Champions: Difference between revisions
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| Line 12: | Line 12: | ||
|[[BB(2)]] | |[[BB(2)]] | ||
|6 | |6 | ||
|{{TM|1RB1LB_1LA1RZ}} {{TM|1RB0LB_1LA1RZ}} {{TM|1RB1RZ_1LB1LA}} {{TM|1RB1RZ_0LB1LA}} {{TM|0RB1RZ_1LA1RB}} | |{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}} | ||
|Discovered and proven by hand by Tibor Radó | |Discovered and proven by hand by Tibor Radó | ||
|- | |- | ||
|[[BB(3)]] | |[[BB(3)]] | ||
|21 | |21 | ||
|{{TM|1RB1RZ_1LB0RC_1LC1LA}} | |{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}} | ||
|Proven by Shen Lin | |Proven by Shen Lin | ||
|- | |- | ||
|[[BB(4)]] | |[[BB(4)]] | ||
|107 | |107 | ||
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA}} | |{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} | ||
|Discovered and proven by Allen Brady | |Discovered and proven by Allen Brady | ||
|- | |- | ||
|[[BB(5)]] | |[[BB(5)]] | ||
|47,176,870 | |47,176,870 | ||
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA}} | |{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} | ||
|Discovered by Heiner Marxen & Jürgen Buntrock in 1989 | |Discovered by Heiner Marxen & Jürgen Buntrock in 1989 | ||
Proven by [[bbchallenge.org]] in 2024 | Proven by [[bbchallenge.org]] in 2024 | ||
| Line 33: | Line 33: | ||
|[[BB(6)]] | |[[BB(6)]] | ||
|<math>> 10 \uparrow\uparrow 15</math> | |<math>> 10 \uparrow\uparrow 15</math> | ||
|{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE}} | |{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}} | ||
|Discovered by Pavel Kropitz in 2022 | |Discovered by Pavel Kropitz in 2022 | ||
|- | |- | ||
| Line 48: | Line 48: | ||
|BB(9) | |BB(9) | ||
|<math>> 10 \uparrow\uparrow 30</math> | |<math>> 10 \uparrow\uparrow 30</math> | ||
|{{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1RI1RG}} | |{{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1RI1RG|halt}} | ||
|Designed by Milton Green in 1964 ([[Green's machines]]) | |Designed by Milton Green in 1964 ([[Green's machines]]) | ||
|- | |- | ||
|BB(10) | |BB(10) | ||
|<math> > 10 \uparrow\uparrow 10^{10^{12}} </math> | |<math> > 10 \uparrow\uparrow 10^{10^{12}} </math> | ||
|{{TM|1LB1RZ_0LC1LC_0LD0LC_1LE1RA_0LF0LE_1LG1RD_0LH0LG_1LI1RF_0LJ0LI_1RJ1RH}} | |{{TM|1LB1RZ_0LC1LC_0LD0LC_1LE1RA_0LF0LE_1LG1RD_0LH0LG_1LI1RF_0LJ0LI_1RJ1RH|halt}} | ||
|[[Green's machines]] | |[[Green's machines]] | ||
|- | |- | ||
|BB(11) | |BB(11) | ||
|<math> > 10 \uparrow\uparrow\uparrow 10^{12} </math> | |<math> > 10 \uparrow\uparrow\uparrow 10^{12} </math> | ||
|{{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1LJ1RG_0LK0LJ_1RK1RI}} | |{{TM|1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1LJ1RG_0LK0LJ_1RK1RI|halt}} | ||
|[[Green's machines]] | |[[Green's machines]] | ||
|- | |- | ||
|BB(12) | |BB(12) | ||
|<math> > 2 \uparrow^{12} 4 > Ack(11) </math> | |<math> > 2 \uparrow^{12} 4 > Ack(11) </math> | ||
|{{TM|1RB1LL_0RC1RC_1LD1LG_0RE1LC_1LD1RF_1RE1RI_1RH0LA_---0RF_0RB1LJ_---0LK_0LF1LF_1RZ0LA}} | |{{TM|1RB1LL_0RC1RC_1LD1LG_0RE1LC_1LD1RF_1RE1RI_1RH0LA_---0RF_0RB1LJ_---0LK_0LF1LF_1RZ0LA|halt}} | ||
|[https://github.com/sligocki/sligocki.github.io/issues/7#issuecomment-2143486164 Compilation] of a BB(3,4) TM by <code>@Iijil1</code> in 2024 | |[https://github.com/sligocki/sligocki.github.io/issues/7#issuecomment-2143486164 Compilation] of a BB(3,4) TM by <code>@Iijil1</code> in 2024 | ||
|- | |- | ||
Revision as of 13:32, 13 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.
| 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) | |||
| BB(9) | 1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1RI1RG (bbch)
|
Designed by Milton Green in 1964 (Green's machines) | |
| BB(10) | 1LB1RZ_0LC1LC_0LD0LC_1LE1RA_0LF0LE_1LG1RD_0LH0LG_1LI1RF_0LJ0LI_1RJ1RH (bbch)
|
Green's machines | |
| BB(11) | 1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1LJ1RG_0LK0LJ_1RK1RI (bbch)
|
Green's machines | |
| BB(12) | 1RB1LL_0RC1RC_1LD1LG_0RE1LC_1LD1RF_1RE1RI_1RH0LA_---0RF_0RB1LJ_---0LK_0LF1LF_1RZ0LA (bbch)
|
Compilation of a BB(3,4) TM by @Iijil1 in 2024
| |
| BB(13) | Designed by @Wythagoras in 2016
| ||
| BB(14) | Designed by Jacobzheng in 2024
| ||
| BB(15) | |||
| BB(16) | Designed by Daniel Nagaj in 2021[1] |
References
- ↑ Shawn Ligocki. 2022. "B(16) > Graham's Number". https://www.sligocki.com/2022/07/11/bb-16-graham.html