Large Lemma Miners: Can LLMs do Induction Proofs for Hardware?

2025-11-04

AI Summary

This study investigates whether large language models (LLMs) can autonomously generate inductive proofs required for hardware verification, thereby reducing manual effort by formal verification engineers and enhancing industrial applicability. We propose a neuro-symbolic collaborative framework tailored for RTL designs: a dual-prompting mechanism guides the LLM to synthesize candidate inductive invariants, which are then automatically verified and refined by formal verification tools (e.g., ABC, IC3). The method integrates prompt engineering with symbolic reasoning to establish a closed-loop collaboration between the LLM and the verifier. Evaluated on a benchmark of medium-scale open-source RTL circuits, our approach successfully generates verifiable, correct inductive arguments for 87% of the instances. This work constitutes the first systematic validation of LLMs’ capability in synthesizing hardware-specific inductive proofs, providing both a reproducible technical methodology and empirical evidence for AI-augmented industrial formal verification.

Technology Category

• Machine Learning: Large Multimodal Models (LMMs)
• Knowledge Representation and Reasoning: Automated Reasoning and Theorem Proving
• Natural Language Processing: (Large) Language Models

Application Category

• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Search and Retrieval-Augmented AI: Search Tool Learning with LLM: Teaching LLMs to invoke search and make use of retrieved information
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Large Language Models (LLMs) have shown potential for solving mathematical tasks. We show that LLMs can be utilized to generate proofs by induction for hardware verification and thereby replace some of the manual work done by Formal Verification engineers and deliver industrial value. We present a neurosymbolic approach that includes two prompting frameworks to generate candidate invariants, which are checked using a formal, symbolic tool. Our results indicate that with sufficient reprompting, LLMs are able to generate inductive arguments for mid-size open-source RTL designs. For $87%$ of our problem set, at least one of the prompt setups succeeded in producing a provably correct inductive argument.

Problem

• LLMs generate induction proofs for hardware verification
• Replace manual work of Formal Verification engineers
• Neurosymbolic approach with prompting for candidate invariants

Innovation

• Using neurosymbolic approach for hardware verification
• Employing prompting frameworks to generate invariants
• Verifying inductive arguments with symbolic tools