Solution of P versus NP Problem

Frank Vega 1
Abstract : The P versus NP problem is one of the most important and unsolved problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? This incognita was first mentioned in a letter written by Kurt Gödel to John von Neumann in 1956. However, the precise statement of the P versus NP problem was introduced in 1971 by Stephen Cook in a seminal paper. We consider a new complexity class, called equivalent-P, which has a close relation with this problem. The class equivalent-P has those languages that contain ordered pairs of instances, where each one belongs to a specific problem in P, such that the two instances share a same solution, that is, the same certificate. We demonstrate that equivalent-P = NP and equivalent-P = P. In this way, we find the solution of P versus NP problem, that is, P = NP.
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Frank Vega. Solution of P versus NP Problem. 2015. ⟨hal-01161668⟩

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