4 papers · 1 filter
Lines in Every Direction with No ee-Random Points
Neil Lutz, Spencer Park Martin, Rain White
We prove that in every direction in the Euclidean plane, there exists a line containing no double exponential time random (ee-random) points. This means each point on these lines h…
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…
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…