The 4/$\delta$ Bound: Designing Predictable LLM-Verifier Systems for Formal Method Guarantee
arXiv:2512.02080v3 Announce Type: replace-cross Abstract: The integration of Formal Verification tools with Large Language Models (LLMs) offers a path to scale software verification beyond manual workflows. However, current methods remain unreliable: without a solid theoretical footing, the refinement process acts as a black box that may oscillate, loop, or diverge. This work bridges this critical gap by developing an LLM-Verifier Convergence Theorem, providing the first formal framework with provable guarantees for termination in multi-stage verification pipelines. We model the interaction no
The rapid deployment of LLMs into critical systems necessitates a more rigorous approach to their reliability and predictability, particularly as their integration with formal verification tools becomes more common.
This work addresses a critical bottleneck in scaling software verification through LLMs by providing a theoretical foundation and provable guarantees for complex multi-stage verification pipelines, which is a key barrier to broader adoption in high-assurance environments.
The ability to predictably design and implement LLM-verifier systems moves from ad-hoc experimentation towards formally guaranteed convergence, mitigating risks of oscillation or divergence in critical applications.
- · Software verification tool vendors
- · High-assurance software developers
- · AI safety researchers
- · Industries requiring formal methods (e.g., aerospace, automotive, finance)
- · Companies relying solely on empirical or black-box LLM refinement
- · Manual software verification processes
Increased confidence and adoption of LLM-powered verification tools in industrial settings.
Expansion of formal methods into broader software development, potentially reducing critical bugs and increasing system reliability across sectors.
Acceleration of autonomous AI agent development where provable correctness is a prerequisite for deployment, impacting industries from self-driving cars to automated financial trading algorithms.
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Read at arXiv cs.LG