Communications of the ACM
Average case complete problems
SIAM Journal on Computing
Journal of Computer and System Sciences
Learning simple concepts under simple distributions
SIAM Journal on Computing
Average case complexity under the universal distribution equals worst-case complexity
Information Processing Letters
On the theory of average case complexity
Journal of Computer and System Sciences
The complexity of malign measures
SIAM Journal on Computing
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
Simple PAC Learning of Simple Decision Lists
ALT '95 Proceedings of the 6th International Conference on Algorithmic Learning Theory
A note on universal distributions for polynomial-time computable distributions
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
Computational depth: concept and applications
Theoretical Computer Science - Foundations of computation theory (FCT 2003)
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The equivalence of the universal distribution, the a priori probability and the negative exponential of Kolmogorov complexity is a well known result. The natural analogs of Kolmogorov complexity and of a priori probability in the time-bounded setting are not efficiently computable under reasonable assumptions. In contrast, it is known that for every polynomial p, distributions universal for the class of p-time computable distributions can be computed in polynomial time. We show that in the time-bounded setting the universal distribution gives rise to sensible notions of Kolmogorov complexity and of a priori probability.