On Higher Order Busy Beaver Function

Zining Cao

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arXiv · 2507.20321

On Higher Order Busy Beaver Function

Zining Cao

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Abstract

In this paper, we extend Busy Beaver function to a class of higher order Busy Beaver functions based on Turing oracle machine. We prove some results about the relation between decidability of number theoretical formula and higher order Busy Beaver functions, and the relation between computability of max-min partial recursive functions and higher order Busy Beaver functions. We also present some conjectures on higher order Busy Beaver functions.

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BibTeX RIS

Zining Cao. 2025-07-27. On Higher Order Busy Beaver Function. https://arxiv.org/abs/2507.20321

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