User:RobinCodes/Work on BB Domains: Difference between revisions

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Update BB(2,6) and BB(2,7)
 
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== Progress ==
== Progress ==
As of 1 April 2026,
As of May 2026,


'''Domains with active filtering going on (decider-wise): [[BB(2,6)]], [[BB(7)]] - Andrew Ducharme'''
'''Domains with active filtering going on (decider-wise): [[BB(2,6)]], [[BB(7)]], [[BB(4,3)]] - Andrew Ducharme. [[BB(4,3)|BB(3,4)]] -  [[User:XnoobSpeakable|XnoobSpeakable]]'''


{| class="wikitable"
{| class="wikitable"
Line 9: Line 9:
!7-state
!7-state
!8-state
!8-state
!9-state
|-   
|-   
! 2-symbol  
! 2-symbol  
Line 16: Line 17:
| [[BB(5)]] = 47,176,870
| [[BB(5)]] = 47,176,870
2 Jul 2024
2 Jul 2024
| style="background: #A8613E;" | 1161
| style="background: #A8613E;" | 1101
[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Holdouts list]
[https://docs.google.com/spreadsheets/d/1mMp8bAcTFT91j7azn72liX8NSTwc2E_ozKnOGTfRCfw/edit?gid=1330361301#gid=1330361301 Holdouts list]
(+1 informal)
(+15 Rocq-holdouts)
16+6 Cryptids
16+6 Cryptids


[[BB(6)]]
[[BB(6)]]
| style="background: #A06B10;" | 18,036,852
| style="background: #A06B10;" | 17,823,260
No Handwork
No Handwork
Andrew Ducharme, Terry Ligocki
Andrew Ducharme, Terry Ligocki
Line 28: Line 34:
[[BB(7)]]
[[BB(7)]]
| style="background: #AA8519;" |Expected no. of holdouts: 147 billion (<math>1.47 \cdot 10^{11}</math>)
| style="background: #AA8519;" |Expected no. of holdouts: 147 billion (<math>1.47 \cdot 10^{11}</math>)
[[BB(8)]]
| style="background: #ECC652;" |
|-
|-
! 3-symbol
! 3-symbol
Line 37: Line 45:


[[BB(3,3)]]
[[BB(3,3)]]
| style="background: #A06B10;" | 9,401,447
| style="background: #A06B10;" | 5,127,263
No Handwork
No Handwork


Terry Ligocki Phase 2, Stage 2
Terry Ligocki, Andrew Ducharme Phase 2, Stage 3


[[BB(4,3)]]
[[BB(4,3)]]
Line 47: Line 55:
| style="background: #ECC652;" |
| style="background: #ECC652;" |
| style="background: #ECC652;" |
| style="background: #ECC652;" |
| style="background: #A8973E;" |
|-
|-
! 4-symbol   
! 4-symbol   
| [[BB(2,4)]] = 3,932,964
| [[BB(2,4)]] = 3,932,964
| style="background: #A06B10;" | 12,435,284
| style="background: #A06B10;" | 11,362,197
No Handwork
No Handwork
[[User:XnoobSpeakable|XnoobSpeakable,]] [[User:WarpedWartWars|Lúkos]], Andrew Ducharme


[[User:XnoobSpeakable|XnoobSpeakable,]] [[User:WarpedWartWars|Lúkos]]
Phase 3 Stage 2
 
Phase 2, Stage 10C


[[BB(3,4)]]
[[BB(3,4)]]
| style="background: #D8B446;" |Expected no. of holdouts: 1.53 quadrillion (<math>1.53 \cdot 10^{15}</math>)
| style="background: #D8B446;" |Expected no. of holdouts: 1.53 quadrillion (<math>1.53 \cdot 10^{15}</math>)
[[BB(4,4)]]
[[BB(4,4)]]
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
Line 68: Line 77:
| style="background: #A8613E;" | 60
| style="background: #A8613E;" | 60
[[BB(2,5)#Holdouts|Holdouts list]]
[[BB(2,5)#Holdouts|Holdouts list]]
(9 informal)
(5 informal)


