算法与复杂性
Lean 4 中经机器验证的自然证明障碍
A Machine-Verified Natural Proofs Barrier in Lean 4
工作论文 · Zenodo首次公开
研究概述
在存在伪随机函数生成器的假设下形式化自然证明障碍,同时形式化 Shannon 的计数论证。
原文摘要(英文)
The natural proofs barrier (Razborov--Rudich 1997) has had no machine-verified formalization in any proof assistant. We formalize it in Lean 4: if pseudorandom function generators exist, then no natural combinatorial property is useful against P/poly. The formalization is approximately 400 lines of Lean 4 with no unresolved proof obligations. We identify definition choices that make the barrier proof mechanizable without probabilistic infrastructure and analyze why simpler alternatives fail. We also formalize the Shannon counting argument: most Boolean functions require large circuits.
Computer ScienceAlgorithms & complexityformal verificationLean 4natural proofs barriercircuit complexityRazborov-Rudichproof assistant