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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.<\/jats:p>","DOI":"10.3233\/com-230486","type":"journal-article","created":{"date-parts":[[2024,7,19]],"date-time":"2024-07-19T10:36:01Z","timestamp":1721385361000},"page":"38-62","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":2,"title":["Solovay reducibility via Lipschitz functions and signed-digit representation"],"prefix":"10.1177","volume":"14","author":[{"given":"Masahiro","family":"Kumabe","sequence":"first","affiliation":[{"name":"Department of Liberal Arts, The Open University of Japan, Chiba, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Kenshi","family":"Miyabe","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Meiji University, Kawasaki, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Toshio","family":"Suzuki","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, Tokyo Metropolitan University, Hachioji, Japan"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"179","published-online":{"date-parts":[[2024,6,27]]},"reference":[{"key":"e_1_3_3_2_2","doi-asserted-by":"publisher","DOI":"10.1006\/jcom.2000.0561"},{"key":"e_1_3_3_3_2","doi-asserted-by":"publisher","unstructured":"Brattka V. 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