Computability and logic: 3rd ed.
Computability and logic: 3rd ed.
Computer Studies of Turing Machine Problems
Journal of the ACM (JACM)
Frontier between decidability and undecidability: a survey
Theoretical Computer Science - Special issue on universal machines and computations
New Turing Omnibus
The busy beaver, the placid platypus and other crazy creatures
CATS '06 Proceedings of the 12th Computing: The Australasian Theroy Symposium - Volume 51
Languages and Machines: An Introduction to the Theory of Computer Science (3rd Edition)
Languages and Machines: An Introduction to the Theory of Computer Science (3rd Edition)
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 problem is to find the maximum number of 1's that can be printed by an n-state Turing machine of a particular type. A critical step in the evaluation of this value is to determine whether or not a given n-state Turing machine halts. Whilst this is undecidable in general, it is known to be decidable for n ≤ 3, and undecidable for n ≥ 19. In particular, the decidability question is still open for n = 4 and n = 5. In this paper we discuss our evaluation techniques for busy beaver machines based on induction methods to show the non-termination of particular classes of machines. These are centred around the generation of inductive conjectures about the execution of the machine and the evaluation of these conjectures on a particular evaluation engine. Unlike previous approaches, our aim is not limited to reducing the search space to a size that can be checked by hand; we wish to eliminate hand analysis entirely, if possible, and to minimise it where we cannot. We describe our experiments for the n = 4 and n = 5 cases appropriate inductive conjectures.