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Pré-Publication, Document De Travail Année : 2024

Note for the P versus NP Problem

Frank Vega

Résumé

P versus NP is considered as one of the most fundamental open problems in computer science. This consists in knowing the answer of the following question: Is P equal to NP? It was essentially mentioned in 1955 from a letter written by John Nash to the United States National Security Agency. However, a precise statement of the P versus NP problem was introduced independently by Stephen Cook and Leonid Levin. Since that date, all efforts to find a proof for this problem have failed. Another major complexity class is NP-complete. It is well-known that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NP-complete. We show that the Monotone Weighted Xor 2-satisfiability problem (MWX2SAT) is NP-complete and P at the same time. Certainly, we make a polynomial time reduction from every directed graph and positive integer k in the K-CLOSURE problem to an instance of MWX2SAT. In this way, we show that MWX2SAT is also an NP-complete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MWX2SAT. Consequently, we prove that P = NP.
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Dates et versions

hal-04420462 , version 1 (26-01-2024)
hal-04420462 , version 2 (06-02-2024)
hal-04420462 , version 3 (02-03-2024)
hal-04420462 , version 4 (14-03-2024)
hal-04420462 , version 5 (28-03-2024)
hal-04420462 , version 6 (06-04-2024)

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  • HAL Id : hal-04420462 , version 6

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Frank Vega. Note for the P versus NP Problem. 2024. ⟨hal-04420462v6⟩
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