Maximum Consecutive Ones Function - Revision history

Sligocki: Indicate which values are known exactly and which are bounds.

2025-12-27T16:55:29Z

Indicate which values are known exactly and which are bounds.

← Older revision		Revision as of 16:55, 27 December 2025
Line 11:		Line 11:
	!Source		!Source
	\|-		\|-
	\| [[BB(1)]]\|\| 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\| [[BB(1)]]\|\| = 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
	\|[[BB(2)]]		\|[[BB(2)]]
	\|4		\|= 4
	\|{{TM\|1RB1LB_1LA1LZ\|halt}}		\|{{TM\|1RB1LB_1LA1LZ\|halt}}
	\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^3 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^3 \; 0^\infty</math>
Line 21:		Line 21:
	\|-		\|-
	\|[[BB(3)]]		\|[[BB(3)]]
	\|6		\|= 6
	\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others		\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others
	\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^5 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^5 \; 0^\infty</math>
Line 27:		Line 27:
	\|-		\|-
	\|[[BB(4)]]		\|[[BB(4)]]
	\|12		\|= 12
	\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}		\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}
	\|<math>0^\infty \; 1^{12} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{12} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
Line 33:		Line 33:
	\|-		\|-
	\|[[BB(5)]]		\|[[BB(5)]]
	\|165		\|= 165
	\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}		\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
Line 39:		Line 39:
	\|-		\|-
	\|[[BB(2,3)]]		\|[[BB(2,3)]]
	\|6		\|= 6
	\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}		\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}
	\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>		\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>
Line 45:		Line 45:
	\|-		\|-
	\|[[BB(3,3)]]		\|[[BB(3,3)]]
	\|12		\|≥ 12
	\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}		\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}
	\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{10} \; 0^\infty</math>		\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{10} \; 0^\infty</math>

Polygon: /* Champions */ added num(2,3)

2025-12-27T12:37:03Z

Champions: added num(2,3)

← Older revision		Revision as of 12:37, 27 December 2025
Line 37:		Line 37:
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
			\|-
			\|[[BB(2,3)]]
			\|6
			\|{{TM\|1RB1LA1LB_0LA2RA1RZ\|halt}}
			\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{4} \; 0^\infty</math>
			\|
	\|-		\|-
	\|[[BB(3,3)]]		\|[[BB(3,3)]]

Polygon: /* Champions */ num(4,3) is an approximation

2025-12-27T11:55:15Z

Champions: num(4,3) is an approximation

← Older revision		Revision as of 11:55, 27 December 2025
Line 45:		Line 45:
	\|-		\|-
	\|[[BB(4,3)]]*		\|[[BB(4,3)]]*
	\|<math>10 {\uparrow}^{4} 4</math>		\|<math>> 10 {\uparrow}^{4} 4</math>
	\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}		\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}
	\|<math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 1 \; (11)^{2e_4 + 8} \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 1 \; (11)^{2e_4 + 8} \; 0^\infty</math>

Polygon: /* Champions */ added halting tape for num(3,3)

2025-12-27T11:51:22Z

Champions: added halting tape for num(3,3)

← Older revision		Revision as of 11:51, 27 December 2025
Line 41:		Line 41:
	\|12		\|12
	\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}		\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}
	\|		\|<math>0^\infty \; 1^2 \; \textrm{Z}\textrm{>} \; 1^{10} \; 0^\infty</math>
	\|		\|
	\|-		\|-

Polygon: This needs the 1RZ transition as otherwise there is a 2 in between the ones

2025-12-27T11:38:51Z

This needs the 1RZ transition as otherwise there is a 2 in between the ones

← Older revision		Revision as of 11:38, 27 December 2025
Line 40:		Line 40:
	\|[[BB(3,3)]]		\|[[BB(3,3)]]
	\|12		\|12
	\|{{TM\|~~1RB1RA---_1LC1LC2LA_2RA1LB1LA~~\|halt}}		\|{{TM\|1RB1RA1RZ_1LC1LC2LA_2RA1LB1LA\|halt}}
	\|		\|
	\|		\|

Polygon: forgot to actually remove it :I

2025-12-27T11:37:09Z

forgot to actually remove it :I

← Older revision		Revision as of 11:37, 27 December 2025
Line 37:		Line 37:
	\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
	\|-
	~~\|[[BB(2,3)]]~~
	\|5
	~~\|{{TM\|1RB1LB1RC_1LC1LA---\|halt}}~~
	\|
	\|
	\|-		\|-
	\|[[BB(3,3)]]		\|[[BB(3,3)]]

Polygon: /* Champions */ removing num(2,3) (its a num(3,2) contender, reformatting the TM into (2,3) format yields no result)

2025-12-27T11:36:24Z

Champions: removing num(2,3) (its a num(3,2) contender, reformatting the TM into (2,3) format yields no result)

