Cycler - Revision history

Polygon: Added information about the decider for cyclers

2025-08-28T11:44:51Z

Added information about the decider for cyclers

← Older revision		Revision as of 11:44, 28 August 2025
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	[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]{{Stub}}		[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]{{Stub}}
	A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.		A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero. The [[decider]] for cyclers works by memorizing all configurations which are visited by a TM. If a configuration is visited twice, the TM is shown to be non-halting.

	The rule for identifying cyclers is simple:		The rule for identifying cyclers is simple:
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	* [https://github.com/bbchallenge/bbchallenge-proofs/blob/build-latex-pdf/deciders/correctness-deciders.pdf Section 2] of bbchallenge's deciders write-up.		* [https://github.com/bbchallenge/bbchallenge-proofs/blob/build-latex-pdf/deciders/correctness-deciders.pdf Section 2] of bbchallenge's deciders write-up.

	[[Category:Zoology]]		[[Category:Zoology]][[Category:Deciders]]

Polygon: Mentioned BBS and BBP

2025-08-17T11:01:10Z

Mentioned BBS and BBP

← Older revision		Revision as of 11:01, 17 August 2025
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	'''û''' → '''û'''		'''û''' → '''û'''
	where '''û''' is any headed tape segment.		where '''û''' is any headed tape segment.

			==Related Functions==

			* Busy Preperiodic Beaver ([[BBS]](n,m)): The longest possible preperiod of a cycler or translated cycler with n states and m symbols.
			* Busy Periodic Beaver ([[BBP]](n,m)): The longest possible period of a cycler or translated cycler with n states and m symbols.

	== See also ==		== See also ==

Polygon: Used Template:Stub

2025-08-10T22:33:34Z

Used Template:Stub

← Older revision		Revision as of 22:33, 10 August 2025
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	[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]		[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]{{Stub}}
	A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.		A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.

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	[[Category:Zoology]]		[[Category:Zoology]]
	~~[[Category:Stub]]~~

Polygon: Changed wording.

2025-08-10T10:22:57Z

Changed wording.

← Older revision		Revision as of 10:22, 10 August 2025
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	[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]		[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]
	A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever~~, so~~ is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.		A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever and thus is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.

	The rule for identifying cyclers is simple:		The rule for identifying cyclers is simple:

Polygon: Added link to deciders write-up

2025-08-09T11:16:41Z

Added link to deciders write-up

← Older revision		Revision as of 11:16, 9 August 2025
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	* [[Translated cycler]]		* [[Translated cycler]]
			* [https://github.com/bbchallenge/bbchallenge-proofs/blob/build-latex-pdf/deciders/correctness-deciders.pdf Section 2] of bbchallenge's deciders write-up.

	[[Category:Zoology]]		[[Category:Zoology]]
	[[Category:Stub]]		[[Category:Stub]]

Icy at 03:45, 10 November 2024

2024-11-10T03:45:43Z

← Older revision		Revision as of 03:45, 10 November 2024
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	[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]		[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]
	A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a [[~~Non~~-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.		A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a [[non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.

	The rule for identifying cyclers is simple:		The rule for identifying cyclers is simple:

Icy at 03:45, 10 November 2024

2024-11-10T03:45:28Z

← Older revision		Revision as of 03:45, 10 November 2024
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	[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]		[[File:1RB0LB 1LB1LC 0RC1RA.png\|alt=1RB0LB_1LB1LC_0RC1RA\|thumb\|upright=1.5\|The record 3-state 2-symbol cycler {{TM\|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]
	A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a [[Non-halting Turing machine]].		A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a [[Non-halting Turing machine]]. A cycler may be seen as a special case of a [[translated cycler]] which has offset zero.

	The rule for identifying cyclers is simple:		The rule for identifying cyclers is simple:
	'''û''' → '''û'''		'''û''' → '''û'''
	where '''û''' is any headed tape segment.		where '''û''' is any headed tape segment.

			== See also ==

			* [[Translated cycler]]

	[[Category:Zoology]]		[[Category:Zoology]]
	[[Category:Stub]]		[[Category:Stub]]

Icy at 03:43, 10 November 2024

2024-11-10T03:43:44Z

← Older revision		Revision as of 03:43, 10 November 2024
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	where '''û''' is any headed tape segment.		where '''û''' is any headed tape segment.

			[[Category:Zoology]]
	[[Category:Stub]]		[[Category:Stub]]

Icy: Created page with "1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4. A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a Non-halting Turing machine. The rule for identifying cyclers is simple: '''û''' → '''û''' where '''û''' is any headed tape segment. Category:Stub"

2024-11-10T03:43:31Z

Created page with "alt=1RB0LB_1LB1LC_0RC1RA|thumb|upright=1.5|The record 3-state 2-symbol cycler {{TM|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4. A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a Non-halting Turing machine. The rule for identifying cyclers is simple: '''û''' → '''û''' where '''û''' is any headed tape segment. Category:Stub"

New page

[[File:1RB0LB 1LB1LC 0RC1RA.png|alt=1RB0LB_1LB1LC_0RC1RA|thumb|upright=1.5|The record 3-state 2-symbol cycler {{TM|1RB0LB_1LB1LC_0RC1RA}}, which has period 18 and preperiod 4.]]
A '''cycler''' is a Turing machine that eventually enters a repeating cycle. Such a Turing machine runs forever, so is a [[Non-halting Turing machine]].

The rule for identifying cyclers is simple:
'''û''' → '''û'''
where '''û''' is any headed tape segment.

[[Category:Stub]]