CB(n) or delta(n) So, the chess board is a hypothetical Turing machine thing.
The maximum sum of n-1’s that can be written (in the finished plane), with n state and a n colour halting Turing machine. Note that we do not use a tape but a Plane. As well as that, we allow for movement in 8 directions. Up, down, left, right, up right, up left, down right, down left.
We have a read and write head moving on the infinite paper. Instead of turning it into a 0 or 1, it turns it into 0,1,2, etc, with n-1 as the maximum number. It reads and writes, until it eventually halts. The final question, is what is the sum of all n-1s?
Also called Delta(n) It should be more powerful.
Instead of asking what is the sum of all n-1s, we ask what is the sum of all numbers that are not 0.
The maximum sum of all nonzero numbers that can be written (in the finished plane), with a n state and a n colour halting Turing machine. Note that we do not use a tape but a Plane. As well as that, we allow for movement in 8 directions. Up, down, left, right, up right, up left, down right, down left.