User:Azerty/Busy Beaver Functions: Difference between revisions
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Created page with "This is a list of Busy Beaver functions for Turing machines and other simple Turing-complete systems and their current lower bounds. All functions here grow uncomputably fast like the original Busy Beaver function. There is no function that grow much faster like the Beeping Busy Beaver function here. I will add more functions soon. == Turing Machines == {| class="wikitable" !Function !Value |- |BB(2) |6 |- |BB(3) |21 |- |BB(2,3) |38 |- |BB(4) |107 |- |..." |
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| Line 9: | Line 9: | ||
!Function | !Function | ||
!Value | !Value | ||
!Champion | |||
|- | |- | ||
|[[BB(2)]] | |[[BB(2)]] | ||
|6 | |6 | ||
|{{TM|1RB1LB_1LA1RZ|halt}} | |||
|- | |- | ||
|[[BB(3)]] | |[[BB(3)]] | ||
|21 | |21 | ||
|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}} | |||
|- | |- | ||
|[[BB(2,3)]] | |[[BB(2,3)]] | ||
|38 | |38 | ||
|{{TM|1RB2LB1RZ_2LA2RB1LB|halt}} | |||
|- | |- | ||
|[[BB(4)]] | |[[BB(4)]] | ||
|107 | |107 | ||
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}} | |||
|- | |- | ||
|[[BB(2,4)]] | |[[BB(2,4)]] | ||
|3,932,964 | |3,932,964 | ||
|{{TM|1RB2LA1RA1RA_1LB1LA3RB1RZ|halt}} | |||
|- | |- | ||
|[[BB(5)]] | |[[BB(5)]] | ||
|47,176,870 | |47,176,870 | ||
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}} | |||
|- | |- | ||
|[[BB(3,3)]] | |[[BB(3,3)]] | ||
|<math>\ | |<math>> 1.191 \times 10^{17}</math> | ||
|{{TM|0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC|halt}} | |||
|- | |- | ||
| | |[[BB(2,5)]] | ||
| | |<math>> 10^{10^{10^{3\,314\,360}}}</math> | ||
|{{TM|1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ|halt}} | |||
|- | |||
|[[BB(2,6)]] | |||
|<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10^{10^{115}}</math><ref name=":1">S. Ligocki, "[https://www.sligocki.com/2023/05/20/bb-2-6-p3.html BB(2,6) > 10↑↑10↑↑10↑↑3]". Blog post, 2023. Accessed 15 August 2025.</ref> | |||
|{{TM|1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA|halt}} | |||
|- | |- | ||
| | |[[BB(6)]] | ||
| | |<math>> 10 \uparrow\uparrow 10 \uparrow\uparrow 10 \uparrow\uparrow 8</math><ref name=":1" /> | ||
|{{TM|1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE|halt}} | |||
|- | |- | ||
| | |[[BB(4,3)]] | ||
| | |<math>> 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10 \uparrow\uparrow\uparrow 10^{28}</math> | ||
|{{TM|1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD|halt}} | |||
|- | |- | ||
| | | | ||
| | | | ||
| | | | ||
|} | |} | ||
Revision as of 10:35, 4 December 2025
This is a list of Busy Beaver functions for Turing machines and other simple Turing-complete systems and their current lower bounds.
All functions here grow uncomputably fast like the original Busy Beaver function. There is no function that grow much faster like the Beeping Busy Beaver function here.
I will add more functions soon.
Turing Machines
| Function | Value | Champion |
|---|---|---|
| BB(2) | 6 | 1RB1LB_1LA1RZ (bbch)
|
| BB(3) | 21 | 1RB1RZ_1LB0RC_1LC1LA (bbch)
|
| BB(2,3) | 38 | 1RB2LB1RZ_2LA2RB1LB (bbch)
|
| BB(4) | 107 | 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch)
|
| BB(2,4) | 3,932,964 | 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
|
| BB(5) | 47,176,870 | 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch)
|
| BB(3,3) | 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
| |
| BB(2,5) | 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
| |
| BB(2,6) | [1] | 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)
|
| BB(6) | [1] | 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
|
| BB(4,3) | 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch)
| |
- ↑ 1.0 1.1 S. Ligocki, "BB(2,6) > 10↑↑10↑↑10↑↑3". Blog post, 2023. Accessed 15 August 2025.