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Quasi-Isometric Reductions Between Infinite Strings
- Publication Year :
- 2024
-
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 $\alpha$ and $\beta$ such that $\alpha$ is strictly quasi-isometrically reducible to $\beta$, but the reduction cannot be made recursive. This answers an open problem posed by Khoussainov and Takisaka.
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2407.14105
- Document Type :
- Working Paper