17 citations · 26 across the 27 of their papers we have counts for
30 papers · 1 filter
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…
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…
Extending the Reach of the Point-to-Set Principle
Jack H. Lutz, Neil Lutz, Elvira Mayordomo
The point-to-set principle of J. Lutz and N. Lutz (2018) has recently enabled the theory of computing to be used to answer open questions about fractal geometry in Euclidean spaces…
Who Asked Us? How the Theory of Computing Answers Questions about Analysis
Jack H. Lutz, Neil Lutz
Algorithmic fractal dimensions -- constructs of computability theory -- have recently been used to answer open questions in classical geometric measure theory, questions of mathema…
Real-Time Computability of Real Numbers by Chemical Reaction Networks
Xiang Huang, Titus H. Klinge, James I. Lathrop +2
We explore the class of real numbers that are computed in real time by deterministic chemical reaction networks that are integral in the sense that all their reaction rate constant…