Lecture 1: Introduction

In today’s lecture, we saw two “disparate” interpretations of languages in NP: in particular, the proof-verifier definition of NP (and PCPs) and approximation algorithms for NP-complete problems (3ESAT in particular). We also saw the statement of the wonderful and mysterious PCP theorem.

Next lecture, we will wrap up some left over discussion about these two views and then go on to show that the views are actually the same.

Today’s lecture was based on these lecture notes.

Also in class I mentioned that the PCP theorem has an very interesting history. For a very nice description, see this writeup by Ryan O’Donnell.