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Note for the P versus NP Problem

EasyChair Preprint no. 11886, version 4

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4 pagesDate: February 3, 2024


$P$ 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.

Keyphrases: completeness, complexity classes, computational algorithm, polynomial time, reduction

BibTeX entry
BibTeX does not have the right entry for preprints. This is a hack for producing the correct reference:
  author = {Frank Vega},
  title = {Note for the P versus NP Problem},
  howpublished = {EasyChair Preprint no. 11886},

  year = {EasyChair, 2024}}
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