LECTURE 23: OR

2 Literature on Average-Case Complexity Some of important surveys on average case complexity (very far from being all of them) are, in approximate chronological order: • Levin [1] formalized the idea that average case complexity is about problems plus a distribution over inputs (i.e., hardness depends on the the distribution). • Impagliazzo [2] wrote a survey giving his “Personal View of Average-Case Complexity” describing 5 possible worlds (we live in exactly one of them; we just don’t know which one, yet). • Goldreich wrote a survey, that made its way into his book [3]. • Ajtai [4] gave a talk at ICM’02 on connections between Worst-Case complexity and Average-Case Complexity, specifically, in the context on lattice problems. • Bogdanov and Trevisan [5] recently wrote a survey on “Average-Case Complexity”. In this lecture, we discuss Impagliazzo’s five possible worlds, as well as Ajtai’s lattice problems.