Abstract

We present a compositional proof of correctness for a binary decision diagram (BDD) manager used in the context of a propositional satisfiability checker implemented using SingleThreaded Objects (stobjs) in ACL2. The use of stobjs affords the definition of an efficient BDD manager which ensures unique construction, allows constant-time comparison, and caches previously computed results. The use of ACL2 means we can prove that the BDD manager implements the prescribed task of building a normal-form representation of a boolean formula. We divide the proof requirements into (1) showing that a simpler set of BDD functions is correct, and (2) showing that the stobj-based BDD functions return values consistent with these simpler functions. We conclude the paper with a discussion of future extensions and refinements to the BDD manager presented.

Citations