Revision as of 19:22, 1 February 2025

5-state busy beaver winner (Remake)

The 5-state busy beaver (BB(5)) winner is 1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA (bbch). Discovered by Heiner Marxen and Jürgen Buntrock in 1989^[1], this machine proved that $\operatorname {BB} (5)\geq 47176870{\phantom {}}$ and $\Sigma (5)\geq 4098$ at the time.

Analysis

Let $g(x):=0^{\infty }\;{\textrm {<A}}\,1^{x}\;0^{\infty }$ . Then,

{\begin{array}{lll}g(3x)&{\phantom {}}\xrightarrow {5x^{2}+19x+15} &g(5x+6),\\g(3x+1)&{\phantom {}}\xrightarrow {5x^{2}+25x+27} &g(5x+9),\\g(3x+2){\phantom {}}&\xrightarrow {6x+12} &0^{\infty }\;1\;{\textrm {Z>}}\;01\;001^{x+1}\;1\;0^{\infty }\end{array}}

↑ 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

[1] 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

[1]

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+=5-state busy beaver winner (Remake)=
 The 5-state busy beaver ([[BB(5)]]) winner is {{TM|1RB1LC_1RC1RB_1RD0LE_1LA1LD_1RZ0LA|halt}}. Discovered 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>, this machine proved that <math>\operatorname{BB}(5)\ge 47176870\phantom{}</math> and <math>\Sigma(5)\ge 4098</math> at the time.
 == Analysis ==

User:MrSolis/Playground: Difference between revisions

Revision as of 19:22, 1 February 2025

5-state busy beaver winner (Remake)

Analysis

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