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Solovay reducibility via Lipschitz functions and signed-digit representation

履歴
2023年11月7日：投稿

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

種類
研究論文

出版情報
TBA

要旨
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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