Algorithmic Unverifiability of Safety for Fixed and Recursively Self-Improving Systems
Existing impossibility results for AI verification concern a fixed system. Self-modifying systems (agents that rewrite their own code, recursive self-improvement loops) raise a different question: can a safety property that holds now be certified, in advance, to keep holding after the system rewrites itself? We model one step of self-modification as a total computable transformation of code, and preservation as 'safe now and safe after the step'. If the transformation depends only on behaviour, preservation is Rice's theorem one level up; if it reads the code, as self-modification does, preservation is no longer semantic, yet at least as hard as the halting problem, by the same s-m-n redu...
| Authors | Jose Pascual Gumbau Mezquita |
|---|---|
| Primary category | cs.LO |
| Published | 26 June 2026 |
| Last updated at source | 14 October 2026 |
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