Two Open Problems on Effective Dimension

  • Elvira Mayordomo
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3988)


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.


Complexity Class Fractal Geometry SIAM Journal Kleinian Group Packing Dimension 
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© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Elvira Mayordomo
    • 1
  1. 1.Dept. de Informática e Ing. de SistemasUniversidad de ZaragozaZaragozaSpain

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