We incorporate equations in binary decision diagrams (BDD). The resulting objects are called EQ-BDDs. A straightforward notion of ordered EQ-BDDs (EQ-OBDD) is defined, and it is proved that each EQ-BDD is logically equivalent to an EQ-OBDD. Moreover, on EQ-OBDDs 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 is proved to be correct and terminating, by means of recursive path ordering. The algorithm has been implemented, and applied to benchmarks known from literature. The performance of a prototype implementation is comparable to existing proposals.

Classical first-order logic (msc 03B10), Subsystems of classical logic (including intuitionistic logic) (msc 03B20), Mechanization of proofs and logical operations (msc 03B35), Logic in computer science (msc 03B70), Theorem proving (deduction, resolution, etc.) (msc 68T15)
Software Engineering [SEN]
Specification and Analysis of Embedded Systems

Groote, J.F, & van de Pol, J.C. (2000). Equational binary decision diagrams. Software Engineering [SEN]. CWI.