Cook-Levin: SAT is NP complete
Think about a computation history
- This is the sequence of states the tape is in, along with the position of the head
- We know there are at most nk computations
Here’s an example checking 0n1n :
- q0 0 0 0 1 1 1
- X q1 0 0 1 1 1
- X 0 q1 0 1 1 1
- X 0 0 q1 1 1 1
- 0 0 0 q2 X 1 1
- .....