Graph-Based Algorithms for Boolean Function Manipulation

TLDR

Functions are represented by directed acyclic graphs similar to Lee and Akers but with stricter variable ordering, and although worst‑case size is exponential, many practical functions admit more reasonable representations. The paper introduces a new data structure for representing Boolean functions and a set of manipulation algorithms. The data structure uses directed acyclic graphs with restricted variable ordering, and the algorithms operate with time complexity proportional to graph size, making them efficient when graphs remain moderate. Experimental results on logic design verification problems show the practicality of the proposed approach.

Abstract

In this paper we present a new 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 introduced by Lee [1] and Akers [2], 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 have time complexity proportional to the sizes of the graphs being operated on, and hence are quite efficient as long as the graphs do not grow too large. We present experimental results from applying these algorithms to problems in logic design verification that demonstrate the practicality of our approach.