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fix: incorrect descriptions of the P = NP problem (#8084)

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Fuchen Shi
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# P = NP
The P = NP problem is one of the most famous problems in computer science. It asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of solving the given input. In other words, it asks if the problem of determining if a given input belongs to a certain class of problems is as hard as the problem of determining if a given input belongs to a certain class of problems. This problem is also known as the Halting Problem.
The P = NP problem is one of the most famous problems in computer science. It asks whether a problem that can be solved in polynomial time on a non-deterministic machine (i.e., the problem is in NP) can also be solved in polynomial time on a deterministic machine (i.e., the problem is in P).
If you can find a polynomial-time solution to an NP-complete problem, then all problems in NP can be solved in polynomial time. This shows that P = NP.
If you can prove for any single NP-complete problem that it is only solvable in exponential time, then all NP-complete problems are only solvable in exponential time. This shows that P ≠ NP.
So far, we don't know whether P = NP or P ≠ NP.
Visit the following resources to learn more: