BB(1,m) - Revision history

Polygon: Added link to single symbol TMs

2025-12-07T12:34:24Z

Added link to single symbol TMs

← Older revision		Revision as of 12:34, 7 December 2025
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	BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1. Note that Σ(1,1) = 0 as 1-symbol TMs cannot print non-zero symbols.		BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1. Note that Σ(1,1) = 0 as [[BB(n,1)\|1-symbol TMs]] cannot print non-zero symbols.

	==Champions==		==Champions==

Polygon: Added note about Σ(1,1)

2025-08-30T15:54:32Z

Added note about Σ(1,1)

← Older revision		Revision as of 15:54, 30 August 2025
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	BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1.		BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1. Note that Σ(1,1) = 0 as 1-symbol TMs cannot print non-zero symbols.

	==Champions==		==Champions==

Polygon: /* Champions */ Made champions section consistent with other domain pages

2025-08-30T14:30:39Z

Champions: Made champions section consistent with other domain pages

← Older revision		Revision as of 14:30, 30 August 2025
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	==Champions==		==Champions==
	S(1,m) = 1~~, achieved by:~~		S(1,m) = 1 and Σ(1,m) = 1 are both achieved by only one [[champion]] in TNF:
	* {{TM\|1RZ---\|halt}}
	Σ(1,m) = 1, achieved by:
	* {{TM\|1RZ---\|halt}}		* {{TM\|1RZ---\|halt}}
	[[Category:BB Domains]]		[[Category:BB Domains]]

Sligocki: Update to BB(1,m)

2025-08-25T20:40:56Z

Update to BB(1,m)

← Older revision		Revision as of 20:40, 25 August 2025
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	BB(1) ~~refers to~~ the ~~busy beaver~~ problem for 1 state ~~and 2 symbols~~. ~~It is~~ relatively trivial ~~with~~ only 3 different turing machines in [[TNF]]: One halting: ~~{{TM\|~~1RZ~~---\|halt}}~~ and ~~two~~ trivial [[Translated Cyclers]]: ~~{{TM\|~~0RA~~---}}~~ and ~~{{TM\|~~1RA~~---}}~~. ~~TMs in BB domains with just a single state have the special property of only having access to one of their transitions (A0),~~ effectively ~~making them~~ 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1.		BB(1,m) is the Busy Beaver problem for 1-state, m-symbol TMs. They are relatively trivial. No matter how many symbols you have, [[TNF]] only has access to a single transition, the initial <code>A0</code> transition. In fact, there are only 3 different turing machines in [[TNF]]: One halting: <code>A0:1RZ</code> and 2 trivial [[Translated Cyclers]]: <code>A0:0RA</code> and <code>A0:1RA</code>. These are effectively 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1.

	==Champions==		==Champions==
	S(1) = 1, achieved by:		S(1,m) = 1, achieved by:
	* {{TM\|1RZ---\|halt}}		* {{TM\|1RZ---\|halt}}
	Σ(1) = 1, achieved by:		Σ(1,m) = 1, achieved by:
	* {{TM\|1RZ---\|halt}}		* {{TM\|1RZ---\|halt}}
	[[Category:BB Domains]]		[[Category:BB Domains]]

Sligocki: Sligocki moved page BB(1) to BB(1,m): Generalize to 1 state BB

2025-08-25T20:33:34Z

Sligocki moved page BB(1) to BB(1,m): Generalize to 1 state BB

← Older revision		Revision as of 20:33, 25 August 2025
(No difference)

Polygon: Mentioned 1-state TMs also being BBi(1) TMs

2025-08-25T10:50:43Z

Mentioned 1-state TMs also being BBi(1) TMs

← Older revision		Revision as of 10:50, 25 August 2025
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	BB(1) refers to the busy beaver problem for 1 state and 2 symbols. It is relatively trivial with only 3 different turing machines in [[TNF]]: One halting: {{TM\|1RZ---\|halt}} and two trivial [[Translated Cyclers]]: {{TM\|0RA---}} and {{TM\|1RA---}}. TMs in BB domains with just a single state have the special property of only having access to one of their transitions (A0). As a result S(1,m) = 1 and Σ(1,m) = 1.		BB(1) refers to the busy beaver problem for 1 state and 2 symbols. It is relatively trivial with only 3 different turing machines in [[TNF]]: One halting: {{TM\|1RZ---\|halt}} and two trivial [[Translated Cyclers]]: {{TM\|0RA---}} and {{TM\|1RA---}}. TMs in BB domains with just a single state have the special property of only having access to one of their transitions (A0), effectively making them 1-instruction TMs in [[BBi]]. As a result S(1,m) = 1 and Σ(1,m) = 1.

	==Champions==		==Champions==

Polygon: Added additional information

2025-08-24T21:24:20Z

Added additional information

← Older revision		Revision as of 21:24, 24 August 2025
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	BB(1) refers to the busy beaver problem for 1 state and 2 symbols. It is relatively trivial with only 3 different turing machines in [[TNF]]: One halting: {{TM\|1RZ---\|halt}} and two trivial [[Translated Cyclers]]: {{TM\|0RA---}} and {{TM\|1RA---}}.		BB(1) refers to the busy beaver problem for 1 state and 2 symbols. It is relatively trivial with only 3 different turing machines in [[TNF]]: One halting: {{TM\|1RZ---\|halt}} and two trivial [[Translated Cyclers]]: {{TM\|0RA---}} and {{TM\|1RA---}}. TMs in BB domains with just a single state have the special property of only having access to one of their transitions (A0). As a result S(1,m) = 1 and Σ(1,m) = 1.

	==Champions==		==Champions==

Sligocki: Note how small this domain is.

2025-08-24T21:13:15Z

Note how small this domain is.

← Older revision		Revision as of 21:13, 24 August 2025
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	BB(1) refers to the busy beaver problem for 1 state and 2 symbols.		BB(1) refers to the busy beaver problem for 1 state and 2 symbols. It is relatively trivial with only 3 different turing machines in [[TNF]]: One halting: {{TM\|1RZ---\|halt}} and two trivial [[Translated Cyclers]]: {{TM\|0RA---}} and {{TM\|1RA---}}.

	==Champions==		==Champions==
	S(1) = 1, achieved by:		S(1) = 1, achieved by:

Polygon: Made champions section more consistent with other BB domain pages.

2025-08-24T21:04:51Z

Made champions section more consistent with other BB domain pages.

← Older revision		Revision as of 21:04, 24 August 2025
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	BB(1) refers to the busy beaver problem for 1 state and 2 symbols.		BB(1) refers to the busy beaver problem for 1 state and 2 symbols.
	==Champions==		==Champions==
	~~{\| class~~=~~"wikitable"~~		S(1) = 1, achieved by:
	~~! !!~~1~~-state~~		* {{TM\|1RZ---\|halt}}
	\|-		Σ(1) = 1, achieved by:
	~~! 2~~-~~symbol~~		* {{TM\|1RZ---\|halt}}
	~~\| [[BB~~(1)]] = 1 ~~(Halt)~~
	\|}

	[[Category:BB Domains]]		[[Category:BB Domains]]

Polygon: Added introduction

2025-08-24T20:55:14Z

Added introduction

← Older revision		Revision as of 20:55, 24 August 2025
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			BB(1) refers to the busy beaver problem for 1 state and 2 symbols.
			==Champions==
	{\| class="wikitable"		{\| class="wikitable"
	! !!1-state		! !!1-state