BB(2,7): Difference between revisions

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Updated Phase 1, Stage 1 text and initial (almost empty) table of results
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== Phase 1 ==
== Phase 1 ==


The initial phase of enumeration and reduction of [[holdouts]] started in November 2025 using [https://github.com/ccz181078/TM 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.
The initial phase of enumeration and reduction of [[holdouts]] started in November 2025 using [https://github.com/ccz181078/TM 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 ===
=== Stage 1 ===


The code provided by mxdys breaks up the BB(2,7) enumeration into 1 million subtasks which each run for about xxx minutes and leave ~xxx holdouts.
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 [https://github.com/ccz181078/TM 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:
<pre>
#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
</pre>
 
Results:
 
{| class="wikitable sortable"
!Task range
!Done by
!Completed
!# holdouts
!Source
|-
|00xxxx
|Terry Ligocki
|Yes
|1,545,673
|
|-
|01xxxx
|TBD
|No
|TBD
|
|-
|02xxxx
|TBD
|No
|TBD
|
|-
|03xxxx
|TBD
|No
|TBD
|
|-
|04xxxx
|TBD
|No
|TBD
|
|-
|05xxxx
|TBD
|No
|TBD
|
|-
|06xxxx
|TBD
|No
|TBD
|
|-
|07xxxx
|TBD
|No
|TBD
|
|-
|08xxxx
|TBD
|No
|TBD
|
|-
|09xxxx
|TBD
|No
|TBD
|
|-
|10xxxx
|TBD
|No
|TBD
|
|-
|11xxxx
|TBD
|No
|TBD
|
|-
|12xxxx
|TBD
|No
|TBD
|
|-
|13xxxx
|TBD
|No
|TBD
|
|-
|14xxxx
|TBD
|No
|TBD
|
|-
|15xxxx
|TBD
|No
|TBD
|
|-
|16xxxx
|TBD
|No
|TBD
|
|-
|17xxxx
|TBD
|No
|TBD
|
|-
|18xxxx
|TBD
|No
|TBD
|
|-
|19xxxx
|TBD
|No
|TBD
|
|-
|20xxxx
|TBD
|No
|TBD
|
|-
|21xxxx
|TBD
|No
|TBD
|
|-
|22xxxx
|TBD
|No
|TBD
|
|-
|23xxxx
|TBD
|No
|TBD
|
|-
|24xxxx
|TBD
|No
|TBD
|
|-
|25xxxx
|TBD
|No
|TBD
|
|-
|26xxxx
|TBD
|No
|TBD
|
|-
|27xxxx
|TBD
|No
|TBD
|
|-
|28xxxx
|TBD
|No
|TBD
|
|-
|29xxxx
|TBD
|No
|TBD
|
|-
|30xxxx
|TBD
|No
|TBD
|
|-
|31xxxx
|TBD
|No
|TBD
|
|-
|32xxxx
|TBD
|No
|TBD
|
|-
|33xxxx
|TBD
|No
|TBD
|
|-
|34xxxx
|TBD
|No
|TBD
|
|-
|35xxxx
|TBD
|No
|TBD
|
|-
|36xxxx
|TBD
|No
|TBD
|
|-
|37xxxx
|TBD
|No
|TBD
|
|-
|38xxxx
|TBD
|No
|TBD
|
|-
|39xxxx
|TBD
|No
|TBD
|
|-
|40xxxx
|TBD
|No
|TBD
|
|-
|41xxxx
|TBD
|No
|TBD
|
|-
|42xxxx
|TBD
|No
|TBD
|
|-
|43xxxx
|TBD
|No
|TBD
|
|-
|44xxxx
|TBD
|No
|TBD
|
|-
|45xxxx
|TBD
|No
|TBD
|
|-
|46xxxx
|TBD
|No
|TBD
|
|-
|47xxxx
|TBD
|No
|TBD
|
|-
|48xxxx
|TBD
|No
|TBD
|
|-
|49xxxx
|TBD
|No
|TBD
|
|-
|50xxxx
|TBD
|No
|TBD
|
|-
|51xxxx
|TBD
|No
|TBD
|
|-
|52xxxx
|TBD
|No
|TBD
|
|-
|53xxxx
|TBD
|No
|TBD
|
|-
|54xxxx
|TBD
|No
|TBD
|
|-
|55xxxx
|TBD
|No
|TBD
|
|-
|56xxxx
|TBD
|No
|TBD
|
|-
|57xxxx
|TBD
|No
|TBD
|
|-
|58xxxx
|TBD
|No
|TBD
|
|-
|59xxxx
|TBD
|No
|TBD
|
|-
|60xxxx
|TBD
|No
|TBD
|
|-
|61xxxx
|TBD
|No
|TBD
|
|-
|62xxxx
|TBD
|No
|TBD
|
|-
|63xxxx
|TBD
|No
|TBD
|
|-
|64xxxx
|TBD
|No
|TBD
|
|-
|65xxxx
|TBD
|No
|TBD
|
|-
|66xxxx
|TBD
|No
|TBD
|
|-
|67xxxx
|TBD
|No
|TBD
|
|-
|68xxxx
|TBD
|No
|TBD
|
|-
|69xxxx
|TBD
|No
|TBD
|
|-
|70xxxx
|TBD
|No
|TBD
|
|-
|71xxxx
|TBD
|No
|TBD
|
|-
|72xxxx
|TBD
|No
|TBD
|
|-
|73xxxx
|TBD
|No
|TBD
|
|-
|74xxxx
|TBD
|No
|TBD
|
|-
|75xxxx
|TBD
|No
|TBD
|
|-
|76xxxx
|TBD
|No
|TBD
|
|-
|77xxxx
|TBD
|No
|TBD
|
|-
|78xxxx
|TBD
|No
|TBD
|
|-
|79xxxx
|TBD
|No
|TBD
|
|-
|80xxxx
|TBD
|No
|TBD
|
|-
|81xxxx
|TBD
|No
|TBD
|
|-
|82xxxx
|TBD
|No
|TBD
|
|-
|83xxxx
|TBD
|No
|TBD
|
|-
|84xxxx
|TBD
|No
|TBD
|
|-
|85xxxx
|TBD
|No
|TBD
|
|-
|86xxxx
|TBD
|No
|TBD
|
|-
|87xxxx
|TBD
|No
|TBD
|
|-
|88xxxx
|TBD
|No
|TBD
|
|-
|89xxxx
|TBD
|No
|TBD
|
|-
|90xxxx
|TBD
|No
|TBD
|
|-
|91xxxx
|TBD
|No
|TBD
|
|-
|92xxxx
|TBD
|No
|TBD
|
|-
|93xxxx
|TBD
|No
|TBD
|
|-
|94xxxx
|TBD
|No
|TBD
|
|-
|95xxxx
|TBD
|No
|TBD
|
|-
|96xxxx
|TBD
|No
|TBD
|
|-
|97xxxx
|TBD
|No
|TBD
|
|-
|98xxxx
|TBD
|No
|TBD
|
|-
|99xxxx
|TBD
|No
|TBD
|
|}


