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NP Problem in Computer Science

Collected knowledge about 50 years old computer science problem P=NP

P = NP is 50 years old computer science problem.

In the 1960s computer scientists, especially Steve Cook and Richard Karp developed the theory of NP-complete problem domains. Problems in these domains are solvable, but seem to take time exponential in the size of the problem.

Asking Bing's ChatGPT this prompt "Steve Cook np problem explain in two paragraphs"

Answer of Bing's ChatGPT below

The P vs. NP problem is one of the most important open problems in computer science. It was introduced by Stephen Cook in 1971. The problem asks whether every problem whose solution can be verified by a computer in polynomial time (P) can also be solved by a computer in "N" polynomial time. In other words, it asks whether P = NP. If P = NP, then many problems that are currently considered computationally infeasible would become feasible. Stephen Cook’s contribution to the field of computer science is immense. In his seminal 1971 paper, he formalized the notions of polynomial-time reduction and NP-completeness, and proved the existence of an NP-complete problem by showing that the Boolean satisfiability problem is NP-complete. The P vs. NP problem remains unsolved to this day and is listed on the Clay Mathematical Institute’s Millennium Problems

Brief summary of the theory P = NP

The letter variable P represent any problem that computer already solved in acceptable computing speed. Example Google and Bing search engine solution.

The letter variables NxP or NP represents hard computer search problem that has many constraints to satisfy. Constraint 1 is represented by variable N1, constraint 2 is represented by variable N2, constraint 3 is represented by variable N3 and so on.

The theory said if we know how to solve search problem (P) for example at reasonable computing speed then we can use the known solution (P) to solve very hard problem associated to search problem because it has many constraint to satisfy at reasonable computing speed.

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