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Bridging Computational Notions of Depth: Members of Deep Classesby@computational

Bridging Computational Notions of Depth: Members of Deep Classes

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