5-state busy beaver winner: Difference between revisions
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{{machine|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA}} | {{machine|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA}} | ||
The 5-state busy beaver champion (and winner!) is: [https://bbchallenge.org/1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA&status=halt https://bbchallenge.org/1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA] | The 5-state busy beaver champion (and winner!) is: [https://bbchallenge.org/1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA&status=halt https://bbchallenge.org/1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA]. It was found by Heiner Marxen and Jürgen Buntrock in 1989<ref>H. Marxen and J. Buntrock. Attacking the Busy Beaver 5. Bulletin of the EATCS, 40, pages 247-251, February 1990. https://turbotm.de/~heiner/BB/mabu90.html</ref>. The machine halts after 47,176,870 steps and with 4098 1's on the tape, showing that <math>BB(5) \ge 47,176,870</math> and <math>\Sigma(5) \ge 4098</math>. | ||
This machine repeatedly applies the following map, starting with <math>x = 0</math><ref>Aaronson, S. (2020). The Busy Beaver Frontier. Page 10-11. https://www.scottaaronson.com/papers/bb.pdf</ref>: | |||
<math display="block">\begin{align} | |||
g(x) & \to g\left(\frac{5x+18}{3}\right) && \text{if }x \equiv 0 \pmod{3} \\ | |||
g(x) & \to g\left(\frac{5x+22}{3}\right) && \text{if }x \equiv 1 \pmod{3} \\ | |||
g(x) & \to \text{HALT} && \text{if }x \equiv 2 \pmod{3} | |||
\end{align}</math> | |||
The full orbit from <math>x = 0</math> is: | |||
<math display="block">\begin{array}{l} | |||
0 & \to & 6 & \to & 16 & \to & 34 & \to & 64 & \to & \\ | |||
114 & \to & 196 & \to & 334 & \to & 564 & \to & 946 & \to & \\ | |||
1584 & \to & 2646 & \to & 4416 & \to & 7366 & \to & 12284 & \to & \text{HALT} | |||
\end{array}</math> | |||
Revision as of 20:50, 4 July 2024
The 5-state busy beaver champion (and winner!) is: https://bbchallenge.org/1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA. It was found by Heiner Marxen and Jürgen Buntrock in 1989[1]. The machine halts after 47,176,870 steps and with 4098 1's on the tape, showing that and .
This machine repeatedly applies the following map, starting with [2]:
The full orbit from is:
- ↑ H. Marxen and J. Buntrock. Attacking the Busy Beaver 5. Bulletin of the EATCS, 40, pages 247-251, February 1990. https://turbotm.de/~heiner/BB/mabu90.html
- ↑ Aaronson, S. (2020). The Busy Beaver Frontier. Page 10-11. https://www.scottaaronson.com/papers/bb.pdf