Scalable Probabilistic Program Verification via Typed Extended Decision Diagrams

Abstract

Weakest pre-expectations are the probabilistic program analogue to weakest preconditions in classical programs. Deductive verification approaches aim to establish bounds on these quantitative expectations. Their automation has been successful in analysing a variety of discrete probabilistic programs. Key routines in that automation require reasoning about (partially unrolled) loops, however, the logical representation of weakest pre-expectations on such unrollings often explodes. In this paper, we develop typed extended decision diagrams (TEDDs), inspired by various extensions to binary decision diagrams. We demonstrate computing WPs represented as TEDDs, SMT-based pruning to further shrink their representation, and we lift some proof rules to operate on TEDDs. Finally, we demonstrate that TEDDs boost the scalability of deductive probabilistic program verification by orders of magnitudes over the state of the art.