Category and measure in complexity classes
SIAM Journal on Computing
Almost everywhere high nonuniform complexity
Journal of Computer and System Sciences
Genericity and measure for exponential time
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
The quantitative structure of exponential time
Complexity theory retrospective II
Genericity and randomness over feasible probability measures
Theoretical Computer Science - Special issue In Memoriam of Ronald V. Book
Journal of Computer and System Sciences
Dimension in Complexity Classes
COCO '00 Proceedings of the 15th Annual IEEE Conference on Computational Complexity
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Resource-bounded Baire category: a stronger approach
SCT '95 Proceedings of the 10th Annual Structure in Complexity Theory Conference (SCT'95)
Hausdorff Dimension in Exponential Time
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
The dimensions of individual strings and sequences
Information and Computation
Theoretical Computer Science
Small Spans in Scaled Dimension
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Journal of Computer and System Sciences - Special issue on COLT 2002
Baire categories on small complexity classes and meager--comeager laws
Information and Computation
Generic density and small span theorem
FCT'05 Proceedings of the 15th international conference on Fundamentals of Computation Theory
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We refine the genericity concept of Ambos-Spies, by assigning a real number in [0,1] to every generic set, called its generic density. We construct sets of generic density any E-computable real in [0,1], and show a relationship between generic density and Lutz resource bounded dimension. We also introduce strong generic density, and show that it is related to packing dimension. We show that all four notions are different. We show that whereas dimension notions depend on the underlying probability measure, generic density does not, which implies that every dimension result proved by generic density arguments, simultaneously holds under any (biased coin based) probability measure. We prove such a result: we improve the small span theorem of Juedes and Lutz, to the packing dimension setting, for k-bounded-truth-table reductions, under any (biased coin) probability measure.