Download PDFOpen PDF in browserCurrent versionP versus NPEasyChair Preprint 3061, version 714 pages•Date: June 24, 2020AbstractP versus NP is considered as one of the most important 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. It is one of the seven Millennium Prize Problems selected by the Clay Mathematics Institute to carry a US 1,000,000 prize for the first correct solution. Another major complexity classes are FP and SharpP. Whether FP = SharpP is another fundamental question that it is as important as it is unresolved. We know if FP = SharpP, then P = NP. We demonstrate there is a problem in SharpPcomplete that can be solved in polynomial time. In this way, we prove the complexity class P is equal to NP. Keyphrases: completeness, complexity classes, logarithmic space, oneway, polynomial time, reduction
