Idea: Finite State Machine that ask for as much memory as it needs. That is, finite state, but unbounded memory.
Simplest One: Change 0s to 1s in the input.
| state | Tape Symbol | New State | New tape Symbol | Tape Direction |
| 0 | 1 | right | ||
| 1 | 1 | right | ||
| space | space | stay |
Key point: Computation is local in some sense5.