Note for the P versus NP Problem

EasyChair Preprint 11886, version 2

Abstract

$P$ 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 $NP$-complete. It is well-known that $P$ is equal to $NP$ under the assumption of the existence of a polynomial time algorithm for some $NP$-complete. We show that the Monotone one-in-three 3-satisfiability ($M-1IN3-3SAT$) is $NP$-complete and $P$ at the same time.

Keyphrases: completeness, complexity classes, computational algorithm, polynomial time, reduction

@booklet{EasyChair:11886,
  author    = {Frank Vega},
  title     = {Note for the P versus NP Problem},
  howpublished = {EasyChair Preprint 11886},
  year      = {EasyChair, 2024}}