BB(n,1) - Revision history

Polygon: Linked champions, added See also with a link to BB(1,m)

2026-02-20T12:34:37Z

Linked champions, added See also with a link to BB(1,m)

← Older revision		Revision as of 12:34, 20 February 2026
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	'''BB(n,1)''' is the Busy Beaver problem for n-state, 1-symbol TMs. It is trivial that Σ(n,1) = 0, as 1-symbol TMs cannot print any non-zero symbols. As any transition back to an already visited state will put the machine in an infinite loop, the most effective halting strategy is to pass through the states one by one, halting only in the final state, thus making BB(n,1) = n.		'''BB(n,1)''' is the Busy Beaver problem for n-state, 1-symbol TMs. It is trivial that Σ(n,1) = 0, as 1-symbol TMs cannot print any non-zero symbols. As any transition back to an already visited state will put the machine in an infinite loop, the most effective halting strategy is to pass through the states one by one, halting only in the final state, thus making BB(n,1) = n.

	==Champions==		== Champions ==
	By translating state names into numbers (such that A=1, B=2, etc.), the 1-symbol champions can be defined in the following way:		By translating state names into numbers (such that A=1, B=2, etc.), the 1-symbol [[champions]] can be defined in the following way:
	* 0R[1,a] = 0RZ		* 0R[1,a] = 0RZ
	* 0R[n,a] = 0Ra_0R[n-1,a+1] for n>1		* 0R[n,a] = 0Ra_0R[n-1,a+1] for n>1
	For the n-state champion, start with 0R[n,2].		For the n-state champion, start with 0R[n,2].
	[[Category:BB Domains]]		[[Category:BB Domains]]

			== See also ==
			* [[BB(1,m)]]

Polygon: /* Champions */ Added champions

2025-08-30T15:49:17Z

Champions: Added champions

← Older revision		Revision as of 15:49, 30 August 2025
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	==Champions==		==Champions==
			By translating state names into numbers (such that A=1, B=2, etc.), the 1-symbol champions can be defined in the following way:
			* 0R[1,a] = 0RZ
			* 0R[n,a] = 0Ra_0R[n-1,a+1] for n>1
			For the n-state champion, start with 0R[n,2].
	[[Category:BB Domains]]		[[Category:BB Domains]]

Polygon: Added champions section and category

2025-08-30T15:37:57Z

Added champions section and category

← Older revision		Revision as of 15:37, 30 August 2025
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	'''BB(n,1)''' is the Busy Beaver problem for n-state, 1-symbol TMs. It is trivial that Σ(n,1) = 0, as 1-symbol TMs cannot print any non-zero symbols. As any transition back to an already visited state will put the machine in an infinite loop, the most effective halting strategy is to pass through the states one by one, halting only in the final state, thus making BB(n,1) = n.		'''BB(n,1)''' is the Busy Beaver problem for n-state, 1-symbol TMs. It is trivial that Σ(n,1) = 0, as 1-symbol TMs cannot print any non-zero symbols. As any transition back to an already visited state will put the machine in an infinite loop, the most effective halting strategy is to pass through the states one by one, halting only in the final state, thus making BB(n,1) = n.

			==Champions==
			[[Category:BB Domains]]

Polygon: Created page for 1-symbol TMs

2025-08-30T15:33:21Z

Created page for 1-symbol TMs

New page

'''BB(n,1)''' is the Busy Beaver problem for n-state, 1-symbol TMs. It is trivial that Σ(n,1) = 0, as 1-symbol TMs cannot print any non-zero symbols. As any transition back to an already visited state will put the machine in an infinite loop, the most effective halting strategy is to pass through the states one by one, halting only in the final state, thus making BB(n,1) = n.