Average case complete problems
SIAM Journal on Computing
On the theory of average case complexity
Journal of Computer and System Sciences
A Pseudorandom Generator from any One-way Function
SIAM Journal on Computing
Foundations of Cryptography: Basic Tools
Foundations of Cryptography: Basic Tools
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Foundations and Trends® in Theoretical Computer Science
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
No better ways to generate hard NP instances than picking uniformly at random
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Notes on Levin's theory of average-case complexity
Studies in complexity and cryptography
| Hi-index | 0.00 |
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. In particular: - We currently view average-case complexity as referring to the performance on "average" (or rather typical) instances, and not as the average performance on random instances. (Thus, it may be more justified to refer to this theory by the name typical-case complexity, but we retain the name average-case for historical reasons.) - We include a treatment of search problems, and a presentation of the reduction of "NP with sampleable distributions" to "NP with P-computable distributions" (due to Impagliazzo and Levin, 31st FOCS, 1990). - We include Livne's result (ECCC, TR06-122, 2006) by which all natural NPC-problems have average-case complete versions. This result seems to shed doubt on the association of P-computable distributions with natural distributions.