P vs. NP is a theoretical computer science problem. The problem asks whether a P-time solution to an NP problem is possible.
Let’s have a look at all terms that describe the complexity of a problem:
- P (polynomial time) is a class for solvable problems in polynomial time.
- NP (non-deterministic polynomial time) is a class of problems whose solution is verifiable in polynomial time.
- Co-NP (complement of NP) is a class of a problem solution that isn’t verifiable in polynomial time.
- NP-Hard is a class for problems that is the hardest.
- NP-complete is a class that is NP and NP-hard.
What if P=NP?
The implications are significant. On the one hand, cryptography algorithms will be vulnerable. On the other hand, optimization of logistics and transportation would improve because the solution is in P-time. Despite it, the question remains open, and there is no proof yet.
I hope this helps!