1RB0LF 1RC1RB 1LD0RA 1LB0LE 1RZ0LC 1LA1LF - Revision history

Polygon: /* Analysis by Shawn Ligocki */ Added link to existing user page

2025-10-09T19:17:04Z

Analysis by Shawn Ligocki: Added link to existing user page

← Older revision		Revision as of 19:17, 9 October 2025
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	</pre>		</pre>

	== Analysis by Shawn Ligocki==		== Analysis by [[User:Sligocki\|Shawn Ligocki]] ==
	https://discord.com/channels/960643023006490684/1375512968569028648/1378925307544997898		https://discord.com/channels/960643023006490684/1375512968569028648/1378925307544997898

Polygon: Removed links from analysis headings (consistency with other pages)

2025-10-09T18:59:06Z

Removed links from analysis headings (consistency with other pages)

← Older revision		Revision as of 18:59, 9 October 2025
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	{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}} is a long running halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.		{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}} is a long running halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.

	== Analysis by ~~[[User:isokate\|~~Katelyn Doucette]]==		== Analysis by Katelyn Doucette==
	(These rules were automatically generated by https://github.com/Laturas/shift_overflow_subset_decider)		(These rules were automatically generated by https://github.com/Laturas/shift_overflow_subset_decider)

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	</pre>		</pre>

	== Analysis by ~~[[User:sligocki\|~~Shawn Ligocki]]==		== Analysis by Shawn Ligocki==
	https://discord.com/channels/960643023006490684/1375512968569028648/1378925307544997898		https://discord.com/channels/960643023006490684/1375512968569028648/1378925307544997898

Int-y1: add category BB(6)

2025-09-27T04:45:03Z

add category BB(6)

← Older revision		Revision as of 04:45, 27 September 2025
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	{{TM\|1RB1LE_1RC1RC_1LD0LF_1LE1LD_1RF0LC_1RZ0RA}} exhibits similar behavior but never halts. See proof at: ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]).		{{TM\|1RB1LE_1RC1RC_1LD0LF_1LE1LD_1RF0LC_1RZ0RA}} exhibits similar behavior but never halts. See proof at: ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]).

			[[Category:BB(6)]]

Polygon: Added "halt" to bbch-link

2025-08-16T18:12:53Z

Added "halt" to bbch-link

← Older revision		Revision as of 18:12, 16 August 2025
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	{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}		{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}
	{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.		{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF\|halt}} is a long running halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.

	== Analysis by [[User:isokate\|Katelyn Doucette]]==		== Analysis by [[User:isokate\|Katelyn Doucette]]==

Polygon: Changed "halting" to lowercase

2025-08-06T09:50:08Z

Changed "halting" to lowercase

← Older revision		Revision as of 09:50, 6 August 2025
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	{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}		{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}
	{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running ~~Halting~~ [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.		{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.

	== Analysis by [[User:isokate\|Katelyn Doucette]]==		== Analysis by [[User:isokate\|Katelyn Doucette]]==

Int-y1: 2nd -> 4th

2025-07-09T01:14:12Z

2nd -> 4th

← Older revision		Revision as of 01:14, 9 July 2025
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	{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}		{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}
	{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the ~~second~~ longest known running halting [[BB(6)]] TM.		{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the 4th longest known running halting [[BB(6)]] TM.

	== Analysis by [[User:isokate\|Katelyn Doucette]]==		== Analysis by [[User:isokate\|Katelyn Doucette]]==

Isokate: /* Related TMs */

2025-06-04T15:49:39Z

Related TMs

← Older revision		Revision as of 15:49, 4 June 2025
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	All of these machines are fundamentally characterized by the rule <code>A(a, 2^n - 1, c) -> A(a + 2^n (4(4^c - 1)/3) - 3c, 2^{n+2c} - 1, 0)</code> and only differ in starting conditions and reset behavior.		All of these machines are fundamentally characterized by the rule <code>A(a, 2^n - 1, c) -> A(a + 2^n (4(4^c - 1)/3) - 3c, 2^{n+2c} - 1, 0)</code> and only differ in starting conditions and reset behavior.

