Re:How the Slowest Computer Programs Illuminate Math’s Funda...
by tromp on Friday December 11, 2020 @03:56PM
(#25390881)
> if it's going to halt we don't really care what it does immediately before.
The final move does not matter, but the symbol written matters to the extent that BB(n) is defined as the number of 1s on the tape upon halting.
So, while redundant, the 4(n+1) count is chosen for parsimony. If one is willing to specialize the transition to halt to have no move and a mandatory write of 1, then a count of 4n+1 still agrees upon the same value of BB(n).
The final move does not matter, but the symbol written matters to the extent that BB(n) is defined as the number of 1s on the tape upon halting.
So, while redundant, the 4(n+1) count is chosen for parsimony. If one is willing to specialize the transition to halt to have no move and a mandatory write of 1, then a count of 4n+1 still agrees upon the same value of BB(n).