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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.04876 |
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| _version_ | 1866911569927995392 |
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| author | Hasan, Munawar |
| author_facet | Hasan, Munawar |
| contents | Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains. While limitations of verification are often attributed to combinatorial complexity and model expressiveness, we show that they arise from intrinsic information-theoretic limits. We formalize policy compliance as a verification problem over encoded system behaviors and analyze it using Kolmogorov complexity. We prove an incompleteness result: for any fixed sound computably enumerable verifier, there exists a threshold beyond which true policy-compliant instances cannot be certified once their complexity exceeds that threshold. Consequently, no finite formal verifier can certify all policy-compliant instances of arbitrarily high complexity. This reveals a fundamental limitation of AI safety verification independent of computational resources, and motivates proof-carrying approaches that provide instance-level correctness guarantees. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_04876 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Incompleteness of AI Safety Verification via Kolmogorov Complexity Hasan, Munawar Artificial Intelligence Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains. While limitations of verification are often attributed to combinatorial complexity and model expressiveness, we show that they arise from intrinsic information-theoretic limits. We formalize policy compliance as a verification problem over encoded system behaviors and analyze it using Kolmogorov complexity. We prove an incompleteness result: for any fixed sound computably enumerable verifier, there exists a threshold beyond which true policy-compliant instances cannot be certified once their complexity exceeds that threshold. Consequently, no finite formal verifier can certify all policy-compliant instances of arbitrarily high complexity. This reveals a fundamental limitation of AI safety verification independent of computational resources, and motivates proof-carrying approaches that provide instance-level correctness guarantees. |
| title | Incompleteness of AI Safety Verification via Kolmogorov Complexity |
| topic | Artificial Intelligence |
| url | https://arxiv.org/abs/2604.04876 |