What’s P = NP?

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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!