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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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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.

Cite AsGet BibTex

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

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.

Subject Classification

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

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References

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