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Algorithmic Dimensions via Learning Functions

Authors Jack H. Lutz , Andrei N. Migunov

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Author Details

Jack H. Lutz
  • Department of Computer Science, Iowa State University, Ames, IA, USA
Andrei N. Migunov
  • Department of Mathematics and Computer Science, Drake University, Des Moines, IA, USA

Funding

  • Lutz, Jack H.: This research was supported in part by National Science Foundation research grants 1545028 and 1900716.
  • Migunov, Andrei N.: This research was supported in part by National Science Foundation research grants 1545028 and 1900716.

Cite As Get BibTex

Jack H. Lutz and Andrei N. Migunov. Algorithmic Dimensions via Learning Functions. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 72:1-72:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.72

Abstract

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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Computability
  • Theory of computation → Models of learning
Keywords
  • algorithmic dimensions
  • learning functions
  • randomness

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