Champions: Difference between revisions

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(Add "Verification" column to champions table and comment about self-reporting. Also streamline "Discovered By" column a bit and add Discord link to Racheline's discovery of BB(14) Graham number champion.)
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== 2-Symbol TMs ==
== 2-Symbol TMs ==
Rows are blank if no champion has been found which surpasses a smaller size problem. Take also note that the <math> f_{x}(n) </math> used in the lowerbounds represent the [https://googology.fandom.com/wiki/Fast-growing_hierarchy Fast Growing Hierarchy].
Rows are blank if no champion has been found which surpasses a smaller size problem. Take also note that the <math> f_{x}(n) </math> used in the lowerbounds represent the [https://googology.fandom.com/wiki/Fast-growing_hierarchy Fast Growing Hierarchy]. Note that most champions above 6 states are self-reported and have not been independently verified.
 
{| class="wikitable"
{| class="wikitable"
|+
|+
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!Runtime
!Runtime
!Champions
!Champions
!Comment
!Discovered By
!Verification
|-
|-
|[[BB(2)]]
|[[BB(2)]]
|<math> 6 </math>
|<math> 6 </math>
|{{TM|1RB1LB_1LA1RZ|halt}} {{TM|1RB0LB_1LA1RZ|halt}} {{TM|1RB1RZ_1LB1LA|halt}} {{TM|1RB1RZ_0LB1LA|halt}} {{TM|0RB1RZ_1LA1RB|halt}}
|{{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
|Tibor Radó
|Direct Simulation
|-
|-
|[[BB(3)]]
|[[BB(3)]]
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|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}}
|{{TM|1RB1RZ_1LB0RC_1LC1LA|halt}}
|Proven by Shen Lin
|Proven by Shen Lin
|Direct Simulation
|-
|-
|[[BB(4)]]
|[[BB(4)]]
|<math> 107 </math>
|<math> 107 </math>
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}}
|{{TM|1RB1LB_1LA0LC_1RZ1LD_1RD0RA|halt}}
|Discovered and proven by Allen Brady
|Allen Brady
|Direct Simulation
|-
|-
|[[BB(5)]]
|[[BB(5)]]
|<math> 47\,176\,870 </math>
|<math> 47\,176\,870 </math>
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}}
|{{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}}
|Discovered by Heiner Marxen & Jürgen Buntrock in 1989
|Heiner Marxen & Jürgen Buntrock in 1989
Proven by [[bbchallenge.org]] in 2024
|Direct Simulation
|-
|-
|[[BB(6)]]
|[[BB(6)]]
|<math> > 10 \uparrow\uparrow 15 </math>
|<math> > 10 \uparrow\uparrow 15 </math>
|{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}}
|{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}}
|Discovered by Pavel Kropitz in 2022
|Pavel Kropitz in 2022
|[https://www.sligocki.com/2022/06/21/bb-6-2-t15.html Analysis by Shawn Ligocki]
|-
|-
|[[BB(7)]]
|[[BB(7)]]
|
|
|
|
|
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|<math> > 2 \uparrow^5 4 > f_6(2) </math>
|<math> > 2 \uparrow^5 4 > f_6(2) </math>
|{{TM|1RH1RF_0LC0LH_0RD1LC_0RE1RA_1RB1RE_1RZ1RG_1RF0RE_1LB1LH|halt}}
|{{TM|1RH1RF_0LC0LH_0RD1LC_0RE1RA_1RB1RE_1RZ1RG_1RF0RE_1LB1LH|halt}}
|Discovered by Racheline in 2024
|Racheline in 2024
|
|-
|-
|BB(9)
|BB(9)
|<math> > f_\omega(f_9(2)) </math>
|<math> > f_\omega(f_9(2)) </math>
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}}
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH|halt}}
|Discovered by Jacobzheng in 2024
|Jacobzheng in 2024
|
|-
|-
|BB(10)
|BB(10)
|<math> > f_\omega^2(25) </math>
|<math> > f_\omega^2(25) </math>
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}}
|{{TM|1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ|halt}}
|Discovered by Racheline in 2024
|Racheline in 2024
|
|-
|-
|BB(11)
|BB(11)
