Equational Binary Decision Diagrams

Abstract We allow equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of reduced ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQOBDDs satisfiability and tautology checking can be done in constant time. Several procedures to eliminate equality from BDDs have been reported in the literature. Typical for our approach is that we keep equalities, and as a consequence do not employ the finite domain property. Furthermore, our setting does not strictly require Ackermann's elimination of function symbols. This makes our setting much more amenable to combinations with other techniques in the realm of automatic theorem proving, such as term rewriting. We introduce an algorithm, which for any propositional formula with equations finds an EQ-OBDD that is equivalent to it. The algorithm has been implemented, and applied to benchmarks known from literature. The performance of a prototype implementation is comparable to existing proposals.

Authors

• Jan Friso Groote
• Jaco van de Pol

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