Bridging Computational Notions of Depth: Members of Deep Classes

Introducing the members of deep classes and proving that they are strongly deep.


This content originally appeared on HackerNoon and was authored by Computational Technology for All

Abstract and 1 Introduction

2 Background

3 On the slow growth law

4 Members of Deep Π0 1 classes

5 Strong depth is Negligible

6 Variants of Strong Depth

References

Appendix A. Proof of Lemma 3

\

\

\ By Lemma 3, we can conclude that X is order-deep.

\ One immediate consequence of Theorem 9 is the following.

\

\ The converse of this result does not hold.

\

\

\

\

\ As an immediate consequence of Theorem 9 and the above results from [BP16], we have:

\

\

\

\

\ Next, we have:

\

\

\

\

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

:::

:::info Authors:

(1) Laurent Bienvenu;

(2) Christopher P. Porter.

:::

\


This content originally appeared on HackerNoon and was authored by Computational Technology for All


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Computational Technology for All | Sciencx (2025-01-16T01:09:44+00:00) Bridging Computational Notions of Depth: Members of Deep Classes. Retrieved from https://www.scien.cx/2025/01/16/bridging-computational-notions-of-depth-members-of-deep-classes/

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