2+4 Cryptids
2+4 Cryptids
Line 76: Line 85:
Expected no. of holdouts: 11.3 trillion (<math>1.13 \cdot 10^{13}</math>)
Expected no. of holdouts: 11.3 trillion (<math>1.13 \cdot 10^{13}</math>)
[[BB(3,5)]]
[[BB(3,5)]]
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
Line 83: Line 93:
|-
|-
! 6-symbol  
! 6-symbol  
| style="background: #A06B10;" | 545,005
| style="background: #A06B10;" | 412,086
No Handwork
No Handwork
Andrew Ducharme,
Andrew Ducharme,
Line 92: Line 102:
[[BB(2,6)]]
[[BB(2,6)]]
| style="background: #ECC652;" |
| style="background: #ECC652;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
Line 100: Line 111:
!7-symbol
!7-symbol
| style="background: #AA8519;" |Enumeration started!
| style="background: #AA8519;" |Enumeration started!
09xxx done
37% Done
 
(10/100)


Expected no. of holdouts: 3 billion (<math>3 \cdot 10^9</math>)
Expected no. of holdouts: 3 billion (<math>3 \cdot 10^9</math>)


Current: 300 million
Current: ~1 billion


[[BB(2,7)]]
[[BB(2,7)]]
| style="background: #ECC652;" |
| style="background: #ECC652;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
Line 117: Line 127:
|-
|-
!8-symbol
!8-symbol
| style="background: #ECC652;" |
| style="background: #ECC652;" |Expected no. of holdouts: 5.51 trillion (<math display="inline">5.51 \cdot 10^{12}</math>)
[[BB(2,8)]]
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
| style="background: #A8973E;" |
Line 125: Line 137:
| style="background: #A8973E;" |
| style="background: #A8973E;" |
|}
|}
Futher domains with small information:  
Futher domains with some information:  


* [[BB(8)]]:
* [[BB(11)]]: Lower bound: (Racheline 2024)
* [[BB(11)]]: Lower bound: (Racheline 2024)
<math display="block">f_\omega^2(2 \uparrow\uparrow 12)</math>
<math display="block">f_\omega^2(2 \uparrow\uparrow 12)</math>
Line 133: Line 144:
* [[BB(12)]]: Lower bound: (Racheline 2024)
* [[BB(12)]]: Lower bound: (Racheline 2024)
<math display="block">f_\omega^4(2 \uparrow\uparrow\uparrow 4-3)</math>
<math display="block">f_\omega^4(2 \uparrow\uparrow\uparrow 4-3)</math>
* [[BB(2,8)]]: Expected no. of holdouts: 5.51 trillion (<math display="inline">5.51 \cdot 10^{12}</math>)
== Enumeration ==
== Enumeration ==
The enumeration process for [[BB(2,7)]] has started, and 5% has so far been completed. [[BB(8)]] is (tested from a random sample) even harder to enumerate. These processes will take a very long time and much collaborative work to complete. As for BB(3x5), BB(4x4), BB(5x3), enumeration may still be possible, but also incredibly difficult. Any domains after these are probably complete out-of-reach of current technology, just to enumerate. Using crowdsourced enumeration, one more layer may be possible.
The enumeration process for [[BB(2,7)]] has started, and 10% has so far been completed. [[BB(8)]] is (tested from a random sample) even harder to enumerate. These processes will take a very long time and much collaborative work to complete. As for BB(3x5), BB(4x4), BB(5x3), enumeration may still be possible, but also incredibly difficult. Any domains after these are probably complete out-of-reach of current technology, just to enumerate. Using crowdsourced enumeration, one more layer may be possible.


