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 17: 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]


(2 informal)
(+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 43: 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 57: Line 59:
! 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)]]
Line 76: Line 77:
| style="background: #A8613E;" | 60
| style="background: #A8613E;" | 60
[[BB(2,5)#Holdouts|Holdouts list]]
[[BB(2,5)#Holdouts|Holdouts list]]
(6 informal)
(5 informal)


2+4 Cryptids
2+4 Cryptids
Line 92: 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 110: 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)]]
Line 146: Line 145:
<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>
== 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: 8 total'''
'''Unconfirmed, informal proofs of machines for each domain by equivalence class: 6 total'''
{| class="wikitable"
{| class="wikitable"
!Domain
!Domain
Line 163: Line 162:
|0
|0
|0
|0
|'''2'''
|'''1'''
|-
|-
!3-symbol
!3-symbol
Line 180: Line 179:
|-
|-
!5-symbol
!5-symbol
|'''6'''
|'''5'''
| ---
| ---
| ---
| ---
Line 186: Line 185:
| ---
| ---
|}
|}
=== [[BB(6)]]: 1 March 2026 ===
=== [[BB(6)]]: June 1 2026 ===


===== 2 informal =====
===== 1 informal =====


*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>
*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>
*<code>1RB0RC_0LC0LB_0LD1LC_0LE1LA_0LF---_1RF1RA</code> (halt, Racheline, informal language)


=== [[BB(2,5)]]: 1 April 2026 ===
=== [[BB(2,5)]]: June 1 2026 ===


===== 5+1 informal =====
===== 4+1 informal =====


* Dyuan:  
* Dyuan:  
Line 203: Line 201:
*# <code>1RB3LA4LA1LA2RA_2LA4RB---0RA0LA</code> ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 2])
*# <code>1RB3LA4LA1LA2RA_2LA4RB---0RA0LA</code> ([https://discord.com/channels/960643023006490684/1084047886494470185/1254518334406266964 2])
*# <code>1RB3LA4LA2RB1LA_2LA4RB---3RA3LA</code> ([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]: <code>1RB2LB---4LB0RB_1LA3RB4RB4RA1LB</code>
=== [[BB(3,3)]]: June 1 2026 ===
=== [[BB(3,3)]]: 28 March 2026 ===
''None''
''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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