Designing Predictable LLM-Verifier Systems for Formal Method Guarantee (arxiv.org)

A recent study introduces the LLM-Verifier Convergence Theorem, a significant advancement in merging Formal Verification tools with Large Language Models (LLMs) to enhance software verification processes. Traditional verification methods have struggled with reliability due to their opaque refinement mechanisms, often leading to erratic behaviors like looping or divergence. This new framework, grounded in theoretical principles, models the verification stages—Code Generation, Compilation, Invariant Synthesis, and SMT Solving—using a sequential absorbing Markov Chain, demonstrating that systems will reliably reach a 'Verified' state given any non-zero success probability. The implications of this work are profound for the AI/ML community, establishing a structured approach to software verification that replaces guesswork with rigorous validation strategies. A key technical finding is the derived latency bound of \( \mathbb{E}[n] \leq 4/\delta \), which was validated through an empirical study of over 90,000 trials, supporting its predictive accuracy. The research delineates three operational zones—marginal, practical, and high-performance—and introduces a dynamic calibration strategy to adapt to real-world variations, laying the groundwork for more predictable and efficient resource planning in safety-critical software applications.