== Informal Proofs ==
== Informal Proofs ==
'''Unconfirmed, informal proofs of machines for each domain by equivalence class: 11 total'''
'''Unconfirmed, informal proofs of machines for each domain by equivalence class: 6 total'''
{| class="wikitable"
{| class="wikitable"
!Domain
!Domain
Line 153: Line 162:
|0
|0
|0
|0
|'''2'''
|'''1'''
|-
|-
!3-symbol
!3-symbol
Line 170: Line 179:
|-
|-
!5-symbol
!5-symbol
|9
|'''5'''
| ---
| ---
| ---
| ---
Line 176: Line 185:
| ---
| ---
|}
|}
=== [[BB(6)]]: 1 March 2026 ===
=== [[BB(6)]]: June 1 2026 ===


===== 1 informal, 1 unverified =====
===== 1 informal =====


* Likely correct: (2)
*mxdys, Pomme, Autumn Pan, vyx<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1441124403801755730 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1443295684878143579 <nowiki>[2]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444047803935490190 <nowiki>[3]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444051070186819836 <nowiki>[4]</nowiki>]</sup>: <code>1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---</code>
** <s>[https://discord.com/channels/960643023006490684/1421782442213376000/1431483206208852001 Shawn, star, Pomme, @mxdys]: BMO 7 verified</s>
** mxdys, Pomme, Autumn Pan, vyx<sup>[https://discord.com/channels/960643023006490684/1239205785913790465/1441124403801755730 <nowiki>[1]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1443295684878143579 <nowiki>[2]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444047803935490190 <nowiki>[3]</nowiki>][https://discord.com/channels/960643023006490684/1443295684878143579/1444051070186819836 <nowiki>[4]</nowiki>]</sup>: <code>1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---</code>
** 1RB0RC_0LC0LB_0LD1LC_0LE1LA_0LF---_1RF1RA (halt, Racheline, informal)


=== [[BB(3,3)]]: 28 March 2026 ===
=== [[BB(2,5)]]: June 1 2026 ===
''None''
 
=== [[BB(2,5)]]: 28 March 2026 ===


===== 7 informal, 2 unverified (6 informal, 1 unverified by eqv. class) =====
===== 4+1 informal =====


* Dyuan:  
* Dyuan:  
*# [[Beaver Math Olympiad#3. 1RB0RB3LA4LA2RA 2LB3RA---3RA4RB (bbch) and 1RB1RB3LA4LA2RA 2LB3RA---3RA4RB (bbch)|BMO 3]] (2 machines in 1 eqv. class) ([https://discord.com/channels/960643023006490684/1084047886494470185/1252634913220591728 source])
*# Dekaheptoid, unverified: [[1RB3RB1LB---2RB_2LA1RA4LB2LA2RA]] ([https://discord.com/channels/960643023006490684/1259770421046411285/1267650177389432913 source]), equivalently (1.2) <code>1RB3RA2LB1LB1RB_2LA2RA4LA1LA---</code>
*# Dekaheptoid, unverified: [[1RB3RB1LB---2RB_2LA1RA4LB2LA2RA]] ([https://discord.com/channels/960643023006490684/1259770421046411285/1267650177389432913 source]), equivalently 1RB3RA2LB1LB1RB_2LA2RA4LA1LA---  
*# BMO 3 variant: 1RB0RA3LA4LA2RA_2LB3LA---4RA3RB ([https://discord.com/channels/960643023006490684/1259770421046411285/1415337575543214132 source])
* Legion:
* Legion:
*# 1RB2RA3LA4LA2RB_2LA---1LA1RA3RA (<small>[https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 1]</small>)
*# <code>1RB2RA3LA4LA2RB_2LA---1LA1RA3RA</code> ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 1])
*# 1RB3LA4LA1LA2RA_2LA4RB---0RA0LA ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 2])
*# <code>1RB3LA4LA1LA2RA_2LA4RB---0RA0LA</code> ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 2])
*# 1RB3LA4LA2RB1LA_2LA4RB---3RA3LA ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 3])
*# <code>1RB3LA4LA2RB1LA_2LA4RB---3RA3LA</code> ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 3])
* [https://discord.com/channels/960643023006490684/1259770421046411285/1329663999700111471 Racheline]: 1RB2LB---4LB0RB_1LA3RB4RB4RA1LB
=== [[BB(3,3)]]: June 1 2026 ===
|}
''None''

