Certificate-Aware Property-Directed Reachability

2026-05-15

AI Summary

This work addresses the limitations of traditional Property Directed Reachability (PDR) methods in hardware security verification, which often neglect certificate size, independent checking time, and reproducibility, thereby failing to meet end-to-end cost requirements in certification workflows. The paper proposes CAPDR, a certificate-aware PDR variant that, for the first time, treats certificate quality as a primary optimization objective. While preserving the soundness of standard PDR, CAPDR jointly optimizes runtime, certificate size, and checking time through a learning-driven strategy that governs blocking clause generalization, obligation ordering, and clause pushing. High-assurance and efficient certificate generation is further ensured via SAT-solver state transitions and a replay logging mechanism for verification. Evaluated on the 2024 Hardware Model Checking Competition benchmarks, CAPDR solves six additional instances, reduces the median proxy metric for certificate size by 24.6%, cuts checker time by 49%, and achieves further compression through post-processing.

Abstract

Property-Directed Reachability (PDR/IC3) is a standard workhorse for hardware safety verification, but most implementations are tuned primarily for time-to-answer and treat the produced invariant or counterexample as a secondary byproduct. In certified workflows, including recent hardware model checking competition rules, the certificate becomes a deliverable whose size, independent checking time, and reproducibility directly affect end-to-end cost. We present CAPDR, a certificate-aware variant of PDR that targets a joint objective over runtime, certificate size, and checker time, while keeping learning outside the trusted computing base. CAPDR exposes a small set of PDR choice points (blocker generalization, obligation ordering, clause pushing, and optional extensions) to a learned ranking policy, but preserves trust by design: every state-changing action is guarded by the same SAT checks as standard PDR, and a SAFE/UNSAFE claim is reported only after an independent checker validates the emitted invariant or trace. We formalize certificate-centric metrics and a replay log that records nondeterministic choices for artifact-grade reproducibility. On the 2024 Hardware Model Checking Competition bit-level safety benchmarks, CAPDR solves six more instances than the baseline. Over each configuration's checker-accepted solved set, the median certificate-size proxy decreases by 24.6% and the median checker time by 49%. Post-fixpoint invariant minimization yields further reductions.

Problem

• Certificate-Aware
• Property-Directed Reachability
• Hardware Safety Verification
• Certificate Size
• Independent Checking Time

Innovation

• Certificate-Aware
• Property-Directed Reachability
• Hardware Model Checking
• Invariant Minimization
• Learned Ranking Policy