Download PDFOpen PDF in browserCurrent versionNote for the P Versus NP Problem (II)EasyChair Preprint 13469, version 15 pages•Date: May 29, 2024AbstractP 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 NPcomplete. It is wellknown that P is equal to NP under the assumption of the existence of a polynomial time algorithm for some NPcomplete. We show that the Monotone Weighted2satisfiability problem (MW2SAT) is NPcomplete and P at the same time. Certainly, we make a polynomial time reduction from every undirected graph and positive integer k in the Vertex Cover problem to an instance of MW2SAT. In this way, we show that MW2SAT is also an NPcomplete problem. Moreover, we create and implement a polynomial time algorithm which decides the instances of MW2SAT. Consequently, we prove that P = NP. Keyphrases: Boolean formula, completeness, complexity classes, graph, polynomial time
