User blog:Wythagoras/My Turing machines

This blog post is about Turing Machines and bounds for \(\Sigma(n,m)\)

\(\Sigma(12,3)\)
This machine outputs a string of more than \(f_{\omega+1}(n)\) 1's when  \(1\textunderscore1^n\) is entered. 0 _ 1 r bb1 0 1 2 l 0 0 2 1 l bb2 bb1 _ _ l 0 bb1 1 2 r bb1 bb1 2 1 l bb1 bb2 _ 1 l 8 bb2 1 1 r 0 bb2 2 1 r bb2 0a _ 1 r 0a 0a 1 _ l 0a 0a 2 1 r 1 1 1 2 l 3 1 2 2 r 2 1 _ 1 r 7 2 _ 1 r 7 2 2 2 r 2 2 1 2 l 4 3 2 1 l 3 3 1 1 l 3 3 _ 1 l 0a 4 2 1 l 5 4 1 1 l 4 4 _ 2 r 4 5 2 2 l 4 5 1 1 l 6 6 1 1 l 6 6 2 2 l 6 6 _ 2 l 0a 7 _ _ r halt 7 1 _ l bb2 7 2 _ l bb2 8 2 2 l 8 8 1 2 l 8 8 _ _ l 6 This proves \(\Sigma(12,3) > f_{\omega+1}(374676381)\)