Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Measure, Stochasticity, and the Density of Hard Languages
SIAM Journal on Computing
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
SIAM Journal on Computing
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Resource bounded randomness and weakly complete problems
Theoretical Computer Science
Measure on P: strength of the notion
Information and Computation
The quantitative structure of exponential time
Complexity theory retrospective II
Measure on P: Robustness of the Notion
MFCS '95 Proceedings of the 20th International Symposium on Mathematical Foundations of Computer Science
Observations on Measure and Lowness for Delta^P_2
STACS '96 Proceedings of the 13th Annual Symposium on Theoretical Aspects of Computer Science
A Comparison of Weak Completeness Notions
CCC '96 Proceedings of the 11th Annual IEEE Conference on Computational Complexity
Constant depth circuits and the Lutz hypothesis
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Theoretical Computer Science
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We revisit the problem of generalising Lutz's resource-bounded measure (RBM) to small complexity classes, and propose a definition of a random-based RBM on P=∪k∈N DTIME (O(nk)), which we argue as being a good generalisation to P of Lutz's RBM. We cannot unconditionally prove the existence of such a measure, but we give sufficient and necessary conditions for its existence. We also revisit µτ, an RBM for P defined by Strauss [Inform. Comput. 136(1) (1997) 1], and correct an erroneous claim concerning the relations between µτ and random sets. A correction to this mistake is then proposed, which is a less powerful but accurate relation between µτ and random sets.In order to obtain these results, we introduce a mathematical structure called a measuring system, which is a general setting that can be used to compare different RBMs on any fixed complexity class through a partial ordering relation.