1RB0LB2LA 1LA0RC0LB 2RC2RB0LC: Difference between revisions
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Actually, linking to the champions page here makes no sense |
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{{machine|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}} | {{machine|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}} | ||
{{TM|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}} is the current [[Beeping Busy Beaver#Champions|BBB(3,3)]] champion. It was discovered in March 2025 by Nick Drozd and runs for <math>10 \uparrow \uparrow 6</math> steps before [[Quasihalt|quasihalting]].<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> | {{TM|1RB0LB2LA_1LA0RC0LB_2RC2RB0LC}} is the current [[Beeping Busy Beaver#Champions|BBB(3,3)]] champion. It was discovered in March 2025 by Nick Drozd and runs for <math>10 \uparrow \uparrow 6</math> steps before [[Quasihalt|quasihalting]].<ref>https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps</ref> | ||
Using an extension of up-arrow notation<ref>S. Ligocki, "[https://www.sligocki.com/2022/06/25/ext-up-notation.html Extending Up-arrow Notation]". Blog Post, 2022. Accessed 15 August 2025.</ref>, a more precise runtime of <math>10 \uparrow \uparrow 6.74</math> steps before quasihalting can be determined.<ref name=":Nick Drozd Tetrational Blank26">Nick Drozd, "[https://nickdrozd.github.io/2026/09/01/tetrational-self-cleaning-turing-machine.html A Tetrational Self-Cleaning Turing Machine]". Blog post, September 2026. Accessed 17 October 2026.</ref> | |||
== Analysis by [[User:Sligocki|Shawn Ligocki]] == | == Analysis by [[User:Sligocki|Shawn Ligocki]] == | ||
Latest revision as of 12:14, 17 October 2026
1RB0LB2LA_1LA0RC0LB_2RC2RB0LC (bbch) is the current BBB(3,3) champion. It was discovered in March 2025 by Nick Drozd and runs for steps before quasihalting.[1]
Using an extension of up-arrow notation[2], a more precise runtime of steps before quasihalting can be determined.[3]
Analysis by Shawn Ligocki
D(a, d) = 0^inf <C 0^a 1 2^d 1 0^inf
D(a, d+3) --> D(2^{a+6} - 2, d)
D(a, 0) --> Spin out
D(a, 1) --> C(14, a+1)
D(a, 2) --> C(14, a+4)
Start: D(14, 2)
This is actually a Collatz-like pentation-level TM that got unlucky! Each "reset" it iterates a tetration level function:
D(14, 3k+r) --> D(> 2^^k, r)
But in this case, the TM only resets once before spinning out:
D(14, 2) --> D(14, 18) --> Spin out
See also
https://nickdrozd.github.io/2025/03/24/bbb-3-3.html
References
- ↑ https://groups.google.com/g/busy-beaver-discuss/c/EuIXSir4Eps
- ↑ S. Ligocki, "Extending Up-arrow Notation". Blog Post, 2022. Accessed 15 August 2025.
- ↑ Nick Drozd, "A Tetrational Self-Cleaning Turing Machine". Blog post, September 2026. Accessed 17 October 2026.