1RB0LD 1RC0RF 1LC1LA 0LE1RZ 1LF0RB 0RC0RE: Difference between revisions
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{{machine|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE | {{machine|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE}}{{Stub}} | ||
{{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE}} | {{TM|1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE|halt}} is a former [[BB(6)]] champion. It was discovered by Pavel Kropitz on 30 May 2022. This TM runs for over 10 ↑↑ 15 steps. An improved bound for this TMs runtime was achieved by Shawn Ligocki, using an extended version of tetration: <math>10 \uparrow\uparrow 15.60463 < \mathrm{Score} < \mathrm{Runtime} < 10 \uparrow\uparrow 15.60466</math>.<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><ref>S. Ligocki, "[https://www.sligocki.com/2022/06/21/bb-6-2-t15.html BB(6, 2) > 10↑↑15]". Blog post, 2022. Accessed 20 June 2024.</ref> | ||
It simulates the following Collatz-like rules, starting at <math>C(5)</math>, on tape configurations <math>C(n):= 0^\infty\; 1\; 0^n\; 11\; 0^5\; \textrm{C}\textrm{>}\; 0^\infty</math>: | |||
It simulates the following Collatz-like rules starting at C(5): | |||
<math display="block">\begin{array}{l} | <math display="block">\begin{array}{l} | ||
C(4k) & \to & Halt(\frac{3^{k+3} - 11}{2}) \\ | C(4k) & \to & \operatorname{Halt}\Bigl(\frac{3^{k+3} - 11}{2}\Bigr) \\ | ||
C(4k+1) & \to & C(\frac{3^{k+3} - 11}{2}) \\ | C(4k+1) & \to & C\Bigl(\frac{3^{k+3} - 11}{2}\Bigr) \\ | ||
C(4k+2) & \to & C(\frac{3^{k+3} - 11}{2}) \\ | C(4k+2) & \to & C\Bigl(\frac{3^{k+3} - 11}{2}\Bigr) \\ | ||
C(4k+3) & \to & C(\frac{3^{k+3} + 1}{2}) \\ | C(4k+3) & \to & C\Bigl(\frac{3^{k+3} + 1}{2}\Bigr) \\ | ||
\end{array}</math> | \end{array}</math> | ||
[[Category: | |||
==References== | |||
<references /> | |||
[[Category:BB(6)]] | |||
Latest revision as of 22:18, 7 October 2025
1RB0LD_1RC0RF_1LC1LA_0LE1RZ_1LF0RB_0RC0RE (bbch) is a former BB(6) champion. It was discovered by Pavel Kropitz on 30 May 2022. This TM runs for over 10 ↑↑ 15 steps. An improved bound for this TMs runtime was achieved by Shawn Ligocki, using an extended version of tetration: .[1][2]
It simulates the following Collatz-like rules, starting at , on tape configurations :
References
- ↑ S. Ligocki, "Extending Up-arrow Notation". Blog Post, 2022. Accessed 15 August 2025.
- ↑ S. Ligocki, "BB(6, 2) > 10↑↑15". Blog post, 2022. Accessed 20 June 2024.