Download PDFOpen PDF in browserCurrent versionP versus NPEasyChair Preprint 3061, version 1113 pages•Date: July 18, 2020Abstract$P$ 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 class is $\textit{PSel}$. $\textit{PSel}$ is the class of decision problems for which there is a polynomial time algorithm (called a selector) with the following property: Whenever it's given two instances, a "yes" and a "no" instance, the algorithm can always decide which is the "yes" instance. It is known that if $NP$ is contained in $\textit{PSel}$, then $P = NP$. We claim a possible selector for $3SAT$ and thus, $P = NP$. Keyphrases: completeness, complexity classes, logarithmic space, oneway, polynomial time, reduction
