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Incompleteness of AI Safety Verification via Kolmogorov Complexity

Munawar Hasan · Apr 6, 2026 · Citations: 0

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How to use this page

Low trust

Use this as background context only. Do not make protocol decisions from this page alone.

Best use

Background context only

What to verify

Read the full paper before copying any benchmark, metric, or protocol choices.

Evidence quality

Low

Derived from extracted protocol signals and abstract evidence.

Abstract

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.

Abstract-only analysis — low confidence

All signals on this page are inferred from the abstract only and may be inaccurate. Do not use this page as a primary protocol reference.

This paper looks adjacent to evaluation work, but not like a strong protocol reference.
The available metadata is too thin to trust this as a primary source.
The abstract does not clearly describe the evaluation setup.
The abstract does not clearly name benchmarks or metrics.

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Should You Rely On This Paper?

This paper is adjacent to HFEPX scope and is best used for background context, not as a primary protocol reference.

Best use

Background context only

Use if you need

Background context only.

Main weakness

This paper looks adjacent to evaluation work, but not like a strong protocol reference.

Trust level

Low

Usefulness score

0/100 • Low

Treat as adjacent context, not a core eval-method reference.

Human Feedback Signal

Not explicit in abstract metadata

Evaluation Signal

Weak / implicit signal

Usefulness for eval research

Adjacent candidate

Extraction confidence 15%

If you are doing eval pipeline work, start here:

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What We Could Verify

These are the protocol signals we could actually recover from the available paper metadata. Use them to decide whether this paper is worth deeper reading.

Human Feedback Types

missing

None explicit

No explicit feedback protocol extracted.

"Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains."

Evaluation Modes

missing

None explicit

Validate eval design from full paper text.

"Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains."

Quality Controls

missing

Not reported

No explicit QC controls found.

"Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains."

Benchmarks / Datasets

missing

Not extracted

No benchmark anchors detected.

"Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains."

Reported Metrics

missing

Not extracted

No metric anchors detected.

"Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains."

Human Feedback Details

Uses human feedback: No
Feedback types: None
Rater population: Not reported
Expertise required: Math

Evaluation Details

Evaluation modes:
Agentic eval: None
Quality controls: Not reported
Evidence quality: Low
Use this page as: Background context only

Protocol And Measurement Signals

Benchmarks / Datasets

No benchmark or dataset names were extracted from the available abstract.

Reported Metrics

No metric terms were extracted from the available abstract.

Research Brief

Metadata summary

Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains.

Based on abstract + metadata only. Check the source paper before making high-confidence protocol decisions.

Key Takeaways

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.

Researcher Actions

Compare this paper against nearby papers in the same arXiv category before using it for protocol decisions.
Check the full text for explicit evaluation design choices (raters, protocol, and metrics).
Use related-paper links to find stronger protocol-specific references.

Caveats

Generated from abstract + metadata only; no PDF parsing.
Signals below are heuristic and may miss details reported outside the abstract.

Recommended Queries

Research Summary

Contribution Summary

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.
This reveals a fundamental limitation of AI safety verification independent of computational resources, and motivates proof-carrying approaches that provide instance-level correctness guarantees.

Why It Matters For Eval

Ensuring that artificial intelligence (AI) systems satisfy formal safety and policy constraints is a central challenge in safety-critical domains.
This reveals a fundamental limitation of AI safety verification independent of computational resources, and motivates proof-carrying approaches that provide instance-level correctness guarantees.

Researcher Checklist

Gap: Human feedback protocol is explicit

No explicit human feedback protocol detected.
Gap: Evaluation mode is explicit

No clear evaluation mode extracted.
Gap: Quality control reporting appears

No calibration/adjudication/IAA control explicitly detected.
Gap: Benchmark or dataset anchors are present

No benchmark/dataset anchor extracted from abstract.
Gap: Metric reporting is present

No metric terms extracted.

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