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Solovay reducibility via Lipschitz functions and signed-digit representation

News
7 Nov 2023: submitted to a journal
13 Sep 2025: Published online

Title
Solovay reducibility via Lipschitz functions and signed-digit representation
Masahiro Kumabe, Kenshi Miyabe, and Toshio Suzuki

Type
Research article

Publication
Kumabe M, Miyabe K, Suzuki T.
Solovay reducibility via Lipschitz functions and signed-digit representation.
Computability. 2025;14(1):38-62.
doi:10.3233/COM-230486
https://journals.sagepub.com/doi/10.3233/COM-230486

Abstract
We explore Solovay reducibility in the context of computably approximable reals, extending its natural characterization for left-c.e. reals via computable Lipschitz functions. Our paper offers two distinct characterizations: the first employs Lipschitz functions, while the second utilizes Turing reductions with bounded use with respect to signed-digit representation. Additionally, we examine multiple related reducibilities and establish separations among them. These results contribute to a refined perspective of the relationship between Solovay reducibility and computable Lipschitz functions.

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preprint (23 May, 2024)
Read the paper on Meiji University Institutional Repository