Instruction-Limited Busy Beaver - Revision history

Loader3229: /* Champions */

2026-11-10T11:39:17Z

Champions

← Older revision		Revision as of 11:39, 10 November 2026
Line 285:		Line 285:
	\|-		\|-
	\| style="text-align: right;" \| 33		\| style="text-align: right;" \| 33
	\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(6)</math>		\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(7)</math>
	\| colspan="2" \|<span style="word-break:break-all">{{TM\|~~1LD2RG2LA3LG_~~---~~2LH2RB2RF_0RI1RC2RB3LG_0RC1RC1LD3RD_3RD1LE1LE3LE_1RZ3LD2LE3LE_1RG1LH2RG3LG_1RC2LH1LA1LE_3LI3LE~~---~~3LA~~\|halt}}</span>		\| colspan="2" \|<span style="word-break:break-all">{{TM\|1LD2RG2LA3LG---_---2LH2RB2RF---_4LE1RC2RB3LG4RE_0RC1RC1LD3RD3LA_3RD1LE1LE3LE---_1RZ3LD2LE3LE---_1RG1LH2RG3LG3LF_1RC2LH1LA1LE---\|halt}}</span>
	\|[[User:Loader3229]] in 2026		\|[[User:Loader3229]] in 2026
	\|		\|

Loader3229: /* Champions */

2026-11-10T11:25:06Z

Champions

← Older revision		Revision as of 11:25, 10 November 2026
Line 278:		Line 278:
	\|-		\|-
	\| style="text-align: right;" \| 32		\| style="text-align: right;" \| 32
	\| colspan="2" style="text-align: right;" \| <math>> f_{\omega ~~\times~~ 2+1}(~~130~~)</math>		\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(4)</math>
	\| colspan="2" \|<span style="word-break:break-all">{{TM\|~~5LF3LB1LG2RA4LB~~---~~_2LC3RB1LD2RA3LF2LB_3RB1LB3LC2RC4LC0LE_3RB~~---~~3LC2RC~~---~~3RE_5RC3RE2LF4LC---0RB_5RB---2LE1LF------_------1LG3LG---0LE~~\|halt}}</span>		\| colspan="2" \|<span style="word-break:break-all">{{TM\|1LD2RG2LA3LG_---2LH2RB2RF_3LI1RC2RB3LG_0RC1RC1LD3RD_3RD1LE1LE3LE_1RZ3LD2LE3LE_1RG1LH2RG3LG_1RC2LH1LA1LE_3LA3LE------\|halt}}</span>
	\|[[User:Loader3229]] in 2026		\|[[User:Loader3229]] in 2026
	\|		\|
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	\|-		\|-
	\| style="text-align: right;" \| 33		\| style="text-align: right;" \| 33
	\| colspan="2" \|		\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(6)</math>
	\| colspan="2" \|		\| colspan="2" \|<span style="word-break:break-all">{{TM\|1LD2RG2LA3LG_---2LH2RB2RF_0RI1RC2RB3LG_0RC1RC1LD3RD_3RD1LE1LE3LE_1RZ3LD2LE3LE_1RG1LH2RG3LG_1RC2LH1LA1LE_3LI3LE---3LA\|halt}}</span>
	\|		\|[[User:Loader3229]] in 2026
	\|		\|
	\|		\|
	\|-		\|-
	\| style="text-align: right;" \| 34		\| style="text-align: right;" \| 34
	\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(5)</math>		\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}(16)</math>
	\| colspan="2" \|<span style="word-break:break-all">{{TM\|~~2LG3LB~~---~~2RA4LB---_4LG3RB1LD2RA3LF5RB_3RB1LB3LC2RC4LC1LE_3RB3RE3LC2RC---3RD_5RB3RE---4LC3LG5LE_5RB5RB---1LF---5LF_5LF---1LC1LG---5LG~~\|halt}}</span>		\| colspan="2" \|<span style="word-break:break-all">{{TM\|1LD2RG2LA3LG_3LI2LH2RB2RF_1LG1RC2RB3LG_0RC1RC1LD3RD_3RD1LE1LE3LE_1RZ3LD2LE3LE_1RG1LH2RG3LG_1RC2LH1LA1LE_3LD3LI3LI---\|halt}}</span>
	\|[[User:Loader3229]] in 2026		\|[[User:Loader3229]] in 2026
	\|Cryptid: Goldbach		\|Cryptid: Goldbach

