New operator proves undecidability of self-modifying system properties

A new paper introduces the Semantic Elevation Operator, a formal method to analyze whether properties of self-modifying systems are preserved during transformations. This operator, formalized using Kleene's recursion theorem, demonstrates that even when breaking the extensionality required by Rice's theorem, the elevated property remains undecidable. The research shows that the class of non-verifiable properties is closed under this operator, leading to {\Pi}^0_2-completeness and suggesting that no finite tower of verifiers can guarantee unconditional certificates for these systems. AI

IMPACT Establishes theoretical limits on the verifiability of self-modifying systems, impacting future AI safety and verification research.

RANK_REASON The cluster contains a new academic paper detailing theoretical computer science research. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv cs.CL →

• arXiv
• cs.CL
• cs.LO
• Hugging Face
• Jose Pascual Gumbau Mezquita
• Kleene's recursion theorem
• Lawvere's fixed-point theorem
• Rice's theorem

• paper
• safety

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