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Donate arxiv logo > cs > arXiv:2512.02080 [ ] Help | Advanced Search [All fields ] Search arXiv logo Cornell University Logo [ ] GO quick links * Login * Help Pages * About Computer Science > Artificial Intelligence arXiv:2512.02080 (cs) [Submitted on 30 Nov 2025 (v1), last revised 16 Dec 2025 (this version, v2)] Title:The 4/$d$ Bound: Designing Predictable LLM-Verifier Systems for Formal Method Guarantee Authors:PIerre Dantas, Lucas Cordeiro, Youcheng Sun, Waldir Junior View a PDF of the paper titled The 4/$\delta$ Bound: Designing Predictable LLM-Verifier Systems for Formal Method Guarantee, by PIerre Dantas and 3 other authors View PDF HTML (experimental) 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 not as a generic loop, but as a sequential absorbing Markov Chain comprising four essential engineering stages: \texttt{CodeGen}, \texttt {Compilation}, \texttt{InvariantSynth}, and \texttt{SMTSolving}. We prove that for any non-zero stage success probability ($\delta > 0$), the system reaches the \texttt{Verified} state almost surely. Furthermore, because of the sequential nature of the pipeline, we derive a precise latency bound of $\mathbb{E}[n] \ leq 4/\delta$. We stress-tested this prediction in an extensive empirical campaign comprising over 90,000 trials. The results match the theory with striking consistency: every run reached verification, and the empirical convergence factor clustered tightly around $C_f\approx 1.0$, confirming that the $4/\delta$ bound accurately mirrors system behavior rather than serving as a loose buffer. Based on this data, we identify three distinct operating zones -- marginal, practical, and high-performance -- and propose a dynamic calibration strategy to handle parameter drift in real-world environments. Together, these contributions replace heuristic guesswork with a rigorous architectural foundation, enabling predictable resource planning and performance budgeting for safety-critical software. Comments: 36 pages, 9 figures Artificial Intelligence (cs.AI); Formal Languages and Subjects: Automata Theory (cs.FL); Machine Learning (cs.LG); Software Engineering (cs.SE) Cite as: arXiv:2512.02080 [cs.AI] (or arXiv:2512.02080v2 [cs.AI] for this version) https://doi.org/10.48550/arXiv.2512.02080 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Pierre Dantas [view email] [v1] Sun, 30 Nov 2025 22:19:09 UTC (459 KB) [v2] Tue, 16 Dec 2025 22:28:30 UTC (491 KB) Full-text links: Access Paper: View a PDF of the paper titled The 4/$\delta$ Bound: Designing Predictable LLM-Verifier Systems for Formal Method Guarantee, by PIerre Dantas and 3 other authors * View PDF * HTML (experimental) * TeX Source view license Current browse context: cs.AI < prev | next > new | recent | 2025-12 Change to browse by: cs cs.FL cs.LG cs.SE References & Citations * NASA ADS * Google Scholar * Semantic Scholar export BibTeX citation Loading... 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