in polynomial time. Our result is important because no polynomial-time algorithm for non-disjoint decomposition of Boolean functions is known. A set of experiments on benchmark circuits illustrates our approach.