A note on busy beavers and other creatures

@article{BenAmram2005ANO,
  title={A note on busy beavers and other creatures},
  author={Amir M. Ben-Amram and Bryant A. Julstrom and Uri Zwick},
  journal={Mathematical systems theory},
  year={2005},
  volume={29},
  pages={375-386}
}
Consider Turing machines that read and write the symbols 1 and 0 on a one-dimensional tape that is infinite in both directions, and halt when started on a tape containing all O's. Rado'sbusy beaver function ones(n) is the maximum number of 1's such a machine, withn states, may leave on its tape when it halts. The function ones(n) is noncomputable; in fact, it grows faster than any computable function.Other functions with a similar nature can also be defined. The function time(n) is the maximum… 
The Busy Beaver Competition: a historical survey
TLDR
The successive record holders in the Busy Beaver Competition are displayed, with their discoverers, the date they were found, and, for some of them, an analysis of their behavior.
An Automated, Symbolic Induction Prover for Nonhalting Turing Machines
TLDR
To compute the exact value of SHnL, the halting question for H4 n + 1L2 n n-state binary Turing machines is decided and this huge number can be reduced by applying well-known techniques such as tree normalization, backtracking, and simple loop detection.
Bibliography on the Busy Beaver Problem
In 1981 the editor of this bibliography was attracted to the Busy Beaver Problem by a reference in the Dutch translation of Ogilvy’s Tomorrow’s Math [Ogi72]. Tracing back in time one finds of course
Appendix A Formal ( In ) Computability and Randomness
  • Computer Science
  • 2018
TLDR
A very brief survey of the consequences of Turing’s work, and a hint on the fact that almost all elements of the continuum, and, in particular, almost all reals, are incomputable, head on to modern, algorithmic, definitions of randomness, and of random reals.

References

SHOWING 1-8 OF 8 REFERENCES
A bound on the shift function in terms of the Busy Beaver function
TLDR
This paper shows that S(n) is non-computable and shows a construction used in the proof of the bound on S(20n), then uses this result to prove that both &Sigma;(<i>n</i> and <i>S</i>(n) are non- computable and theirNon-computability is equivalent to the undecidability of the halting problem.
The determination of the value of Rado’s noncomputable function Σ() for four-state Turing machines
TLDR
The well-defined but noncomputable functions E(k) and S( k) given by T. Rado as the "score" and "shift number" for the k-state Turing machine "Busy Beaver Game" were reported by this author, supported the conjecture that these lower bounds are the actual particular values of the functions for k 4.
Attacking the Busy Beaver 5
TLDR
A new approach to the computation of Σ (5) is presented, together with preliminary results, especially Σ(5)≥4098, which includes techniques to reduce the number of inspected Turing machines, to accelerate simulation of Turing machines and to decide nontermination of Turing Machines.
Computer Studies of Turing Machine Problems
TLDR
This paper solves a problem relating to Turing machines arising in connection with the Busy Beaver logical game with the help of a computer program, and the values of two very well-defined positive integers are determined to b~ 6 and 21 respectively.
On non-computable functions
The construction of non-computable functions used in this paper is based on the principle that a finite, non-empty set of non-negative integers has a largest element. Also, this principle is used
Attacking the Busy Beaver Problem 5. Bulletin of the European Association for Theoretical
  • Computer Science,
  • 1990
Noncomputability and the Busy Beaver problem (UMAP Unit 728)
  • The UMAP Journal,
  • 1993
Attacking the Busy Beaver Problem 5
  • Bulletin of the European Association for Theoretical Computer Science
  • 1990