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arXiv · 2407.14105

Quasi-Isometric Reductions Between Infinite Strings

Karen Frilya Celine·Ziyuan Gao·Sanjay Jain·Ryan Lou·Frank Stephan·Guohua Wu
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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 $\alpha$ 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.

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Karen Frilya Celine, Ziyuan Gao, Sanjay Jain, Ryan Lou, Frank Stephan, Guohua Wu. 2024-07-19. Quasi-Isometric Reductions Between Infinite Strings. https://arxiv.org/abs/2407.14105

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