NP-complete problem (NP-C problem) is one of the seven major mathematical problems in the world. The English full name of NP is the problem of nondeterministic polynomials, that is, the uncertainty of polynomial complexity. The simple writing is NP = p? The question is whether NP is equal to p or NP is not equal to p.

The complexity of some NP problems is related to the complexity of the whole class. If any of these problems has a polynomial time algorithm, then all NP problems are solvable in polynomial time. These problems are called NP complete problems (NPC problems).

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P=NP problem can be reformulated by the expressiveness of a specific logical proposition. All languages in P can be expressed by first-order logic plus minimum fixed point operation (in fact, this allows the definition of recursive functions). Similarly, NP can be represented by existential second-order logic-that is, second-order logic that excludes global quantifiers on relationships, functions and subsets. Polynomial level, PH corresponds to all languages in second-order logic.

Dr. Hubert Chen of Cornell University provided proof of this joke that P is not NP: "Reduce to absurdity. Let P = NP. A proof of making y a P = NP. It is proved that Y can be verified by a qualified computer scientist in polynomial time, and we believe that the existence of such a scientist is real. But because P = NP, it is proved that Y can be discovered by such scientists in polynomial time.

References:

Baidu encyclopedia -NP complete problem