User:MrSolis/Playground: Difference between revisions
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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. | 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 == | == Analysis == | ||
===Rules=== | |||
Let <math>g(x):=0^\infty\;\textrm{<A}\,1^x\;0^\infty</math>. Then, | Let <math>g(x):=0^\infty\;\textrm{<A}\,1^x\;0^\infty</math>. Then, | ||
<math display="block">\begin{array}{lll} | <math display="block">\begin{array}{lll} | ||
| Line 8: | Line 9: | ||
g(3x+2)\phantom{}&\xrightarrow{6x+12}&0^\infty\;1\;\textrm{Z>}\;01\;001^{x+1}\;1\;0^\infty | g(3x+2)\phantom{}&\xrightarrow{6x+12}&0^\infty\;1\;\textrm{Z>}\;01\;001^{x+1}\;1\;0^\infty | ||
\end{array}</math> | \end{array}</math> | ||
===Proof=== | |||
WIP | |||
Revision as of 19:23, 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 and at the time.
Analysis
Rules
Let . Then,
Proof
WIP
- ↑ 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