Reduce the
SAT problem to the
CLIQUE problem.
These problems are defined as follows:
- SAT: given a boolean formula $F$ in conjunctive normal form, is $F$
satisfiable?
More formally, this problem can be defined as the following set:
$\{ F=C_1\wedge\ldots\wedge C_n \mid F\text{ satisfiable} \}$
- CLIQUE: given a natural $k$ and an undirected graph $G$, is there a
subset $S$ of nodes with size at least $k$ such that any two distinct nodes of
$S$ are connected by an edge in $G$?
More formally, this problem can be defined as the following set:
$\{ \langle k,G=\langle V,E\rangle\rangle \mid \exists S\subseteq V: (|S|\geq k\;\wedge\;\forall u,v\in S: (u\neq v\;\Rightarrow\;\{u,v\}\in E)) \}$
The input and output of the reduction conform to the following data types: