User:MrSolis/Playground: Difference between revisions
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== Analysis == | == Analysis == | ||
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{ | <math display="block">\begin{array}{lll} | ||
g(3x)& \xrightarrow{5x^2+19x+15}&g(5x+6),\\ | g(3x)&\phantom{}\xrightarrow{5x^2+19x+15}&g(5x+6),\\ | ||
g(3x+1)&\xrightarrow{5x^2+25x+27}&g(5x+9),\ | g(3x+1)&\phantom{}\xrightarrow{5x^2+25x+27}&g(5x+9),\\ | ||
g(3x+2)&\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> | ||
Revision as of 19:16, 1 February 2025
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
Let . Then,
- ↑ 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