Bounding the dimension of points on a line
N Lutz, DM Stull - Information and Computation, 2020 - Elsevier
We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff
dimension of the point (x, a x+ b), given real numbers a, b, and x. We apply our main …
dimension of the point (x, a x+ b), given real numbers a, b, and x. We apply our main …
Fractal intersections and products via algorithmic dimension
N Lutz - ACM Transactions on Computation Theory (TOCT), 2021 - dl.acm.org
Algorithmic fractal dimensions quantify the algorithmic information density of individual
points and may be defined in terms of Kolmogorov complexity. This work uses these …
points and may be defined in terms of Kolmogorov complexity. This work uses these …
Algorithmic fractal dimensions in geometric measure theory
JH Lutz, E Mayordomo - Handbook of Computability and Complexity in …, 2021 - Springer
The development of algorithmic fractal dimensions in this century has had many fruitful
interactions with geometric measure theory, especially fractal geometry in Euclidean spaces …
interactions with geometric measure theory, especially fractal geometry in Euclidean spaces …
Optimal oracles for point-to-set principles
DM Stull - arXiv preprint arXiv:2101.11152, 2021 - arxiv.org
The point-to-set principle\cite {LutLut17} characterizes the Hausdorff dimension of a subset $
E\subseteq\R^ n $ by the\textit {effective}(or algorithmic) dimension of its individual points …
E\subseteq\R^ n $ by the\textit {effective}(or algorithmic) dimension of its individual points …
Fractal intersections and products via algorithmic dimension
N Lutz - arXiv preprint arXiv:1612.01659, 2016 - arxiv.org
Algorithmic fractal dimensions quantify the algorithmic information density of individual
points and may be defined in terms of Kolmogorov complexity. This work uses these …
points and may be defined in terms of Kolmogorov complexity. This work uses these …
The dimension spectrum conjecture for planar lines
DM Stull - arXiv preprint arXiv:2102.00134, 2021 - arxiv.org
Let $ L_ {a, b} $ be a line in the Euclidean plane with slope $ a $ and intercept $ b $. The
dimension spectrum $\spec (L_ {a, b}) $ is the set of all effective dimensions of individual …
dimension spectrum $\spec (L_ {a, b}) $ is the set of all effective dimensions of individual …
One-Way Functions and Polynomial Time Dimension
This work solves an open problem regarding the rate of time-bounded Kolmogorov
complexity and polynomial-time dimension, conditioned on a hardness assumption …
complexity and polynomial-time dimension, conditioned on a hardness assumption …
Effective Hausdorff dimension in general metric spaces
E Mayordomo - Theory of Computing Systems, 2018 - Springer
We introduce the concept of effective dimension for a wide class of metric spaces whose
metric is not necessarily based on a measure. Effective dimension was defined by Lutz (Inf …
metric is not necessarily based on a measure. Effective dimension was defined by Lutz (Inf …
Polylog space compression, pushdown compression, and Lempel-Ziv are incomparable
E Mayordomo, P Moser, S Perifel - Theory of Computing Systems, 2011 - Springer
The pressing need for efficient compression schemes for XML documents has recently been
focused on stack computation (Hariharan, S., & Shankar, P. in: Proceedings of the 2006 …
focused on stack computation (Hariharan, S., & Shankar, P. in: Proceedings of the 2006 …
Randomness and Solovay degrees
We consider the behaviour of Schnorr randomness, a randomness notion weaker than
Martin-Löf's, for left-re reals under Solovay reducibility. Contrasting with results on Martin-Löf …
Martin-Löf's, for left-re reals under Solovay reducibility. Contrasting with results on Martin-Löf …