	{{TM\|1RB1LE_1RC1RC_1LD0LF_1LE1LD_1RF0LC_1RZ0RA}} ~~is also believed to exhibit~~ similar behavior but ~~has not yet been thoroughly analyzed~~.		{{TM\|1RB1LE_1RC1RC_1LD0LF_1LE1LD_1RF0LC_1RZ0RA}} exhibits similar behavior but never halts. See proof at: ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]).

Sligocki: add machine template

2025-06-03T02:20:01Z

add machine template

← Older revision		Revision as of 02:20, 3 June 2025
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			{{Machine\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}}
	{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the second longest known running halting [[BB(6)]] TM.		{{TM\|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the second longest known running halting [[BB(6)]] TM.

Isokate: Created page with "{{TM|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting BB(6) TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a shift overflow counter that halts with a final sigma score of roughly $10 \uparrow \uparrow 7.52390$ . It is currently the second longest known running halting BB(6) TM. == Analysis by User:isokate|Katel..."

2025-06-02T20:48:02Z

Created page with "{{TM|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting BB(6) TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a shift overflow counter that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the second longest known running halting BB(6) TM. == Analysis by User:isokate|Katel..."

New page

{{TM|1RB0LF_1RC1RB_1LD0RA_1LB0LE_1RZ0LC_1LA1LF}} is a long running Halting [[BB(6)]] TM first analyzed by Katelyn Doucette on 1 Jun 2025 ([https://discord.com/channels/960643023006490684/1375512968569028648/1378916236104171562 Discord Link]). It is a [[shift overflow counter]] that halts with a final sigma score of roughly <math>10 \uparrow \uparrow 7.52390</math>. It is currently the second longest known running halting [[BB(6)]] TM.

== Analysis by [[User:isokate|Katelyn Doucette]]==
(These rules were automatically generated by https://github.com/Laturas/shift_overflow_subset_decider)

<pre>
START = A(5, 2^2 - 1, 0) at step 57
A(3k, 2^n - 1, 0) -> HALT
A(3k + 1, 2^n - 1, 0) -> A(5, 2^2 - 1, n + 2k + 0)
A(3k + 2, 2^n - 1, 0) -> A(5, 2^2 - 1, n + 2k + 1)
A(a, 2^n - 1, c) -> A(a + 2^n (4(4^c - 1)/3) - 3c, 2^{n+2c} - 1, 0)

---------- RULE EVALUATION ----------
START = A(5, 2^2 - 1, 0)
A(5, 2^2 - 1, 0) -> A(5, 2^2 - 1, 5) -> A(5446, 2^12 - 1, 0) (mod 6377292)
A(5446, 2^12 - 1, 0) -> A(5, 2^2 - 1, 3642) -> A(195563, 2^7286 - 1, 0) (mod 708588)
A(195563, 2^7286 - 1, 0) -> A(5, 2^2 - 1, 137661) -> A(72002, 2^39128 - 1, 0) (mod 78732)
A(72002, 2^39128 - 1, 0) -> A(5, 2^2 - 1, 8397) -> A(7430, 2^8048 - 1, 0) (mod 8748)
A(7430, 2^8048 - 1, 0) -> A(5, 2^2 - 1, 1337) -> A(838, 2^732 - 1, 0) (mod 972)
A(838, 2^732 - 1, 0) -> A(5, 2^2 - 1, 318) -> A(107, 2^98 - 1, 0) (mod 108)
A(107, 2^98 - 1, 0) -> A(5, 2^2 - 1, 25) -> A(6, 2^4 - 1, 0) (mod 12)
-> HALT
</pre>

== Analysis by [[User:sligocki|Shawn Ligocki]]==
https://discord.com/channels/960643023006490684/1375512968569028648/1378925307544997898