Loader3229: /* Champions */

2026-11-09T12:24:40Z

Champions

← Older revision		Revision as of 12:24, 9 November 2026
Line 327:		Line 327:
	\|-		\|-
	\| style="text-align: right;" \| 41		\| style="text-align: right;" \| 41
	\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}^2(4 \uparrow\uparrow 341)</math>		\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}^3(4 \uparrow\uparrow 341)</math>
	\| colspan="2" \|<span style="word-break:break-all">{{TM\|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR\|halt}}</span>		\| colspan="2" \|<span style="word-break:break-all">{{TM\|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR\|halt}}</span>
	\|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]		\|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]

Jacobzheng: Undo revision 10440 by Jacobzheng (talk)

2026-11-09T09:38:37Z

Undo revision 10440 by Jacobzheng (talk)

← Older revision		Revision as of 09:38, 9 November 2026
Line 324:		Line 324:
	\|		\|
	\|		\|
			\|
			\|-
			\| style="text-align: right;" \| 41
			\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}^2(4 \uparrow\uparrow 341)</math>
			\| colspan="2" \|<span style="word-break:break-all">{{TM\|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR\|halt}}</span>
			\|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]
			\|Current BB(21) champion
	\|		\|
	\|-		\|-

Jacobzheng: this bound is wrong

2026-11-09T04:17:32Z

this bound is wrong

← Older revision		Revision as of 04:17, 9 November 2026
Line 324:		Line 324:
	\|		\|
	\|		\|
	\|
	\|-
	~~\| style="text-align: right;" \| 41~~
	~~\| colspan="2" style="text-align: right;" \| <math>> f_{\omega^2}^2(4 \uparrow\uparrow 341)</math>~~
	\| colspan="2" \|<span style="word-break:break-all">{{TM\|0LI0LF_0RJ1RG_0RD1LC_1RH1RE_1LO0RH_1LA1LF_0LC1LA_1RB1RH_1RD0LF_1LP0RK_0LM1LL_0LL1LM_1LE1LN_0RQ0LM_0RP1LO_1LR0RH_1LF1RQ_---0LS_1LH0LT_1LH1LU_0LE1LR\|halt}}</span>
	~~\|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]~~
	~~\|Current BB(21) champion~~
	\|		\|
	\|-		\|-

Jacobzheng at 03:12, 9 November 2026

2026-11-09T03:12:14Z

← Older revision		Revision as of 03:12, 9 November 2026
Line 572:		Line 572:
	\|TODO		\|TODO
	\|}		\|}


	* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3932964 = BB(2,4).		* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3932964 = BB(2,4).

Jacobzheng at 03:10, 9 November 2026

2026-11-09T03:10:59Z

← Older revision		Revision as of 03:10, 9 November 2026
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	{\| class="wikitable"		{\| class="wikitable"
	!n		!n
	!BBi(n) ~~([[oeis:A384629\|A384629]])~~		!BBi(n,-,2)
	~~!Σi(n) ([[oeis:A384766\|A384766]])~~		!Champions
	~~!Step Champions~~
	!~~Sigma~~ Champions
	!Discovered by		!Discovered by
	!Notes		!Notes
Line 573:		Line 571:
	\|-		\|-
	\|TODO		\|TODO
	}		\|}

Jacobzheng at 03:09, 9 November 2026

2026-11-09T03:09:48Z

@@ Line 561: / Line 561: @@
 * BBi(nm-1, n, m) = BBi(nm, n, m) - 1 = BB(n, m) - 1 for n>=2, m>=2. With one undefined transition, the number of steps is one less than having a completely filled n x m transition table including a halting instruction, which adds one final step.
 * For i>=1, BBi(i, -, 2) = 1, 3, 5, 16, 20, 37, 106, 793, ….  BBi(9, -, 2) is at least 47176869, but it may be even larger if a more powerful 6-state, 2-symbol machine having three undefined transitions can be found. BBi(10, -, 2) will almost certainly be greater than the current lower bound of 47176870 = BB(5,2).
 * For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3932964 = BB(2,4).

