Average-Case Complexity

Average Case Complexity

We attempt to motivate, justify and survey the average case reduction theory.

Average Case Complexity, Revisited

More than two decades elapsed since Levin set forth a theory of average-case complexity. In this survey we present the basic aspects of this theory as well as some of the main results regarding it. The current presentation deviates from our old “Notes on Levin’s Theory of Average-Case Complexity” (ECCC, TR97-058, 1997) in several aspects.

Structural Average Case Complexity

Levin introduced an average case complexity measure based on a notion of polynomial on average and de ned average case polynomial time many one reducibility among randomized decision problems We generalize his notions of average case complexity classes Random NP and Average P Ben David et al use the notation of hC Fi to denote the set of randomized de cision problems L such that L is a set in C...

Average Case Complexity Theory

Informally, Average case Complexity theory considers the average complexity with respect to a probability distribution over the set of inputs, instead of the complexity on the worst case input, as a criterion for the hardness of a problem. With regard to this theory, we explore the notion of a natural distribution. In particular, we consider different bounds on the minentropy of such distributi...

Texts in Computational Complexity: Average-Case Complexity