← Older revision		Revision as of 11:36, 27 December 2025
Line 40:		Line 40:
	\|[[BB(2,3)]]		\|[[BB(2,3)]]
	\|5		\|5
	\|{{TM\|~~1RB1LB_1RC1LC_1LA~~---\|halt}}		\|{{TM\|1RB1LB1RC_1LC1LA---\|halt}}
	\|		\|
	\|		\|

Polygon: /* Champions */ added halting tape for num(4,3)

2025-12-27T11:30:58Z

Champions: added halting tape for num(4,3)

← Older revision		Revision as of 11:30, 27 December 2025
Line 50:		Line 50:
	\|		\|
	\|-		\|-
	\|[[BB(4,3)]]		\|[[BB(4,3)]]*
	\|<math>10 {\uparrow}^{4} 4</math>		\|<math>10 {\uparrow}^{4} 4</math>
	\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}		\|{{TM\|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD\|halt}}
	\|		\|<math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 1 \; (11)^{2e_4 + 8} \; 0^\infty</math>
	\|		\|
	\|}		\|}
			<nowiki>*</nowiki> <math>e_4 = f_2(\frac{2e_3+4} 3, f_1^{2}(91))</math>, where <math>e_3 = f_2(\frac{2e_2+7} 3, f_1^{2}(91))</math>, where <math>e_2 = f_2(\frac{2e_1+7} 3, f_1^{2}(91))</math>, where <math>e_1 = 2^{95} \times 3 - 5</math>. <math>f_1(n) = 2^{n+4} \times 3 -5</math> and <math>f_2(a,b) = f_1^{2 \times f_2(a-1, b) + 11}(1)</math>, where<math>f_2(0, b) = b</math>.

	Note: All TMs here are listed in [[TNF-1RB]] format with the exception that sometimes the halt transition is chosen to be <code>1LZ</code> when that leads to a "simpler" halting configuration.		Note: All TMs here are listed in [[TNF-1RB]] format with the exception that sometimes the halt transition is chosen to be <code>1LZ</code> when that leads to a "simpler" halting configuration.

Azerty: Added more champions.

2025-12-27T08:49:14Z

Added more champions.

@@ Line 8: / Line 8: @@
 |+ Known Values of num(n) function
 |-
-! Domain !! <math>num(n)</math> !! Champion TM !! Halting Config
+! Domain !! <math>num(n)</math>!! Champion TM !! Halting Config
 !Source
 |-
@@ Line 37: / Line 37: @@
 |<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
 |[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
 |}
 Note: All TMs here are listed in [[TNF-1RB]] format with the exception that sometimes the halt transition is chosen to be <code>1LZ</code> when that leads to a "simpler" halting configuration.

MrSolis: <°ᗨ°)⦣

2025-10-07T23:28:35Z

<°ᗨ°)⦣

← Older revision		Revision as of 23:28, 7 October 2025
Line 11:		Line 11:
	!Source		!Source
	\|-		\|-
	\| [[BB(1)]]\|\| 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z>} \; 0^\infty</math>		\| [[BB(1)]]\|\| 1 \|\| {{TM\|1RZ---\|halt}} \|\| <math>0^\infty \; 1 \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
Line 17:		Line 17:
	\|4		\|4
	\|{{TM\|1RB1LB_1LA1LZ\|halt}}		\|{{TM\|1RB1LB_1LA1LZ\|halt}}
	\|<math>0^\infty \; 1 \; \textrm{<Z} \; 1^3 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^3 \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
Line 23:		Line 23:
	\|6		\|6
	\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others		\|{{TM\|1RB1LC_1RC1LZ_1LA0LB\|halt}} and 3 others
	\|<math>0^\infty \; 1 \; \textrm{<Z} \; 1^5 \; 0^\infty</math>		\|<math>0^\infty \; 1 \; \textrm{<}\textrm{Z} \; 1^5 \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
Line 29:		Line 29:
	\|12		\|12
	\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}		\|{{TM\|1RB0LA_1RC1LB_1LB1RD_1RZ0RA\|halt}}
	\|<math>0^\infty \; 1^{12} \; \textrm{Z>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{12} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|Ben-Amram, Julstrom and Zwick (1996)		\|Ben-Amram, Julstrom and Zwick (1996)
	\|-		\|-
Line 35:		Line 35:
	\|165		\|165
	\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}		\|{{TM\|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB\|halt}}
	\|<math>0^\infty \; 1^{165} \; \textrm{Z>} \; 0^\infty</math>		\|<math>0^\infty \; 1^{165} \; \textrm{Z}\textrm{>} \; 0^\infty</math>
	\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025		\|[https://groups.google.com/g/busy-beaver-discuss/c/pvtXPmuMsAg/m/UP0xcmwoEAAJ Announcement] by Andrés Sancho in Feb 2025
	\|}		\|}