Champions: Difference between revisions
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→3-Symbol TMs: Define last 2x3 transition and add 4x3 champ (for now, I'm sure Pavel has beaten this). |
I added arrays for 4-Symbol and 5-Symbol TMs. |
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|<math> > 10^{14072} </math> | |<math> > 10^{14072} </math> | ||
|{{TM|1RB1RZ2RC_2LC2RD0LC_1RA2RB0LB_1LB0LD2RC|halt}} | |{{TM|1RB1RZ2RC_2LC2RD0LC_1RA2RB0LB_1LB0LD2RC|halt}} | ||
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== 4-Symbol TMs == | |||
{| class="wikitable" | |||
|+ | |||
! | |||
!Runtime | |||
!Champions | |||
!Comment | |||
|- | |||
|BB(2,4) | |||
|3,932,964 | |||
| | |||
| | |||
|- | |||
|BB(3,4) | |||
|<math>2\uparrow^{15}5</math> | |||
| | |||
| | |||
|} | |||
== 5-Symbol TMs == | |||
{| class="wikitable" | |||
|+ | |||
! | |||
!Runtime | |||
!Champions | |||
!Comment | |||
|- | |||
|BB(2,5) | |||
|<math>10^{10^{10^{3314360}}}</math> | |||
| | |||
| | | | ||
|} | |} | ||
Revision as of 18:08, 15 August 2024
Busy Beaver Champions are the current record holding Turing machines who maximize a Busy Beaver function. In this article we focus specifically on the longest running TMs. Some have been proven to be the longest running of all (and so are the ultimate champion) while others are only current champions and may be usurped in the future. For smaller domains, Pascal Michel's website is the canonical source for Busy Beaver champions and the History of Previous Champions.
2-Symbol TMs
Rows are blank if no champion has been found which surpasses a smaller size problem. Take also note that the used in the lowerbounds represent the Fast Growing Hierarchy.
| Runtime | Champions | Comment | |
|---|---|---|---|
| BB(2) | 6 | 1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch)
|
Discovered and proven by hand by Tibor Radó |
| BB(3) | 21 | 1RB1RZ_1LB0RC_1LC1LA (bbch)
|
Proven by Shen Lin |
| BB(4) | 107 | 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
|
Discovered and proven by Allen Brady |
| BB(5) | 47,176,870 | 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
|
Discovered by Heiner Marxen & Jürgen Buntrock in 1989
Proven by bbchallenge.org in 2024 |
| BB(6) | 1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE (bbch)
|
Discovered by Pavel Kropitz in 2022 | |
| BB(7) | |||
| BB(8) | 1RH1RF_0LC0LH_0RD1LC_0RE1RA_1RB1RE_1RZ1RG_1RF0RE_1LB1LH (bbch)
|
Discovered by Racheline in 2024 | |
| BB(9) | |||
| BB(10) | 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch)
|
Discovered by Racheline in 2024 | |
| BB(11) | |||
| BB(12) | |||
| BB(13) | 1RJ1RH_1RC1RB_1LI0RD_1RC1LE_0LE1LF_1LG1RH_1RB0LF_0RA1LE_1RF1LJ_0LK1RZ_1LL1LK_1LM1LM_0LI0LL (bbch)
|
Discovered by Racheline in 2024 | |
| BB(14) | |||
| BB(15) | |||
| BB(16) | Designed by Daniel Nagaj in 2021[1] |
3-Symbol TMs
| Runtime | Champions | Comment | |
|---|---|---|---|
| BB(2,3) | 38 | 1RB2LB1RZ_2LA2RB1LB (bbch)
|
|
| BB(3,3) | 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
| ||
| BB(4,3) | 1RB1RZ2RC_2LC2RD0LC_1RA2RB0LB_1LB0LD2RC (bbch)
|
4-Symbol TMs
| Runtime | Champions | Comment | |
|---|---|---|---|
| BB(2,4) | 3,932,964 | ||
| BB(3,4) |
5-Symbol TMs
| Runtime | Champions | Comment | |
|---|---|---|---|
| BB(2,5) |
References
- ↑ Shawn Ligocki. 2022. "B(16) > Graham's Number". https://www.sligocki.com/2022/07/11/bb-16-graham.html