The geometry of fractal sets
The Complexity and Distribution of Hard Problems
SIAM Journal on Computing
Cook versus Karp-Levin: separating completeness notions if NP is not small
Theoretical Computer Science
Genericity and measure for exponential time
MFCS '94 Selected papers from the 19th international symposium on Mathematical foundations of computer science
Journal of Computer and System Sciences
Twelve problems in resource-bounded measure
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Hausdorff Dimension in Exponential Time
CCC '01 Proceedings of the 16th Annual Conference on Computational Complexity
Dimension in Complexity Classes
SIAM Journal on Computing
The dimensions of individual strings and sequences
Information and Computation
Scaled dimension and nonuniform complexity
Journal of Computer and System Sciences
Small Spans in Scaled Dimension
SIAM Journal on Computing
Effective Strong Dimension in Algorithmic Information and Computational Complexity
SIAM Journal on Computing
Partial Bi-immunity, Scaled Dimension, and NP-Completeness
Theory of Computing Systems
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Effective fractal dimension was defined by Lutz [13]in order to quantitatively analyze the structure of complexity classes. The dimension of a class X inside a base class ${\mathcal{C}}$ is a real number in [0,1] corresponding to the relative size of $X \cap \mathcal{C}$ inside $\mathcal{C}$. Basic properties include monotonicity, so dimension 1 classes are maximal and dimension 0 ones are minimal, and the fact that dimension is defined for every classX, making effective dimension a precise quantitative tool.