Champions
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) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow 15} | 1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE (bbch)
|
Discovered by Pavel Kropitz in 2022 |
| BB(7) | |||
| BB(8) | |||
| BB(9) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow 30} | 1LD1LB_1LZ1LA_0LB1LD_0LE0LD_1LF1RC_0LG0LF_1LH1RE_0LI0LH_1RI1RG (bbch)
|
Designed by Milton Green in 1964 (Green's machines) |
| BB(10) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 10 \uparrow\uparrow 10^{10^{12}} } | 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) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > 2 \uparrow^{12} 4 > Ack(11) } | 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) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > Ack(2045) } | Designed by @Wythagoras in 2016
| |
| BB(14) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > Ack(10 \uparrow\uparrow 5) } | Designed by Jacobzheng in 2024
| |
| BB(15) | |||
| BB(16) | Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle > f_{\omega + 1}(2 \uparrow\uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow\uparrow 9) > g_{64} } | 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