Maximum Space Function - Revision history

Sligocki: Fix, update and expand list of known space values (and champions)

2025-09-21T15:31:14Z

Fix, update and expand list of known space values (and champions)

← Older revision		Revision as of 15:31, 21 September 2025
Line 13:		Line 13:
	\|[[BB(2)]]		\|[[BB(2)]]
	\|4		\|4
	\|{{TM\|~~1RB1LB_1LA1LZ~~\|halt}}		\|{{TM\|1RB1LB_1LA1RZ\|halt}}, {{TM\|1RB0LB_1LA1RZ\|halt}}
	\|-		\|-
	\|[[BB(3)]]		\|[[BB(3)]]
	\|6		\|7
	\|{{TM\|~~1RB1LC_1RC1LZ_1LA0LB~~\|halt}}		\|{{TM\|1RB1RC_1LC1RZ_1RA0LB\|halt}}, {{TM\|1RB0RC_1LC1RZ_1RA0LB\|halt}}
	\|-		\|-
	\|[[BB(4)]]		\|[[BB(4)]]
	\|14		\|16
	\|{{TM\|~~1RB1LB_1LA0LC_1RZ1LD_1RD0RA~~\|halt}}		\|{{TM\|1RB0RA_1LC0RD_0LD0LB_1RA1RZ\|halt}}
	\|-		\|-
	\|[[BB(5)]]		\|[[BB(5)]]
	\|~~> 4098~~		\|12289
	\|{{TM\|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA\|halt}}		\|{{TM\|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA\|halt}}
			\|-
			\|[[BB(2,3)]]
			\|9
			\|{{TM\|1RB2LB1RZ_2LA2RB1LB\|halt}}
			\|-
			\|[[BB(2,4)]]
			\|2050
			\|{{TM\|1RB2LA1RA1RA_1LB1LA3RB1RZ\|halt}}
	\|}		\|}

Polygon: Added Category:Functions

2025-09-21T15:13:48Z

Added Category:Functions

← Older revision		Revision as of 15:13, 21 September 2025
Line 30:		Line 30:
	== References ==		== References ==
	<references />		<references />
			[[Category:Functions]]

Azerty at 07:34, 20 September 2025

2025-09-20T07:34:52Z

← Older revision		Revision as of 07:34, 20 September 2025
Line 20:		Line 20:
	\|-		\|-
	\|[[BB(4)]]		\|[[BB(4)]]
	\|12		\|14
	\|{{TM\|~~1RB0LA_1RC1LB_1LB1RD_1RZ0RA~~\|halt}}		\|{{TM\|1RB1LB_1LA0LC_1RZ1LD_1RD0RA\|halt}}
	\|-		\|-
	\|[[BB(5)]]		\|[[BB(5)]]
	\|~~165~~		\|> 4098
	\|{{TM\|~~1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB~~\|halt}}		\|{{TM\|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA\|halt}}
	\|}		\|}

	== References ==		== References ==
	<references />		<references />

Azerty: Added Maximum Space Function page

2025-09-20T07:29:49Z

Added Maximum Space Function page

New page

The '''Maximum Space''' function (named <math>space(n)</math> by Ben-Amram)<ref>Ben-Amram A.M., Julstrom B.A. and Zwick U. (1996). [http://dx.doi.org/10.1007/BF01192693 A note on busy beavers and other creatures]. ''Mathematical Systems Theory'' '''29''' (4), July-August 1996, 375-386.</ref> is a [[Busy Beaver function]] which measures the total number of tape cells read before halting. According to Ben-Amram, it includes the starting cell, but not necessarily the cell the halting transition moves to.

== Champions ==
{| class="wikitable"
!Domain
!<math>space(n)</math>
!Champion TM
|-
|[[BB(1)]]
|1
|{{TM|1RZ---|halt}}
|-
|[[BB(2)]]
|4
|{{TM|1RB1LB_1LA1LZ|halt}}
|-
|[[BB(3)]]
|6
|{{TM|1RB1LC_1RC1LZ_1LA0LB|halt}}
|-
|[[BB(4)]]
|12
|{{TM|1RB0LA_1RC1LB_1LB1RD_1RZ0RA|halt}}
|-
|[[BB(5)]]
|165
|{{TM|1RB1LA_1RC1LE_1RD1RE_0LA1RC_1RZ0LB|halt}}
|}

== References ==
<references />