P vs NP

Frank Vega (1)

1 Datys

$UNIQUE \ SAT$ is the problem of deciding whether a given Boolean formula has exactly one satisfying truth assignment. The $UNIQUE \ SAT$ is $coNP-hard$. We prove the $UNIQUE \ SAT$ is in $NP$, and therefore, $NP = coNP$. Furthermore, we prove if $NP = coNP$, then some problem in $coNPC$ is in $P$, and thus, $P = NP$. In this way, the $P$ versus $NP$ problem is solved with a positive answer.

Mots clés: Complexity class; NP; coNP; Turing Machine; Language

Domaines: Complexité [cs.CC]

Frank Vega. P vs NP. 2014. ⟨hal-00984866v5⟩