ZERO-ONE-IN-THREE 3SAT is in P

Frank Vega (1)

1 Datys

$ONE-IN-THREE \ 3SAT$ is the problem of deciding whether a given boolean formula $\phi$ in $3CNF$ has a truth assignment such that each clause in $\phi$ has exactly one true literal. This problem is $NP-complete$. We define a similar language: $ZERO-ONE-IN-THREE \ 3SAT$ is the problem of deciding whether a given boolean formula $\phi$ in $3CNF$ has a truth assignment such that each clause in $\phi$ has at most one true literal. Indeed, $ONE-IN-THREE \ 3SAT \subseteq ZERO-ONE-IN-THREE \ 3SAT$. In this work, we prove $ZERO-ONE-IN-THREE \ 3SAT \in P$.

Mots clés: NP; NP-complete; 3SAT

Domaines: Complexité [cs.CC]

Frank Vega. ZERO-ONE-IN-THREE 3SAT is in P. 2014. ⟨hal-01070568⟩