The Unified Theory of Pseudorandomness

Abstract

Pseudorandomness is the theory of efficiently generating objects that look "random" despite being constructed with little or no randomness. One of the achievements of this research area has been the realization that a number of fundamental and widely studied "pseudorandom" objects are all almost equivalent when viewed appropriately. These objects include pseudorandom generators, expander graphs, list-decodable error-correcting codes, averaging samplers, and hardness amplifi ers. In this survey, we describe the connections between all of these objects, showing how they can all be cast within a single "list-decoding framework" that brings out both their similarities and differences.