Latest revision as of 11:07, 6 June 2026

Progress

As of May 2026,

Domains with active filtering going on (decider-wise): BB(2,6), BB(7), BB(4,3) - Andrew Ducharme. BB(3,4) - XnoobSpeakable

Work on BB Domains
2-state 3-state 4-state 5-state 6-state 7-state 8-state 9-state
2-symbol BB(2) = 6 BB(3) = 21 BB(4) = 107 BB(5) = 47,176,870

2 Jul 2024

1101

Holdouts list

(+1 informal)

(+15 Rocq-holdouts)

16+6 Cryptids

BB(6)

17,823,260

No Handwork Andrew Ducharme, Terry Ligocki Phase 2, Stage 6

BB(7)

Expected no. of holdouts: 147 billion (1.47⋅1011)

BB(8)

3-symbol BB(2,3) = 38 4

Holdouts list

1 Cryptid, Exhausted

BB(3,3)

5,127,263

No Handwork

Terry Ligocki, Andrew Ducharme Phase 2, Stage 3

BB(4,3)

4-symbol BB(2,4) = 3,932,964 11,362,197

No Handwork XnoobSpeakable, Lúkos, Andrew Ducharme

Phase 3 Stage 2

BB(3,4)

Expected no. of holdouts: 1.53 quadrillion (1.53⋅1015)

BB(4,4)

5-symbol 60

Holdouts list (5 informal)

2+4 Cryptids

BB(2,5)

Lower bound: (due Racheline 2024)>fω(2↑155)>fω2(15)

Expected no. of holdouts: 11.3 trillion (1.13⋅1013) BB(3,5)

6-symbol 412,086

No Handwork Andrew Ducharme, Terry Ligocki

Phase 2 Stage 4

BB(2,6)

7-symbol Enumeration started!

37% Done

Expected no. of holdouts: 3 billion (3⋅109)

Current: ~1 billion

BB(2,7)

8-symbol Expected no. of holdouts: 5.51 trillion (5.51⋅1012)

BB(2,8)

Futher domains with some information:

  • BB(11): Lower bound: (Racheline 2024)

fω2(2↑↑12)

  • BB(12): Lower bound: (Racheline 2024)

fω4(2↑↑↑4−3)

Enumeration

The enumeration process for BB(2,7) has started, and 10% has so far been completed. BB(8) is (tested from a random sample) even harder to enumerate. These processes will take a very long time and much collaborative work to complete. As for BB(3x5), BB(4x4), BB(5x3), enumeration may still be possible, but also incredibly difficult. Any domains after these are probably complete out-of-reach of current technology, just to enumerate. Using crowdsourced enumeration, one more layer may be possible.

Informal Proofs

Unconfirmed, informal proofs of machines for each domain by equivalence class: 6 total

Domain 2-state 3-state 4-state 5-state 6-state
2-symbol 0 0 0 0 1
3-symbol 0 0 ---- --- ---
4-symbol 0 --- --- --- ---
5-symbol 5 --- --- --- ---

BB(6): June 1 2026

1 informal
  • mxdys, Pomme, Autumn Pan, vyx[1][2][3][4]: 1RB1LA_1RC1RE_1LD0RB_1LA0LC_0RF0RD_0RB---

BB(2,5): June 1 2026

4+1 informal
  • Dyuan:
    1. Dekaheptoid, unverified: 1RB3RB1LB---2RB_2LA1RA4LB2LA2RA (source), equivalently (1.2) 1RB3RA2LB1LB1RB_2LA2RA4LA1LA---
  • Legion:
    1. 1RB2RA3LA4LA2RB_2LA---1LA1RA3RA (1)
    2. 1RB3LA4LA1LA2RA_2LA4RB---0RA0LA (2)
    3. 1RB3LA4LA2RB1LA_2LA4RB---3RA3LA (3)

BB(3,3): June 1 2026

None

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