Verification and Self-Improvement in Agentic AI: Foundations and Limits

Key points

• We compare these changes through bounded verification with hidden terminal randomness.1
• We prove that independent majority amplification preserves both languages, whereas existential acceptance over random tapes can admit incorrect outputs.1
• The randomized-verifier classes satisfy $Σk^{P}\subseteqΣk^{RV}\subseteqΣ{k+1}^{P}$; strict enlargement and depth separation require explicit complexity assumptions, while $BPP=P$ yields exact companions with the same frontiers.1
• For recursive self-improvement, uniformly bounded self-modification under a common sound interpreter and fixed verification protocol remains within the same verification class.1

Sources (1)

• [1]Verification and Self-Improvement in Agentic AI: Foundations and Limits
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 06:47 AM

  Agentic AI systems can improve by searching longer, receiving additional support, or modifying how they propose and verify outputs.

  We compare these changes through bounded verification with hidden terminal randomness.

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