Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
Languages and machines: an introduction to the theory of computer science
Languages and machines: an introduction to the theory of computer science
Computer Studies of Turing Machine Problems
Journal of the ACM (JACM)
New Turing Omnibus
The busy beaver on a one-way infinite tape
ACM SIGACT News
Analysis of busy beaver machines via induction proofs
CATS '07 Proceedings of the thirteenth Australasian symposium on Theory of computing - Volume 65
CATS '11 Proceedings of the Seventeenth Computing: The Australasian Theory Symposium - Volume 119
CATS 2011 Proceedings of the Seventeenth Computing on The Australasian Theory Symposium - Volume 119
Busy beaver machines and the observant otter heuristic
CATS '13 Proceedings of the Nineteenth Computing: The Australasian Theory Symposium - Volume 141
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The busy beaver is an example of a function which is not computable. It is based on a particular class of Turing machines, and is defined as the largest number of 1's that can be printed by a terminating machine with n states. Whilst there have been various quests to determine the precise value of this function (which is known precisely only for n ≤ 4), our aim is not to determine this value per se, but to investigate the properties of this class of machines. On the one hand, these are remarkably simple (and, intuitively, form perhaps the simplest class of computationally complete machines); on the other hand, as some of the machines for n = 6 show, they are capable of representing phenomenally large numbers. We describe our quest to better understand these machines, including the placid platypus problem, ie. to determine the minimum number of states needed by a machine of this type to print a given number of 1's.