diff --git a/semester3/ti-compact/parts/05_complexity.tex b/semester3/ti-compact/parts/05_complexity.tex index b2b6f32..585300d 100644 --- a/semester3/ti-compact/parts/05_complexity.tex +++ b/semester3/ti-compact/parts/05_complexity.tex @@ -187,7 +187,7 @@ where a \textit{dominating} set is is a set $D \subseteq V$ such that for every and where a vertex cover is any set $U \subseteq V$ where all edges $\{ u, v \} \in E$ have at least one endpoint $u, v \in U$ We have $SAT \leq_p \text{CLIQUE}$, $SAT \leq_p 3SAT$, $\text{CLIQUE} \leq_p VC$, $VC \leq_p SCP$ and $SCP \leq_p DS$. -Logically, we also have $SAT \leq_p DS$, etc, since $\leq_p$ is transitive (in fact, all reductions are transitive) +Logically, we also have $SAT \leq_p DS$, etc, since $\leq_p$ is transitive (in fact, all reductions that we covered are transitive) Additionally, $\text{MAX-SAT}$ and $\text{MAX-CL}$, the problem to determine the maximum number of fulfillable clauses in a formula $\Phi$ and the problem to determine the maximum clique, respectively, are $NP$-hard