Every other problem in NP must be able to be transformed (in polynomial time) to this problem.
Lies in the intersection between NP-hard and NP.
What’s the point?
- We want to unify all NP Hard problems such that if we solve one of them, we solve the rest as well!
- Provide a framework, for the parts we are unsure about, use wishful thinking and leave it as a hole That way, we can focus on the holes which are the essence of the problem
- We want to solve NP Hard problems in polynomial time
- solve the holes
How do we prove it?
We are trying to show it lies in the intersection betweenand .
Show it is in(show a satisfiable answer can be verified in polynomial time).
Take a known NP-Complete problem, e.g. 3-SAT and reduce it to our problem, L.
If we can do this in polynomial time, all problems can be reduced to L in polynomial time