0RB1LD 1LC1RB 1LD1RE 1LA1LE 1LZ0RC - Revision history

Azerty: Fixed a link

2025-12-06T21:34:35Z

Fixed a link

← Older revision		Revision as of 21:34, 6 December 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[~~Busy Beaver Functions~~\|num(5)]] champion (the [[BB(5)\|five-state, two-symbol]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with 165 consecutive ones on the tape.		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Maximum Consecutive Ones Function\|num(5)]] champion (the [[BB(5)\|five-state, two-symbol]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with 165 consecutive ones on the tape.

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

MrSolis: :(

2025-10-07T22:39:00Z

← Older revision		Revision as of 22:39, 7 October 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Busy Beaver Functions\|num(5)]] champion (the [[BB(5)\|five-state, two-symbol]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with 165 consecutive ones on the tape.

	~~<math display="block">0^\infty \; <\text{Z} \; 1^{165} \; 0^\infty</math>~~

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

	== Analysis ~~by Shawn Ligocki~~ ==		== Analysis ==
			Let <math>A(a):=0^\infty\;1^a\;\textrm{<}\textrm{A}\;11\;0^\infty</math>. Then,
	<~~pre~~>		<math display="block">\begin{array}{lll}A(3a)&\to&A(4a+2)\\A(3a+1)&\to&A(4a+4)\\A(3a+2)&\to&0^\infty\;\textrm{<}\textrm{Z}\;1^{4a+5}\;0^\infty\end{array}</math>
	A(a~~, b~~) = $ 1^a <A 11^~~b $~~		== Trajectory ==
			This Turing machine starts with <math>A(3)</math> after 13 steps and halts after 10 rule applications:
	~~A(a+3, b) -~~> ~~A(a~~, ~~b+2)~~		<math display="block">A(3)\to A(6)\to A(10)\to A(16)\to A(24)\to A(34)\to A(48)\to A(66)\to A(90)\to A(122)\to 0^\infty\;\textrm{<}\textrm{Z}\;1^{165}\;0^\infty</math>
	~~A(0, b) -~~> ~~A(2b, 1)~~
	~~A(1, b) -> A(0, b+1)~~
	~~A(2, b) -> $ <Z 1^~~{~~2b+3~~} $

	A(~~3k, 1~~) -> A(4k+2~~, 1~~)
	A(3k+1, 1) -> A(4k+4~~, 1~~)
	A(3k+2~~, 1~~) ~~-> $~~ <Z 1^{4k+5} $

	~~@13:~~ A(3~~, 1~~)

	~~Trajectory of~~ "a" ~~values starting from~~ A(3~~, 1~~):
	3 6 10 16 24 34 48 66 90 122 ~~Halt(~~165)
	</~~pre~~>

	== References ==		== References ==
	<references/>		<references/>
	[[Category:BB(5)]]		[[Category:BB(5)]]

RobinCodes: Attempted fix for "math input error" for this page

2025-10-07T19:42:21Z

Attempted fix for "math input error" for this page

← Older revision		Revision as of 19:42, 7 October 2025
Line 2:		Line 2:
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape

	<math display="block">0^\infty \; \~~textrm~~{<Z} \; 1^{165} \; 0^\infty</math>		<math display="block">0^\infty \; <\text{Z} \; 1^{165} \; 0^\infty</math>

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

Polygon: Added Category:BB(5)

2025-09-27T16:48:51Z

Added Category:BB(5)

← Older revision		Revision as of 16:48, 27 September 2025
Line 28:		Line 28:
	== References ==		== References ==
	<references/>		<references/>
			[[Category:BB(5)]]

Polygon: Added halt to bbch-link

2025-08-16T17:51:41Z

Added halt to bbch-link

← Older revision		Revision as of 17:51, 16 August 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape

	<math display="block">0^\infty \; \textrm{<Z} \; 1^{165} \; 0^\infty</math>		<math display="block">0^\infty \; \textrm{<Z} \; 1^{165} \; 0^\infty</math>

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

	== Analysis by Shawn Ligocki ==		== Analysis by Shawn Ligocki ==

Polygon: Removed excess line

2025-08-11T09:53:12Z

Removed excess line

← Older revision		Revision as of 09:53, 11 August 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}

	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape

Sligocki at 16:54, 9 July 2025

2025-07-09T16:54:06Z

← Older revision		Revision as of 16:54, 9 July 2025
Line 3:		Line 3:
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape

	<math display="block">0^\infty <Z \; 1^{165} \; 0^\infty</math>		<math display="block">0^\infty \; \textrm{<Z} \; 1^{165} \; 0^\infty</math>

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

Sligocki at 00:28, 9 February 2025

2025-02-09T00:28:59Z

← Older revision		Revision as of 00:28, 9 February 2025
Line 26:		Line 26:
	3 6 10 16 24 34 48 66 90 122 Halt(165)		3 6 10 16 24 34 48 66 90 122 Halt(165)
	</pre>		</pre>

			== References ==
			<references/>

Sligocki: link to announcement

2025-02-09T00:28:26Z

link to announcement

← Older revision		Revision as of 00:28, 9 February 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}

	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho. It halts after 15590 steps with tape		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}} is the [[Busy Beaver Functions\|num]](5) champion (the [[BB(5)]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with tape

	<math display="block">0^\infty <Z \; 1^{165} \; 0^\infty</math>		<math display="block">0^\infty <Z \; 1^{165} \; 0^\infty</math>

Sligocki: Add permutation TM as well

2025-02-09T00:24:25Z

Add permutation TM as well

← Older revision		Revision as of 00:24, 9 February 2025
Line 4:		Line 4:

	<math display="block">0^\infty <Z \; 1^{165} \; 0^\infty</math>		<math display="block">0^\infty <Z \; 1^{165} \; 0^\infty</math>

			It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).

	== Analysis by Shawn Ligocki ==		== Analysis by Shawn Ligocki ==

← Older revision		Revision as of 21:34, 6 December 2025
Line 1:		Line 1:
	{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}		{{machine\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC}}
	{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[~~Busy Beaver Functions~~\|num(5)]] champion (the [[BB(5)\|five-state, two-symbol]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with 165 consecutive ones on the tape.		{{TM\|0RB1LD_1LC1RB_1LD1RE_1LA1LE_1LZ0RC\|halt}} is the [[Maximum Consecutive Ones Function\|num(5)]] champion (the [[BB(5)\|five-state, two-symbol]] TM which halts leaving the most consecutive ones on the tape) according to Andrés Sancho.<ref>[https://discord.com/channels/960643023006490684/1242208042460647575/1337655697348886558 Discord message] by Andrés Sancho on 8 Feb 2025</ref><ref>https://github.com/MatterAndy/BB5-contiguous-1s</ref> It halts after 15590 steps with 165 consecutive ones on the tape.

	It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).		It is tied for the num(5) championship with {{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}} which is the [[TNF-1RB]] version of the same TM (The [[permutation]] of this TM starting at state B).