Jacobzheng at 02:40, 9 November 2026

2026-11-09T02:40:19Z

← Older revision		Revision as of 02:40, 9 November 2026
Line 561:		Line 561:
	* BBi(nm-1, n, m) = BBi(nm, n, m) - 1 = BB(n, m) - 1 for n>=2, m>=2. With one undefined transition, the number of steps is one less than having a completely filled n x m transition table including a halting instruction, which adds one final step.		* BBi(nm-1, n, m) = BBi(nm, n, m) - 1 = BB(n, m) - 1 for n>=2, m>=2. With one undefined transition, the number of steps is one less than having a completely filled n x m transition table including a halting instruction, which adds one final step.
	* For i>=1, BBi(i, -, 2) = 1, 3, 5, 16, 20, 37, 106, 793, …. BBi(9, -, 2) is at least 47176869, but it may be even larger if a more powerful 6-state, 2-symbol machine having three undefined transitions can be found. BBi(10, -, 2) will almost certainly be greater than the current lower bound of 47176870 = BB(5,2).		* For i>=1, BBi(i, -, 2) = 1, 3, 5, 16, 20, 37, 106, 793, …. BBi(9, -, 2) is at least 47176869, but it may be even larger if a more powerful 6-state, 2-symbol machine having three undefined transitions can be found. BBi(10, -, 2) will almost certainly be greater than the current lower bound of 47176870 = BB(5,2).
	* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of ~~3232964~~ = BB(2,4).		* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3932964 = BB(2,4).

	== Instruction-Limited Busy Beaver Variants ==		== Instruction-Limited Busy Beaver Variants ==

Jacobzheng at 02:39, 9 November 2026

2026-11-09T02:39:47Z

← Older revision		Revision as of 02:39, 9 November 2026
Line 561:		Line 561:
	* BBi(nm-1, n, m) = BBi(nm, n, m) - 1 = BB(n, m) - 1 for n>=2, m>=2. With one undefined transition, the number of steps is one less than having a completely filled n x m transition table including a halting instruction, which adds one final step.		* BBi(nm-1, n, m) = BBi(nm, n, m) - 1 = BB(n, m) - 1 for n>=2, m>=2. With one undefined transition, the number of steps is one less than having a completely filled n x m transition table including a halting instruction, which adds one final step.
	* For i>=1, BBi(i, -, 2) = 1, 3, 5, 16, 20, 37, 106, 793, …. BBi(9, -, 2) is at least 47176869, but it may be even larger if a more powerful 6-state, 2-symbol machine having three undefined transitions can be found. BBi(10, -, 2) will almost certainly be greater than the current lower bound of 47176870 = BB(5,2).		* For i>=1, BBi(i, -, 2) = 1, 3, 5, 16, 20, 37, 106, 793, …. BBi(9, -, 2) is at least 47176869, but it may be even larger if a more powerful 6-state, 2-symbol machine having three undefined transitions can be found. BBi(10, -, 2) will almost certainly be greater than the current lower bound of 47176870 = BB(5,2).
	* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, ~~3232963~~, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3232964 = BB(2,4).		* For i>=1, BBi(i, <=2, -) = 1, 3, 5, 13, 37, 123, 3932963, …. The number of states is specified here as “<=2” rather than “2” so that we can have a valid value for one instruction. (A 1-instruction Turing machine has only one operating state.) BBi(8, <=2, -) will almost certainly be greater than the current lower bound of 3232964 = BB(2,4).

	== Instruction-Limited Busy Beaver Variants ==		== Instruction-Limited Busy Beaver Variants ==