A probabilistically checkable proof (PCP) is a special format for writing proofs that is very robust. In this format, a proof of a false theorem is guaranteed to have so many bugs that it can be checked by reading a constant number of random proof bits.
The celebrated PCP theorem says that every NP language has a robust “PCP” proof.
In the talk we will explain how to construct a PCP by taking any standard NP proof and then routing it through an expander graph (i.e., a graph that is very well-connected).
We will also describe a complementary result that shows how in some restricted sense, every construction of a PCP must be based on an expander.
No prior knowledge will be assumed.
Based in part on joint work with Tali Kaufman.