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Some better results estimating the shift function in terms of busy beaver function

Authors:

Ruiguang Yang,

Longyun Ding,

Shurun XuAuthors Info & Claims

ACM SIGACT News, Volume 28, Issue 1

Pages 43 - 48

https://doi.org/10.1145/250037.250038

Published: 01 March 1997 Publication History

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Abstract

About the relation between the shift function S(n) and the busy beaver function Σ(n), there have been some results. In 1992, A. Julstrom gave his result: S(n) < Σ(20n); in 1994, Wang Kewen and Xu Shurun obtained: S(n) < Σ(10n). In this paper, we shall show that S(n) ≤ Σ(3n -f c)(c is a constant).

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Harland J(2016)Busy beaver machines and the observant otter heuristic (or how to tame dreadful dragons)Theoretical Computer Science10.1016/j.tcs.2016.07.016646:C(61-85)Online publication date: 20-Sep-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.07.016
Harland J(2006)The busy beaver, the placid platypus and other crazy creaturesProceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 5110.5555/2523791.2523802(79-86)Online publication date: 16-Jan-2006
https://dl.acm.org/doi/10.5555/2523791.2523802
Harland J(2006)The busy beaver, the placid platypus and other crazy creaturesProceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 5110.5555/1151785.1151794(79-86)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.5555/1151785.1151794

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Some better results estimating the shift function in terms of busy beaver function

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ACM SIGACT News Volume 28, Issue 1

March 1997

25 pages

ISSN:0163-5700

DOI:10.1145/250037

Editor:
Ian Parberry
Univ. of North Texas

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Association for Computing Machinery

New York, NY, United States

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Published: 01 March 1997

Published in SIGACT Volume 28, Issue 1

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Harland J(2016)Busy beaver machines and the observant otter heuristic (or how to tame dreadful dragons)Theoretical Computer Science10.1016/j.tcs.2016.07.016646:C(61-85)Online publication date: 20-Sep-2016
https://dl.acm.org/doi/10.1016/j.tcs.2016.07.016
Harland J(2006)The busy beaver, the placid platypus and other crazy creaturesProceedings of the Twelfth Computing: The Australasian Theory Symposium - Volume 5110.5555/2523791.2523802(79-86)Online publication date: 16-Jan-2006
https://dl.acm.org/doi/10.5555/2523791.2523802
Harland J(2006)The busy beaver, the placid platypus and other crazy creaturesProceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 5110.5555/1151785.1151794(79-86)Online publication date: 1-Jan-2006
https://dl.acm.org/doi/10.5555/1151785.1151794

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A bound on the shift function in terms of the Busy Beaver function

Estimating gamma function by digamma function

Separation results for boolean function classes

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