<pre>
1RB0LF_1RC1RB_1LD0RA_1LB0LE_---0LC_1LA1LF
0 (5, 2, 5, 2, 0, 1)
1 (((-46 + 2^14)/3), 12, 5, 2, 0, 1)
2 (((-11 + 2^((56 + 2^16)/9) + -1 * 2^15)/3), ((38 + 2^16)/9), 5, 2, 0, 1)
3 (((-14 + 2^((62 + 2^((74 + 2^16)/9))/9) + -1 * 2^((65 + 2^16)/9))/3), ((44 + 2^((74 + 2^16)/9))/9), 5, 2, 0, 1)
4 (((-14 + 2^((62 + 2^((80 + 2^((74 + 2^16)/9))/9))/9) + -1 * 2^((71 + 2^((74 + 2^16)/9))/9))/3), ((44 + 2^((80 + 2^((74 + 2^16)/9))/9))/9), 5, 2, 0, 1)
5 (((-14 + 2^((62 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9) + -1 * 2^((71 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/3), ((44 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9), 5, 2, 0, 1)
6 (((-11 + 2^((56 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9) + -1 * 2^((71 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/3), ((38 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9), 5, 2, 0, 1)
7 (((-14 + 2^((62 + 2^((74 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9))/9) + -1 * 2^((65 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9))/3), ((44 + 2^((74 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9))/9), 5, 2, 0, 1)
Halted with score: ~10↑↑7.52390 = ((34 + 2^((71 + 2^((74 + 2^((80 + 2^((80 + 2^((80 + 2^((74 + 2^16)/9))/9))/9))/9))/9))/9))/9)
</pre>

== Equivalent TMs ==
The following TMs have near identical behavior, producing the same values but do so slightly more efficiently:
<pre>
1RB0LF_1RC1RB_1LD0RA_1LF0LE_---0LC_1LA1LF
1RB0LF_1RC1RB_1LD0RA_1RF0LE_---0LC_1LA1LF
</pre>

== Related TMs ==
This TM is part of a broader family of 15 turing machines with similar rules. The family is made up of the following:
<pre>
1RB1RA_1LC0RF_---0LD_0LE0LB_1LF1LE_1RA0LE
1RB0RE_1LC0RF_1LD1LC_1RA0LB_---0RD_1RB1RF
1RB0LF_1RC1RB_1LD0RA_0RF0LE_---0LC_1LA1LF
1RB0LF_1RC1RB_1LD0RA_0RA0LE_---0LC_1LA1LF
1RB0LF_1LC1LB_1RD0LB_1RE1RD_1LA0RC_---0LE
1RB0LF_1RC1RB_1LD0RA_1RA0LE_---0LC_1LA1LF
1RB0LE_1LC0RD_1LA1LC_---0RA_1LC0RF_1RE1RF
1RB0LF_1RC1RB_1LD0RA_1LA0LE_---0LC_1LA1LF
1RB0LD_1RC0RF_1RD1RC_1LE0RC_1LA1LE_---0RA
1RB0LF_1RC1RB_1LD0RA_1RF0LE_---0LC_1LA1LF
1RB0LD_1RC0RF_1LA1LC_1LC0RE_1RD1RE_---0RA
1RB1RA_1LC0RA_1LD1LC_1RE0LB_0LA0RF_---0RD
1RB0LC_0LC0RF_1LE0RD_1RC1RD_1LA1LE_---0RA
1RB0LF_1RC1RB_1LD0RA_1LB0LE_---0LC_1LA1LF
1RB0LF_1RC1RB_1LD0RA_1LF0LE_---0LC_1LA1LF
</pre>

All of these turing machines have been shown to halt. Interestingly, <code>1RB1RA_1LC0RF_---0LD_0LE0LB_1LF1LE_1RA0LE</code> is the only one to halt when the unary counter is equal to 1 mod 3 or 2 mod 3 instead of 0 mod 3.

All of these machines are fundamentally characterized by the rule <code>A(a, 2^n - 1, c) -> A(a + 2^n (4(4^c - 1)/3) - 3c, 2^{n+2c} - 1, 0)</code> and only differ in starting conditions and reset behavior.

{{TM|1RB1LE_1RC1RC_1LD0LF_1LE1LD_1RF0LC_1RZ0RA}} is also believed to exhibit similar behavior but has not yet been thoroughly analyzed.