Relativizing complexity classes with sparse oracles
Journal of the ACM (JACM)
Almost optimal lower bounds for small depth circuits
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Average case complete problems
SIAM Journal on Computing
SIAM Journal on Computing
Journal of Computer and System Sciences
On the theory of average case complexity
Journal of Computer and System Sciences
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Average-case computational complexity theory
Complexity theory retrospective II
Relativized worlds with an infinite hierarchy
Information Processing Letters
Fine Separation of Average-Time Complexity Classes
SIAM Journal on Computing
Complete distributional problems, hard languages, and resource-bounded measure
Theoretical Computer Science
Defying Upward and Downward Separation
STACS '93 Proceedings of the 10th Annual Symposium on Theoretical Aspects of Computer Science
Cook Versus Karp-Levin: Separating Completeness Notions if NP Is not Small (Extended Abstract)
STACS '94 Proceedings of the 11th Annual Symposium on Theoretical Aspects of Computer Science
Sets Computable in Polynomial Time on Average
COCOON '95 Proceedings of the First Annual International Conference on Computing and Combinatorics
A personal view of average-case complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Separating the polynomial-time hierarchy by oracles
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Decision versus search problems in super-polynomial time
SFCS '89 Proceedings of the 30th Annual Symposium on Foundations of Computer Science
Hi-index | 0.00 |
Define a set L to be distributionally-hard to recognize if for every polynomial-time computable distribution µ with infinite support, L is not recognizable in polynomial time on the µ-average. Cai and Selman [5] defined a modification of Levin's notion of average polynomial time and proved that every P-bi-immune language is distributionally-hard. Pavan and Selman [23] proved that there exist distributionally-hard sets that are not P-bi-immune if and only P contains P-printable-immune sets. We extend this characterizion to include assertions about several traditional questions about immunity, about finding witnesses for NP-machines, and about existence of one-way functions. Similarly, we address the question of whether NP contains sets that are distributionally hard. Several of our results are implications for which we cannot prove whether or not their converse holds. In nearly all such cases we provide oracles relative to which the converse fails. We use the techniques of Kolmogorov complexity to describe our oracles and to simplify the technical arguments.