# Expanders, Property Testing and the PCP theorem

## Lecture 4: Proof that PCP Theorem is equivalent to hardness of Gap-Max-SAT

Posted in lectures by HQN on September 8, 2008

In today’s lecture, I proved that the PCP theorem is equivalent to the fact that

• Gap-MaxE3SAT$_{1,s}$ is NP-Hard for some constant $s \in (0,1)$

From the fact, it’s easy to show that

• MaxE3SAT is NP-Hard to approximate to within some constant $\alpha <1$

I also outlined things that will be discussed about expanders.