Reduce the
VERTEX COVER problem to the
SAT problem.
These problems are defined as follows:
- VERTEX COVER: given a natural $k$ and an undirected graph $G$, is
there a cover for $G$ of size at most $k$? In other words, is there a subset
$S$ of nodes with size at most $k$ such that each edge of $G$ involves a node
from $S$?
More formally, this problem can be defined as the following set:
$\{ \langle k,G=\langle V,E\rangle\rangle \mid \exists S\subseteq V: (|S|\leq k\;\wedge\;\forall \{u,v\}\in E: (u\in S\;\vee\;v\in S)) \}$
- SAT: given a boolean formula $F$ in conjunctive normal form, is $F$
satisfiable?
More formally, this problem can be defined as the following set:
$\{ F=C_1\wedge\ldots\wedge C_n \mid F\text{ satisfiable} \}$
The input and output of the reduction conform to the following data types: