Download PDFOpen PDF in browserCurrent versionNote for the P versus NP ProblemEasyChair Preprint 11886, version 54 pages•Date: February 6, 2024Abstract$P$ 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 wellknown 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 2satisfiability problem ($MWX2SAT$) is $NP$complete and $P$ at the same time. Keyphrases: completeness, complexity classes, computational algorithm, polynomial time, reduction
