P versus NP

Frank Vega (1)

1 Joysonic

$P$ 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, $P = NP$.

Mots clés: polynomial time; logarithmic space; complexity classes; one-way; reduction; combinatorial optimization

Domaines: Complexité [cs.CC]

Frank Vega. P versus NP. 2020. ⟨hal-02199310v12⟩