=== Stage 2 ===
=== Stage 2 ===

Revision as of 20:21, 19 November 2025

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.

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
00xxxx Terry Ligocki Yes 1,545,673
01xxxx TBD No TBD
02xxxx TBD No TBD
03xxxx TBD No TBD
04xxxx TBD No TBD
05xxxx TBD No TBD
06xxxx TBD No TBD
07xxxx TBD No TBD
08xxxx TBD No TBD
09xxxx TBD No TBD
10xxxx TBD No TBD
11xxxx TBD No TBD
12xxxx TBD No TBD
13xxxx TBD No TBD
14xxxx TBD No TBD
15xxxx TBD No TBD
16xxxx TBD No TBD
17xxxx TBD No TBD
18xxxx TBD No TBD
19xxxx TBD No TBD
20xxxx TBD No TBD
21xxxx TBD No TBD
22xxxx TBD No TBD
23xxxx TBD No TBD
24xxxx TBD No TBD
25xxxx TBD No TBD
26xxxx TBD No TBD
27xxxx TBD No TBD
28xxxx TBD No TBD
29xxxx TBD No TBD
30xxxx TBD No TBD
31xxxx TBD No TBD
32xxxx TBD No TBD
33xxxx TBD No TBD
34xxxx TBD No TBD
35xxxx TBD No TBD
36xxxx TBD No TBD
37xxxx TBD No TBD
38xxxx TBD No TBD
39xxxx TBD No TBD
40xxxx TBD No TBD
41xxxx TBD No TBD
42xxxx TBD No TBD
43xxxx TBD No TBD
44xxxx TBD No TBD
45xxxx TBD No TBD
46xxxx TBD No TBD
47xxxx TBD No TBD
48xxxx TBD No TBD
49xxxx TBD No TBD
50xxxx TBD No TBD
51xxxx TBD No TBD
52xxxx TBD No TBD
53xxxx TBD No TBD
54xxxx TBD No TBD
55xxxx TBD No TBD
56xxxx TBD No TBD
57xxxx TBD No TBD
58xxxx TBD No TBD
59xxxx TBD No TBD
60xxxx TBD No TBD
61xxxx TBD No TBD
62xxxx TBD No TBD
63xxxx TBD No TBD
64xxxx TBD No TBD
65xxxx TBD No TBD
66xxxx TBD No TBD
67xxxx TBD No TBD
68xxxx TBD No TBD
69xxxx TBD No TBD
70xxxx TBD No TBD
71xxxx TBD No TBD
72xxxx TBD No TBD
73xxxx TBD No TBD
74xxxx TBD No TBD
75xxxx TBD No TBD
76xxxx TBD No TBD
77xxxx TBD No TBD
78xxxx TBD No TBD
79xxxx TBD No TBD
80xxxx TBD No TBD
81xxxx TBD No TBD
82xxxx TBD No TBD
83xxxx TBD No TBD
84xxxx TBD No TBD
85xxxx TBD No TBD
86xxxx TBD No TBD
87xxxx TBD No TBD
88xxxx TBD No TBD
89xxxx TBD No TBD
90xxxx TBD No TBD
91xxxx TBD No TBD
92xxxx TBD No TBD
93xxxx TBD No TBD
94xxxx TBD No TBD
95xxxx TBD No TBD
96xxxx TBD No TBD
97xxxx TBD No TBD
98xxxx TBD No TBD
99xxxx TBD No TBD

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).

Retrieved from "https://wiki.bbchallenge.org/w/index.php?title=BB(2,7)&oldid=5099"