SAT is NP complete (cont.)
The tape grows to length at most nk
There are at most nk steps
Designate a variable for each cell in each step, and for each possible signal.
- The variable x2, 3, b signals whether the symbol in the second cell of the 3rd step is b.
We can write a large boolean formula representing the statement “There is a valid computation history that goes from the starting state to some accept state”
So we’ve reduced any NP problem to SAT