@inproceedings{xin-etal-2025-bfs,
    title = "{BFS}-Prover: Scalable Best-First Tree Search for {LLM}-based Automatic Theorem Proving",
    author = "Xin, Ran  and
      Xi, Chenguang  and
      Yang, Jie  and
      Chen, Feng  and
      Wu, Hang  and
      Xiao, Xia  and
      Sun, Yifan  and
      Zheng, Shen  and
      Ding, Ming",
    editor = "Che, Wanxiang  and
      Nabende, Joyce  and
      Shutova, Ekaterina  and
      Pilehvar, Mohammad Taher",
    booktitle = "Proceedings of the 63rd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers)",
    month = jul,
    year = "2025",
    address = "Vienna, Austria",
    publisher = "Association for Computational Linguistics",
    url = "https://preview.aclanthology.org/ingestion-acl-25/2025.acl-long.1565/",
    pages = "32588--32599",
    ISBN = "979-8-89176-251-0",
    abstract = "Recent advancements in large language models (LLMs) have spurred growing interest in automatic theorem proving using Lean4, where effective tree search methods are crucial for navigating the underlying large proof search spaces. While the existing approaches primarily rely on value functions and/or Monte Carlo Tree Search (MCTS), the potential of simpler methods like Best-First Tree Search (BFS) remains underexplored. In this paper, we investigate whether BFS can achieve competitive performance in large-scale theorem proving tasks. We present BFS-Prover, a scalable expert iteration framework, featuring three key innovations. First, we implement strategic data filtering at each expert iteration round, excluding problems solvable via beam search node expansion to focus on harder cases. Second, we improve the sample efficiency of BFS through Direct Preference Optimization (DPO) applied to state-tactic pairs automatically annotated with compiler error feedback, refining the LLM{'}s policy to prioritize productive expansions. Third, we employ length normalization in BFS to encourage exploration of deeper proof paths. BFS-Prover achieves a state-of-the-art score of 72.95 on the MiniF2F test set and therefore challenges the perceived necessity of complex tree search methods, demonstrating that BFS can achieve competitive performance when properly scaled."
}