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Creators/Authors contains: "Lutz, Jack H"

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  1. ; (, ACM Transactions on Computation Theory)
    We investigate the relationship between algorithmic fractal dimensions and the classical local fractal dimensions of outer measures in Euclidean spaces. We introduce global and local optimality conditions for lower semicomputable outer measures. We prove that globally optimal outer measures exist. Our main theorem states that the classical local fractal dimensions of any locally optimal outer measure coincide exactly with the algorithmic fractal dimensions. Our proof uses an especially convenient locally optimal outer measureκdefined in terms of Kolmogorov complexity. We discuss implications for point-to-set principles. 
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    Free, publicly-accessible full text available May 7, 2026
  2. ; (, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)
    Kráľovič, Rastislav; Kučera, Antonín (Ed.)
    We characterize the algorithmic dimensions (i.e., the lower and upper asymptotic densities of information) of infinite binary sequences in terms of the inability of learning functions having an algorithmic constraint to detect patterns in them. Our pattern detection criterion is a quantitative extension of the criterion that Zaffora Blando used to characterize the algorithmically random (i.e., Martin-Löf random) sequences. Our proof uses Lutz’s and Mayordomo’s respective characterizations of algorithmic dimension in terms of gales and Kolmogorov complexity. 
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  3. ; ; (, Computability)
    We prove that, for every 0 ⩽ s ⩽ 1, there is a Hamel basis of the vector space of reals over the field of rationals that has Hausdorff dimension s. The logic of our proof is of particular interest. The statement of our theorem is classical; it does not involve the theory of computing. However, our proof makes essential use of algorithmic fractal dimension–a computability-theoretic construct–and the point-to-set principle of J. Lutz and N. Lutz (2018). 
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  4. ; ; (, Information and Computation)
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  5. ; ; (, Theory of Computing Systems)
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  6. ; (, 58th Annual Allerton Conference on Communication, Control, and Computing, Allerton 2022)
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  7. ; ; (, 39th International Symposium on Theoretical Aspects of Computer Science)
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  8. ; (, Information and Computation)
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  9. ; ; ; (, IEEE Transactions on Information Theory)
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  10. ; ; ; ; (, Natural Computing)
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