arXiv 论文证明不可能定理：没有有限规则手册能认证所有安全的 AI 智能体程序
No finite rulebook can certify every safe program: an impossibility theorem for gatekeeping AI agents
AI 导读
一篇 arXiv 论文证明，固定规则下的门控 AI 智能体不存在既完备又可机器有限验证的允许与禁止规则手册。论文指出"永不"和"最终会回答"类性质无法由有限记录确立：违规可被监控捕捉，但安全程序无法被永久放行；任何 n 比特的可靠规则手册都会遗漏约 n 比特的合规程序。基于 220 万随机程序及自指对手的模拟显示，该障碍是对抗性而非典型情况，且更长测试始终无法消除机密性中的活性错误部分。
正文 · 原文
Abstract:An AI assistant writes small programs, and a gatekeeper must decide, from the code alone, whether each one may run. Suppose the rules are fixed: never perform a forbidden action, never let the output depend on a secret, always answer eventually. Can two rulebooks, one listing what is allowed and one listing what is not, both be complete, if every rule must be backed by evidence that a machine can check in finite time? We prove that they cannot. Checkable evidence can only establish what a finite record settles, and ``never'' and ``eventually'' are never settled by a finite record. For prohibitions the failure is one-sided: every violation can be caught by watching, but no safe program can be cleared for good. For confidentiality and responsiveness, neither side can be. We characterise exactly which rules about visible behaviour evidence can confirm, and we show that any sound rulebook of $n$ bits omits a compliant program of about $n$ bits. A time limit makes everything checkable, but only by running the program for essentially the whole limit, so a finite machine is not a feasible one. Finally, we show what a gatekeeper can still guarantee: not a verdict on every program, but a checkable list that contains everything it must allow and nothing it must refuse. Simulations on 2.2 million random programs and on self-referential adversaries show that the obstruction is adversarial rather than typical, and that the one error a longer test never removes is the liveness part of confidentiality.
| Comments: | 34 pages, 4 figures |
| Subjects: | Artificial Intelligence (cs.AI); Cryptography and Security (cs.CR) |
| ACM classes: | I.2.0; I.2.3; I.2.8 |
| Cite as: | arXiv:2611.13367 [cs.AI] |
| (or arXiv:2611.13367v1 [cs.AI] for this version) | |
| https://doi.org/10.48550/arXiv.2611.13367 arXiv-issued DOI via DataCite (pending registration) |
Submission history
From: Tomas Perez-Acle Dr. [view email]
[v1]
Mon, 9 Nov 2026 23:40:32 UTC (1,353 KB)
来源：arXiv cs.AI · arxiv.org