P vs NP PROBLEM

It is concerned with the complexity of computational problems. In particular, it asks whether certain types of problems can be solved efficiently by an algorithm.

To understand the problem, we need to define two classes of problems: P and NP. a) P stands for "polynomial time", and refers to problems that can be solved in a reasonable amount of time by an algorithm. b) NP stands for "non-deterministic polynomial time", and refers to problems that can be verified in a reasonable amount of time by an algorithm, but for which no efficient algorithm for solving them is known.

The P vs NP problem asks whether P = NP, i.e. whether every problem that can be verified efficiently can also be solved efficiently. The problem is important because many real-world problems are NP-complete, meaning that they are at least as hard as the hardest problems in NP.

Despite decades of research, the P vs NP problem remains unsolved, and many experts believe it may be one of the hardest problems in computer science and mathematics.