Scalable Probabilistic Program Verification via Typed Extended Decision Diagrams

2026-06-12

AI Summary

Existing approaches to verifying probabilistic programs suffer from severe scalability limitations due to the combinatorial explosion in the size of weakest pre-expectation (WPE) representations caused by loop unrolling. This work proposes a novel method based on Typed Extended Decision Diagrams (TEDDs), which, for the first time, leverages TEDDs to compactly represent WPEs. By integrating SMT-based pruning with tailored deductive proof rules, the approach enables direct symbolic reasoning at the TEDD level. This strategy dramatically compresses the logical representation, circumventing the state-space explosion inherent in conventional unrolling techniques. As a result, verification efficiency improves by several orders of magnitude, enabling the scalable and effective analysis of complex discrete probabilistic programs.

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.

Problem

• probabilistic program verification
• weakest pre-expectations
• loop unrolling
• representation explosion
• scalability

Innovation

• Typed Extended Decision Diagrams
• Weakest Pre-Expectations
• Probabilistic Program Verification
• SMT-based Pruning
• Deductive Verification