|<math> > f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9)) </math>
|<math> > f_\omega^2(2 \uparrow\uparrow 12) > f_\omega^2(f_3(9)) </math>
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}}
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE|halt}}
|Discovered by Racheline in 2024
|Racheline in 2024
|
|-
|-
|BB(12)
|BB(12)
|<math> > f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2)) </math>
|<math> > f_\omega^4(2 \uparrow\uparrow\uparrow 4-3) > f_\omega^4(f_4(2)) </math>
|{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}}
|{{TM|0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL|halt}}
|Discovered by Racheline in 2024
|Racheline in 2024
|
|-
|-
|BB(13)
|BB(13)
|
|
|
|
|
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|<math> > f_{\omega + 1}(65\,536) > g_{64} </math>
|<math> > f_{\omega + 1}(65\,536) > g_{64} </math>
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}}
|{{TM|1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ---|halt}}
|Discovered by Racheline in 2024
|[https://discord.com/channels/960643023006490684/960643023530762341/1274366178529120287 Racheline in 2024]
|
|-
|-
|BB(15)
|BB(15)
|
|
|
|
|
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|<math> > f_{\omega + 1}(2 \uparrow\uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow\uparrow 9) </math>
|<math> > f_{\omega + 1}(2 \uparrow\uparrow\uparrow\uparrow 2 \uparrow\uparrow\uparrow\uparrow 9) </math>
|
|
|Designed by  Daniel Nagaj in 2021<ref>Shawn Ligocki. 2022. "BB(16) > Graham's Number". https://www.sligocki.com/2022/07/11/bb-16-graham.html</ref>
|Daniel Nagaj in 2021
|[https://www.sligocki.com/2022/07/11/bb-16-graham.html Analysis by Shawn Ligocki]
|-
|-
|BB(17)
|BB(17)
|<math> > f_{\omega + 1}(f_\omega(60)) </math>
|<math> > f_{\omega + 1}(f_\omega(60)) </math>
|[[User:Jacobzheng/BB(17)]]
|Jacobzheng in 2024
|
|
|[[User:Jacobzheng/BB(17)|Discovered]] by Jacobzheng in 2024
|-
|-
|BB(18)
|BB(18)
|<math> > f_{\omega + 1}(f_\omega^2(60)) </math>
|<math> > f_{\omega + 1}(f_\omega^2(60)) </math>
|[[User:Jacobzheng/BB(18)]]
|Jacobzheng in 2024
|
|
|[[User:Jacobzheng/BB(18)|Discovered]] by Jacobzheng in 2024
|-
|-
|BB(19)
|BB(19)
|<math> > f_{\omega + 1}^3(f_\omega(60)) </math>
|<math> > f_{\omega + 1}^3(f_\omega(60)) </math>
|[[User:Jacobzheng/BB(19)]]
|Jacobzheng in 2024
|
|
|[[User:Jacobzheng/BB(19)|Discovered]] by Jacobzheng in 2024
|-
|-
|BB(20)
|BB(20)
|<math> > f_{\omega + 2}^2(21) </math>
|<math> > f_{\omega + 2}^2(21) </math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274414683331366924 Discovered] by Racheline in 2024
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274414683331366924 Racheline in 2024]
|
|-
|-
|BB(21)
|BB(21)
|<math> > f_{\omega^2}^2(4 \uparrow\uparrow 341) </math>
|<math> > f_{\omega^2}^2(4 \uparrow\uparrow 341) </math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Discovered] by Racheline in 2024
|[https://discord.com/channels/960643023006490684/1026577255754903572/1274471360206344213 Racheline in 2024]
|
|-
|-
|BB(41)
|BB(41)
|<math> > f_{\omega^\omega}^4(32) </math>
|<math> > f_{\omega^\omega}^4(32) </math>
|[[User:Jacobzheng/BB(41)]]
|Jacobzheng in 2024
|
|
|[[User:Jacobzheng/BB(41)|Designed]] by Jacobzheng in 2024
|-
|-
|BB(51)
|BB(51)
|<math> > f_{\varepsilon_0 + 1}(8) </math>
|<math> > f_{\varepsilon_0 + 1}(8) </math>
|
|
|[https://discord.com/channels/960643023006490684/1026577255754903572/1276881449685094495 Designed] by Racheline in 2024
|[https://discord.com/channels/960643023006490684/1026577255754903572/1276881449685094495 Racheline in 2024]
|
|}
|}


