Enhancing Word-Level Property Directed Reachability with LLM-Driven Semantic Guidance

2026-09-24

AI Summary

This study addresses the semantic loss inherent in bit-level Property Directed Reachability (PDR) and the difficulty of discovering proof-relevant relationships in word-level PDR by proposing the LLM4PDR framework. This approach is the first to incorporate semantic hints—such as predicates, clauses, and assertions generated by large language models (LLMs)—into word-level PDR search, combined with a counterexample-guided refinement mechanism to accelerate convergence. Experimental results demonstrate that the proposed framework significantly improves the solving rate on arithmetic benchmarks (28/33) and achieves complementary speedups in High-Level Synthesis (HLS) pipeline and Register-Transfer Level (RTL) component verification. By effectively integrating the semantic reasoning capabilities of LLMs with the rigor of formal verification, this work offers a promising direction for enhancing automated proof construction in hardware verification tasks.

Abstract

Property Directed Reachability (PDR) is a prominent algorithm for hardware formal verification. However, bit-level PDR often struggles with datapath-heavy designs because bit-blasting obscures high-level semantics. While word-level PDR addresses this by reasoning over bit-vector and array theories, its performance remains bottlenecked by discovering proof-relevant word-level relations. We propose LLM4PDR, a framework leveraging Large Language Models (LLMs) to guide word-level PDR search through three mechanisms: (1) Predicate Generation, extracting state relationships as candidate predicates during inductive generalization; (2) Clause Generation, producing candidate frame lemmas to accelerate convergence after formal validation; and (3) Assertion Generation, synthesizing helper assertions that strengthen the target property under counterexample-guided refinement. We implement LLM4PDR in the Pono model checker and evaluate it on arithmetic micro-benchmarks, HLS-generated pipelines, open-source RTL components, and hardware model checking competition (HWMCC) instances. Results show LLM-generated guidance improves both solved instances and runtime on datapath-heavy and control-plus-datapath designs. The strongest configuration solves 28 of 33 arithmetic benchmarks, compared to 13 for vanilla Pono and 11 for AVR. On HLS pipelines and open-source RTL, different modes provide complementary speedups: clause guidance is effective for deep pipelines and predicate guidance for bus and memory-controller designs. On HWMCC benchmarks, benefits are instance-dependent, demonstrating notable speedups and timeout avoidance on hard cases. These results suggest that LLM-generated, verifier-checked semantic hints can serve as a practical complement to conventional word-level PDR.

Problem

• Property Directed Reachability
• Hardware Formal Verification
• Word-Level PDR
• Datapath-Heavy Designs

Innovation

• Property Directed Reachability
• Large Language Models
• Formal Verification
• Word-Level Reasoning
• Semantic Guidance