# Automating Formal Verification with Agent-Guided Tree Search

arXiv: https://arxiv.org/abs/2605.27485 · HTML: https://mlsanity.com/paper/2605.27485/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Software engineering coding agents, one of 16 directions in LLM agents and tool use.
- Builds on 48 of its 94 references that are in the map.
- First posted on arXiv 26 May 2026.

## Placed in

- LLM agents and tool use / [Software engineering coding agents](https://mlsanity.com/agents/software-engineering-coding-agents/)

## Builds on (most cited first, 30 of 48)

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- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Qwen3 Technical Report](https://mlsanity.com/paper/2505.09388/) (2025)
- [ReAct: Synergizing Reasoning and Acting in Language Models](https://mlsanity.com/paper/2210.03629/) (2022)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Toolformer: Language Models Can Teach Themselves to Use Tools](https://mlsanity.com/paper/2302.04761/) (2023)
- [Deep reinforcement learning from human preferences](https://mlsanity.com/paper/1706.03741/) (2017)
- [Constitutional AI: Harmlessness from AI Feedback](https://mlsanity.com/paper/2212.08073/) (2022)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [LeanDojo: Theorem Proving with Retrieval-Augmented Language Models](https://mlsanity.com/paper/2306.15626/) (2023)
- [MiniF2F: a cross-system benchmark for formal Olympiad-level mathematics](https://mlsanity.com/paper/2109.00110/) (2021)
- [Generative Language Modeling for Automated Theorem Proving](https://mlsanity.com/paper/2009.03393/) (2020)
- [How Language Model Hallucinations Can Snowball](https://mlsanity.com/paper/2305.13534/) (2023)
- [DeepSeek-Prover-V2: Advancing Formal Mathematical Reasoning via Reinforcement Learning for Subgoal Decomposition](https://mlsanity.com/paper/2504.21801/) (2025)
- [An Overview of Catastrophic AI Risks](https://mlsanity.com/paper/2306.12001/) (2023)
- [HyperTree Proof Search for Neural Theorem Proving](https://mlsanity.com/paper/2205.11491/) (2022)
- [Kimina-Prover Preview: Towards Large Formal Reasoning Models with Reinforcement Learning](https://mlsanity.com/paper/2504.11354/) (2025)
- [PutnamBench: Evaluating Neural Theorem-Provers on the Putnam Mathematical Competition](https://mlsanity.com/paper/2407.11214/) (2024)
- [Measuring AI Ability to Complete Long Software Tasks](https://mlsanity.com/paper/2503.14499/) (2025)
- [Goedel-Prover-V2: Scaling Formal Theorem Proving with Scaffolded Data Synthesis and Self-Correction](https://mlsanity.com/paper/2508.03613/) (2025)
- [Formal Mathematics Statement Curriculum Learning](https://mlsanity.com/paper/2202.01344/) (2022)
- [Proof Artifact Co-training for Theorem Proving with Language Models](https://mlsanity.com/paper/2102.06203/) (2021)
- [BFS-Prover: Scalable Best-First Tree Search for LLM-based Automatic Theorem Proving](https://mlsanity.com/paper/2502.03438/) (2025)
- [An In-Context Learning Agent for Formal Theorem-Proving](https://mlsanity.com/paper/2310.04353/) (2023)
- [Hilbert: Recursively Building Formal Proofs with Informal Reasoning](https://mlsanity.com/paper/2509.22819/) (2025)

## Abstract (arXiv)

Formal verification offers a path to provably correct software, but writing verified code remains expensive enough that the technique is rarely used in production. Recent large language models can accelerate this work, and recent benchmarks measure their ability to translate specifications into code and machine-checked proofs of correctness. This thesis evaluates the state of such LLM-driven verified-code generation ("vericoding") in Lean and develops search-based methods for improving verification performance. We first reproduce a subset of the vericoding-benchmark Lean leaderboard on a current cross-vendor model pool, finding that non-reasoning performance remains roughly steady on US closed-source models while open-weight models have slightly improved. We update the iterative methodology of vericoding-benchmark with an agentic loop equipped with mathlib search, finding that model performance greatly improves and scales with agent budget. GPT-5.4 nearly saturates the benchmark at 95.0% on 423 specs with K=50 LLM calls. We then design two agent-directed tree-search formulations: a state-based orchestrator that branches on partial-proof states, and a context-based orchestrator that branches on full subagent contexts. Compared against the agent baseline, the context-based design solves a wider range of intermediate-difficulty specs at lower token cost, while the agent baseline retains an advantage on the hardest specs, where uninterrupted iteration matters most. We conclude that search structure has selective advantages over a strong agent baseline, and that more challenging benchmarks drawn from modern code are important to measure and drive further progress in automated formal verification. Code available upon request by contacting the author at leoy@mit.edu.