Binary Decision Diagrams by Shared Rewriting

In this paper we propose a uniform description of basic BDD theory and algorithms by means of term rewriting. Since a BDD is a DAG instead of a tree we need a notion of shared rewriting and develop appropriate theory. A rewriting system is presented by which canonical forms can be obtained. Various reduction strategies give rise to di erent algorithms. A layerwise strategy is proposed having the same time complexity as the traditional apply-algorithm, and the lazy strategy is studied, which resembles the existing up-one-algorithm. We show that these algorithms have incomparable performance.