Formal Framework for LLM-Verifier Systems: Convergence Theorem and 4/δ Latency Bound

Summary

This research paper presents a formal framework for integrating Large Language Models with Formal Verification tools, addressing reliability issues in current methods. The authors develop an LLM-Verifier Convergence Theorem that provides provable guarantees for termination in multi-stage verification pipelines. They model the interaction as a sequential absorbing Markov Chain with four stages (CodeGen, Compilation, InvariantSynth, SMTSolving) and prove that for any non-zero stage success probability, the system reaches verification almost surely. The paper derives a precise latency bound of 4/δ and validates the theory through extensive empirical testing of over 90,000 trials. The research identifies three operating zones and proposes dynamic calibration strategies for real-world applications.