LeGend: A Data-Driven Framework for Lemma Generation in Hardware Model Checking

2026-02-27

AI Summary

This work addresses the inefficiency and limited scalability of inductive generalization in IC3/PDR-based hardware model checking, which stems from repeated clause-level graph analyses. To overcome this, the authors propose LeGend, a novel framework that introduces one-time global representation learning into lemma generation for the first time. LeGend employs domain-adaptive self-supervised pretraining to learn latch embeddings that capture global circuit characteristics, coupled with a lightweight prediction model to enable efficient lemma generation. By decoupling the expensive representation learning phase from fast inference, LeGend significantly accelerates two mainstream IC3/PDR engines across a diverse set of benchmarks, demonstrating both effectiveness and strong scalability.

Technology Category

• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Search and Optimization: Learning to Search
• Machine Learning: Hardware-aware ML

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

Property checking of RTL designs is a central task in formal verification. Among available engines, IC3/PDR is a widely used backbone whose performance critically depends on inductive generalization, the step that generalizes a concrete counterexample-to-induction (CTI) cube into a lemma. Prior work has explored machine learning to guide this step and achieved encouraging results, yet most methods adopt a per-clause graph analysis paradigm: for each clause they repeatedly build and analyze graphs, incurring heavy overhead and creating a scalability bottleneck. We introduce LeGend, which replaces this paradigm with one-time global representation learning. LeGend pre-trains a domain-adapted self-supervised model to produce latch embeddings that capture global circuit properties. These precomputed embeddings allow a lightweight model to predict high-quality lemmas with negligible overhead, effectively decoupling expensive learning from fast inference. Experiments show LeGend accelerates two state-of-the-art IC3/PDR engines across a diverse set of benchmarks, presenting a promising path to scale up formal verification.

Problem

• lemma generation
• hardware model checking
• inductive generalization
• IC3/PDR
• formal verification

Innovation

• lemma generation
• global representation learning
• self-supervised learning
• IC3/PDR
• formal verification