arXiv cs.AI· Tomas Perez-Acle·· 10 小时前AI 评分42
没有有限规则手册能认证所有安全程序：AI 智能体把关的不可能性定理
No finite rulebook can certify every safe program: an impossibility theorem for gatekeeping AI agents
AI 导读
一项不可能性定理证明：若每条规则都须由机器在有限时间内可核查的证据支撑，则“允许清单”与“禁止清单”两本规则手册无法同时完备。可核查证据只能确立有限记录所能判定之事，而“永不”与“最终”永远无法被有限记录判定；对禁止性规则，违规总可被观测捕获，但没有安全程序能被永久放行。
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