Is there some distinction to be made between Turing machines with tapes of fixed capacity, and ones whose capacities are limited by their execution substrate, such that they’ll support as much memory as they are “given” by the environment?
I’m picturing here the difference between Turing machines in the Game of Life that take place on a fixed area of the grid, vs. ones that attempt to just index out to whatever grid position they need, whether that causes wraparound or not.
I’m picturing here the difference between Turing machines in the Game of Life that take place on a fixed area of the grid, vs. ones that attempt to just index out to whatever grid position they need, whether that causes wraparound or not.