17 citations · 26 across the 27 of their papers we have counts for
42 papers
A Weyl Criterion for Finite-State Dimension and Applications
Jack H. Lutz, Satyadev Nandakumar, Subin Pulari
Finite-state dimension, introduced early in this century as a finite-state version of classical Hausdorff dimension, is a quantitative measure of the lower asymptotic density of in…
Finite-State Mutual Dimension
Adam Case, Jack H. Lutz
In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the finite-state dimension (a finite-state version of algorithmic dimension) of a sequence and,…
Dimension and the Structure of Complexity Classes
Jack H. Lutz, Neil Lutz, Elvira Mayordomo
We prove three results on the dimension structure of complexity classes. 1. The Point-to-Set Principle, which has recently been used to prove several new theorems in fractal geomet…
The Point-to-Set Principle and the Dimensions of Hamel Bases
Jack H. Lutz, Renrui Qi, Liang Yu
We prove that every real number in [0,1] is the Hausdorff dimension of a Hamel basis of the vector space of reals over the field of rationals. The logic of our proof is of particul…
Algorithmic Fractal Dimensions in Geometric Measure Theory
Jack H. Lutz, Elvira Mayordomo
The development of algorithmic fractal dimensions in this century has had many fruitful interactions with geometric measure theory, especially fractal geometry in Euclidean spaces.…
Algorithmically Optimal Outer Measures
Jack H. Lutz, Neil Lutz
We investigate the relationship between algorithmic fractal dimensions and the classical local fractal dimensions of outer measures in Euclidean spaces. We introduce global and loc…