Revision as of 16:07, 10 December 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. Note that most champions above 6 states are self-reported and have not been independently verified.

Runtime Champions Discovered By Verification
BB(2) 1RB1LB_1LA1RZ (bbch) 1RB0LB_1LA1RZ (bbch) 1RB1RZ_1LB1LA (bbch) 1RB1RZ_0LB1LA (bbch) 0RB1RZ_1LA1RB (bbch) Tibor Radó Direct Simulation
BB(3) 1RB1RZ_1LB0RC_1LC1LA (bbch) Proven by Shen Lin Direct Simulation
BB(4) 1RB1LB_1LA0LC_1RZ1LD_1RD0RA (bbch) Allen Brady Direct Simulation
BB(5) 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch) Heiner Marxen & Jürgen Buntrock in 1989 Direct Simulation
BB(6) 1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE (bbch) Pavel Kropitz in 2022 Analysis by Shawn Ligocki
BB(7)
BB(8) 1RH1RF_0LC0LH_0RD1LC_0RE1RA_1RB1RE_1RZ1RG_1RF0RE_1LB1LH (bbch) Racheline in 2024
BB(9) 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_1LB0LH (bbch) Jacobzheng in 2024
BB(10) 1RB1RA_0LC0LF_0RD1LC_1RA1RG_1RZ0RA_1LB1LF_1LH1RE_0LI1LH_0LF0LJ_1LH0LJ (bbch) Racheline in 2024
BB(11) 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RZ0LI_0LD1LE (bbch) Racheline in 2024
BB(12) 0LJ0RF_1LH1RC_0LD0LG_0RE1LD_1RF1RA_1RB1RF_1LC1LG_1LL1LI_1LK0LH_1RH1LJ_1RZ1LA_1RF1LL (bbch) Racheline in 2024
BB(13)
BB(14) 1LH1LA_1LI1RG_0RD1LC_0RF1RE_1LJ0RF_1RB1RF_0LC1LH_0LC0LA_1LK1LJ_1RL0LI_0LL1LE_1LM1RZ_0LN1LF_0LJ--- (bbch) Racheline in 2024
BB(15)
BB(16) Daniel Nagaj in 2021 Analysis by Shawn Ligocki
BB(17) User:Jacobzheng/BB(17) Jacobzheng in 2024
BB(18) User:Jacobzheng/BB(18) Jacobzheng in 2024
BB(19) User:Jacobzheng/BB(19) Jacobzheng in 2024
BB(20) Racheline in 2024
BB(21) Racheline in 2024
BB(41) User:Jacobzheng/BB(41) Jacobzheng in 2024
BB(51) Racheline in 2024

3-Symbol TMs

Runtime Champions Comment
BB(2,3) 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) 1RB2LA1RA1RA_1LB1LA3RB1RZ (bbch)
BB(3,4) 1RB3LB1RZ2RA_2LC3RB1LC2RA_3RB1LB3LC2RC (bbch)

5-Symbol TMs

Runtime Champions Comment
BB(2,5) 1RB3LA4RB0RB2LA_1LB2LA3LA1RA1RZ (bbch)
BB(3,5) 1RB3LB4LC2RA4LB_2LC3RB1LC2RA1RZ_3RB1LB3LC2RC4LC (bbch)

References

Retrieved from "https://wiki.bbchallenge.org/w/index.php?title=Champions&oldid=1347"