A note on busy beaver bounds

Authors: Tomás Schitter, Sergio Abriola and Nicolás González.

Abstract:
We investigate the relationship between several variations of the Busy Beaver game proposed by Radó (1962), such as the or the functions, establishing new bounds on these functions in terms of each other, as well as some properties about their growth. We also introduce and investigate a new function, to this family of noncomputable functions. We give some specific values for as well as several results concerning its growth and its relationship to the previously studied Busy Beaver functions. We also investigate growth properties and relationships of these functions when considering Turing Machines with non-binary alphabets with a single blank symbol.

More information: https://www.sciencedirect.com/science/article/abs/pii/S0304397525004797