Symbolic Manipulation of Boolean Functions Using a Graphical Representation

In this paper we describe a data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations of Lee and Akers, but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a graph of size exponential in the number of arguments, many of the functions encountered in typical applications have a more reasonable representation. Our algorithms are quite efficient as long as the graphs being operated on do not grow too large. We present performance measurements obtained while applying these algorithms to problems in logic design verification.