Planned intervention: On Wednesday April 3rd 05:30 UTC Zenodo will be unavailable for up to 2-10 minutes to perform a storage cluster upgrade.

There is a newer version of the record available.

Published July 10, 2020 | Version v100
Preprint Open

P versus NP

Creators

  • 1. Joysonic

Description

$P$ 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. Given a Boolean formula $\phi$ in $3CNF$ of $n$ variables and $m$ clauses, then the computing of the number of satisfied clauses between all the truth assignments in $\phi$ can be considered as a weighted Boolean $\#CSP(\mathcal{F})$ problem. We show this problem is in $FP^{\#P}\textit{--complete}$ since every function in $\mathcal{F}$ is nor $``\textit{product type}"$ neither $``\textit{pure affine}"$. Moreover, we prove there is a polynomial time algorithm for this problem. In this way, we demonstrate that the complexity class $P$ is equal to $NP$.

Files

manuscript.pdf

Files (475.4 kB)

Name Size Download all
md5:99203aa2bb2076ce963eb69a44cb247d
475.4 kB Preview Download