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Bridging Computational Notions of Depth: Members of Deep Classes

Written by @computational | Published on 2025/1/16
TL;DR —
Introducing the members of deep classes and proving that they are strongly deep.

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:

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

Authors:

(1) Laurent Bienvenu;

(2) Christopher P. Porter.

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Written by
@computational
Computational: We take random inputs, follow complex steps, and hope the output makes sense. And then blog about it.
Topics and
tags
turing|computation|computational-notions|bennet's-notion|depth-notions|notions-of-depth|martin-lof-random-sequences|randomness
This story on HackerNoon has a decentralized backup on Sia.
Transaction ID: RgbS4hiRwwWOsC_ae9pG2CiDdt8vftxMkXbpPDE78xw