Elements of information theory
Elements of information theory
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Journal of the ACM (JACM)
Theoretical Computer Science
The Complexity and Distribution of Hard Problems
SIAM Journal on Computing
Almost every set in exponential time is P-bi-immune
Theoretical Computer Science
On resource-bounded instance complexity
Theoretical Computer Science
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Random strings make hard instances
Journal of Computer and System Sciences
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
An excursion to the Kolmogorov random strings
Journal of Computer and System Sciences - special issue on complexity theory
An introduction to Kolmogorov complexity and its applications (2nd ed.)
An introduction to Kolmogorov complexity and its applications (2nd ed.)
The quantitative structure of exponential time
Complexity theory retrospective II
NP-Hard Sets Have Many Hard Instances
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
On the Complexity of Random Strings (Extended Abstract)
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
COCO '98 Proceedings of the Thirteenth Annual IEEE Conference on Computational Complexity
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This paper investigates the instance complexities of problems that are hard or weakly hard for exponential time under polynomial time, many-one reductions. It is shown that almost every instance of almost every problem in exponential time has essentially maximal instance complexity. It follows that every weakly hard problem has a dense set of such maximally hard instances. This extends the theorem, due to Orponen, Ko, Schöning and Watanabe (1994), that every hard problem for exponential time has a dense set of maximally hard instances. Complementing this, it is shown that every hard problem for exponential time also has a dense set of unusually easy instances.