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Randomness Versus Superspeedability

Authors Rupert Hölzl, Philip Janicki , Wolfgang Merkle, Frank Stephan

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  • Theory of computation → Computability
Keywords
  • superspeedable numbers
  • speedable numbers
  • regainingly approximable numbers
  • regular numbers
  • left-computable numbers

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Abstract

Speedable numbers are real numbers which are algorithmically approximable from below and whose approximations can be accelerated nonuniformly. We begin this article by answering a question of Barmpalias by separating a strict subclass that we will refer to as superspeedable from the speedable numbers; for elements of this subclass, acceleration is possible uniformly and to an even higher degree. This new type of benign left-approximation of numbers then integrates itself into a hierarchy of other such notions studied in a growing body of recent work. We add a new perspective to this study by juxtaposing this hierachy with the well-studied hierachy of algorithmic randomness notions.

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Rupert Hölzl, Philip Janicki, Wolfgang Merkle, and Frank Stephan. Randomness Versus Superspeedability. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.62

Author Details

Rupert Hölzl
  • Universität der Bundeswehr München, Germany
Philip Janicki
  • Universität der Bundeswehr München, Germany
Wolfgang Merkle
  • Universität Heidelberg, Germany
Frank Stephan
  • National University of Singapore, Singapore

Funding

The investigators acknowledge the following partial support: F. Stephan’s research was supported by Singapore Ministry of Education AcRF Tier 2 grant MOE-000538-00 and AcRF Tier 1 grants A-0008454-00-00 and A-0008494-00-00, the grant A-0008494-00-00 also supported the research visits of R. Hölzl to the National University of Singapore for the work on this paper.

Acknowledgements

The authors would like to thank the referees for helpful and detailed comments.

References

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