Bridging Computational Notions of Depth: Members of Deep Classes

Written by computational | Published 2025/01/16
Tech Story Tags: turing | computation | computational-notions | bennet's-notion | depth-notions | notions-of-depth | martin-lof-random-sequences | randomness

TLDRIntroducing the members of deep classes and proving that they are strongly deep.via the TL;DR App

Table of Links

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.


Written by computational | Computational: We take random inputs, follow complex steps, and hope the output makes sense. And then blog about it.
Published by HackerNoon on 2025/01/16