The P versus NP Problem

Frank Vega (1)

1 Datys

The $P$ versus $NP$ problem has become in one of the most interesting and crucial questions for many fields such as computer science, mathematics, biology and others. This outstanding problem consists in knowing the answer of the following incognita: Is $P$ equal to $NP$? Many computer scientists have believed the most probable answer is $P \neq NP$. A key reason for this belief is the possible solution of $P = NP$ would imply many startling results that are currently believed to be false. Besides $P$ and $NP$, another major complexity class is $coNP$. It is a known result if $P=NP$, then $NP=coNP$. Therefore, if we prove $P \neq coNP$, then this would be sufficient to show $P \neq NP$. Indeed, in this work we have demonstrated the existence of a $coNP$ problem that is not in $P$, and thus, $P \neq coNP$. In this way, we show the belief of almost all computer scientists was a truly supposition.

Mots clés: coNP; NP; P; Turing machine

Domaines: Complexité [cs.CC]

Frank Vega. The P versus NP Problem. 2015. ⟨hal-01114642⟩