BB(2,7): Difference between revisions

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The 2-state, 7-symbol Busy Beaver problem, '''BB(2,7)''', is unsolved. With [[Cryptids]] like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,7). The current BB(2,7) [[champion]] is simply inherited from [[BB(2,6)]] as BB(2,7) is just starting to be explored.
The 2-state, 7-symbol Busy Beaver problem, '''BB(2,7)''', is unsolved. With [[Cryptids]] like [[Hydra]] in the preceding domain [[BB(2,5)]], we know that we must solve a [[Collatz-like]] problem in order to solve BB(2,7).
 
The current BB(2,7) [[champion]] {{TM|1RB3RB4LA1LB5LA6LB5RA_2LA6RA4RB1RZ3LB6LA4RB|halt}} was discovered by roromachine14 in Oct 2026.


== Top Halters ==
== Top Halters ==
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|-
|-
|00-09xxxx
|00-09xxxx
|rowspan='17'|Terry Ligocki
|rowspan='10'|Terry Ligocki
|Yes
|Yes
|309,868,865
|309,868,847
|rowspan='17'|[https://drive.google.com/drive/folders/11AiZYiKJq7v0ns9o5nt-xUsSgSpcuNvZ?usp=drive_link Google Drive]
|rowspan='10'|[https://drive.google.com/drive/folders/11AiZYiKJq7v0ns9o5nt-xUsSgSpcuNvZ?usp=drive_link Google Drive]
|-
|-
|10-19xxxx
|10-19xxxx
Line 45: Line 47:
|20-29xxxx
|20-29xxxx
|Yes
|Yes
|309,968,380
|309,968,370
|-
|-
|30-39xxxx
|30-39xxxx
Line 53: Line 55:
|40-49xxxx
|40-49xxxx
|Yes
|Yes
|309,976,212
|309,976,206
|-
|-
|50-59xxxx
|50-59xxxx
|Yes
|Yes
|314,996,395
|315,047,998
|-
|60xxxx
|Yes
|26,700,472
|-
|-
|61xxxx
|60-69xxxx
|Yes
|Yes
|35,320,029
|309,911,121
|-
|-
|62xxxx
|70-79xxxx
|Yes
|Yes
|26,700,270
|315,355,885
|-
|-
|63xxxx
|80-89xxxx
|Yes
|Yes
|35,329,410
|309,900,123
|-
|-
|64xxxx
|90-99xxxx
|Yes
|Yes
|26,669,417
|315,121,515
|-
|65xxxx
|Yes
|35,348,829
|-
|66xxxx
|Yes
|26,657,839
|-
|67xxxx
|No
|TBD
|-
|68xxxx
|No
|TBD
|-
|69xxxx
|No
|TBD
|-
|70xxxx
|No
|TBD
|-
|71-99xxxx
|TBD
|No
|TBD
| ---
|-
|-
|'''Cumulative'''
|'''Cumulative'''
| ---
| ---
| ---
| ---
|'''2,087,819,664'''
|'''3,125,433,611'''
| ---
| ---
|-
|-
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=== Stage 2 ===
=== Stage 2 ===


The Ligocki's "Enumerate.py" Python code is used to further reduce the number of holdouts and explore more of the [[TNF]] of BB(2,7).
This could be running the Ligocki's "Enumerate.py" Python code to further reduce the number of holdouts and explore more of the [[TNF]] of BB(2,7).


[[Category:BB Domains]]
[[Category:BB Domains]]

Latest revision as of 05:29, 23 October 2026

The 2-state, 7-symbol Busy Beaver problem, BB(2,7), is unsolved. With Cryptids like Hydra in the preceding domain BB(2,5), we know that we must solve a Collatz-like problem in order to solve BB(2,7).

The current BB(2,7) champion 1RB3RB4LA1LB5LA6LB5RA_2LA6RA4RB1RZ3LB6LA4RB (bbch) was discovered by roromachine14 in Oct 2026.

Top Halters

These are the 20 highest scoring machines that were found in the current investigation of BB(2,7). This list does not include TMs from smaller domains:

Phase 1

The initial phase of enumeration and reduction of holdouts started in November 2025 using C++ code mxdys shared. This work is ongoing and further described below. After this is completed, it is planned to run the Ligockis' Enumerate.py code to further reduce the number of holdout TMs.

Stage 1

The code provided by mxdys breaks up the BB(2,7) enumeration into 1 million subtasks which each run for ~10 minutes and leave ~2500 holdouts based on an average of the first 1K subtasks. These values are about 5 times longer than and 25 times larger than the ones for BB(7).

This enumeration began in November 2025 and is summarized in the table below. The mxdys code main.cpp from C++ code was used with two modification: #define BB7 was replaced with #define BB27 and the following block of code was added in the section with BB domain definitions: 

#ifdef BB27
constexpr int64_t N_STATE=2;
constexpr int64_t N_CHAR=7;
constexpr int64_t log2_N_STATE=1;
constexpr int64_t log2_N_CHAR=3;
typedef uint8_t chr_t;
#endif

Results:

Task range Done by Completed # holdouts Source
00-09xxxx Terry Ligocki Yes 309,868,847 Google Drive
10-19xxxx Yes 315,243,072
20-29xxxx Yes 309,968,370
30-39xxxx Yes 315,040,474
40-49xxxx Yes 309,976,206
50-59xxxx Yes 315,047,998
60-69xxxx Yes 309,911,121
70-79xxxx Yes 315,355,885
80-89xxxx Yes 309,900,123
90-99xxxx Yes 315,121,515
Cumulative --- --- 3,125,433,611 ---

Stage 2

This could be running the Ligocki's "Enumerate.py" Python code to further reduce the number of holdouts and explore more of the TNF of BB(2,7).

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