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Quasi-Isometric Reductions Between Infinite Strings

Authors Karen Frilya Celine , Ziyuan Gao, Sanjay Jain , Ryan Lou, Frank Stephan , Guohua Wu

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ACM Subject Classification
  • Theory of computation → Computability
Keywords
  • Quasi-isometry
  • recursion theory
  • infinite strings

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Abstract

This paper studies the recursion-theoretic aspects of large-scale geometries of infinite strings, a subject initiated by Khoussainov and Takisaka (2017). We investigate several notions of quasi-isometric reductions between recursive infinite strings and prove various results on the equivalence classes of such reductions. The main result is the construction of two infinite recursive strings α and β such that α is strictly quasi-isometrically reducible to β, but the reduction cannot be made recursive. This answers an open problem posed by Khoussainov and Takisaka.

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Karen Frilya Celine, Ziyuan Gao, Sanjay Jain, Ryan Lou, Frank Stephan, and Guohua Wu. Quasi-Isometric Reductions Between Infinite Strings. In 49th International Symposium on Mathematical Foundations of Computer Science (MFCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 306, pp. 37:1-37:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.MFCS.2024.37

Author Details

Karen Frilya Celine
  • School of Computing, National University of Singapore, Singapore
Ziyuan Gao
  • School of Science and Technology, Singapore University of Social Sciences, Singapore
  • Kaplan Higher Education Academy, Singapore
Sanjay Jain
  • School of Computing, National University of Singapore, Singapore
Ryan Lou
  • School of Computing, National University of Singapore, Singapore
Frank Stephan
  • Department of Mathematics, National University of Singapore, Singapore
  • School of Computing, National University of Singapore, Singapore
Guohua Wu
  • School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore

Funding

S. Jain and F. Stephan were supported by Singapore Ministry of Education (MOE) AcRF Tier 2 grant MOE-000538-00. Additionally, S. Jain was supported by NUS grant E-252-00-0021-01 and F. Stephan was supported by the AcRF Tier 1 grants A-0008454-00-00 and A-0008494-00-00. G. Wu was partially supported by MOE Tier 1 grants RG111/19 (S) and RG102/23.

Acknowledgements

We thank the anonymous referees for several helpful comments which improved the presentation of the paper.

References

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