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11/07/2021
A Weyl Criterion for Finite-State Dimension
Finite-state dimension, introduced early in this century as a finite-sta...
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09/29/2021
Finite-State Mutual Dimension
In 2004, Dai, Lathrop, Lutz, and Mayordomo defined and investigated the ...
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09/22/2021
The Point-to-Set Principle, the Continuum Hypothesis, and the Dimensions of Hamel Bases
We prove that the Continuum Hypothesis implies that every real number in...
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09/13/2021
Dimension and the Structure of Complexity Classes
We prove three results on the dimension structure of complexity classes....
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07/28/2020
Algorithmic Fractal Dimensions in Geometric Measure Theory
The development of algorithmic fractal dimensions in this century has ha...
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06/15/2020
Algorithmically Optimal Outer Measures
We investigate the relationship between algorithmic fractal dimensions a...
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04/16/2020
The Dimensions of Hyperspaces
We use the theory of computing to prove general hyperspace dimension the...
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11/30/2019
Who Asked Us? How the Theory of Computing Answers Questions about Analysis
Algorithmic fractal dimensions – constructs of computability theory – ha...
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10/30/2019
Algorithmic Randomness in Continuous-Time Markov Chains
In this paper we develop the elements of the theory of algorithmic rando...
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10/30/2019
Asymptotic Divergences and Strong Dichotomy
The Schnorr-Stimm dichotomy theorem concerns finite-state gamblers that ...
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02/16/2019
Robustness and Games Against Nature in Molecular Programming
Matter, especially DNA, is now programmed to carry out useful processes ...
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03/27/2018