P versus NP

EasyChair Preprint no. 3061, version 13

13 pagesDate: September 19, 2020

Abstract

$P$ 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 $NP$? The 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 $\textit{P-Sel}$. $\textit{P-Sel}$ 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 $\textit{P-Sel}$, then $P = NP$. We claim a possible selector for $3SAT$ and thus, $P = NP$.

Keyphrases: completeness, complexity classes, logarithmic space, one-way, polynomial time, reduction