P versus NP

04 December 2020, Version 1
This content is an early or alternative research output and has not been peer-reviewed by Cambridge University Press at the time of posting.

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, $P = NP$.

Keywords

complexity classes
polynomial time
combinatorial optimization
reduction
logarithmic space
one-way

Supplementary weblinks

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