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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!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>\geq 119\,112\,334\,170\,342\,541 > 10^{17}</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) >1.191×1017 0RB2LA1RA_1LA2RB1RC_1RZ1LB1LC (bbch)
BB(2,5) >1010103314360 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(2,6) >10↑↑10↑↑1010115[1] 1RB3RB5RA1LB5LA2LB_2LA2RA4RB1RZ3LB2LA (bbch)
BB(6) >10↑↑10↑↑10↑↑8[1] 1RB1RA_1RC1RZ_1LD0RF_1RA0LE_0LD1RC_1RA0RE (bbch)
BB(4,3) >10↑↑↑10↑↑↑10↑↑↑1028 1RB1RD1LC_2LB1RB1LC_1RZ1LA1LD_0RB2RA2RD (bbch)
  1. ↑ 1.0 1.1 S. Ligocki, "BB(2,6) > 10↑↑10↑↑10↑↑3". Blog post, 2023. Accessed 15 August 2025.
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