User blog:Wythagoras/Bound for Sigma(6,3)

0 * * * 5 1 _ 1 r 2 1 1 1 r 5 2 _ 1 l 3 2 1 _ r 1 3 _ 1 r 4 3 1 _ l 2 3 2 1 r halt 4 _ 1 l 6 4 1 _ r 3 5 _ 2 l 4 5 1 1 r 2 5 2 1 l 1 6 _ 1 r 1 6 1 1 l 4 Again a bound using Pavel Kropitz'  \(\Sigma(6)\) machine and the note by Pascal Michel.

Here 5 is the begin state, the original halt state. It now writes two. Beacause tape looks like


 * 1) _11(H_)# before halting, we can make sure that it halts as it did.

If there is a space before the 2, then we'll end up with 111 where the the head is on second one in state one, which is the same as the asked position (_11 with head on space and state 6) when one step is preformed.

Therefore, \(S(6,3) > \Sigma(6,3) > 10^{10^{10^{10^{18705353}}}}\)