2019/03/20 by Masahiro Kumabe, Kenshi Miyabe, Kumabe, Masahiro +5
Computer Science · Mathematics · #03D78 #68Q30 #Advanced Topology and Set Theory #Computability, Logic, AI Algorithms #FOS: Mathematics #Logic (math.LO) #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1903.08625
openalex publication_date 2019/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The objective of this study is a better understanding of the relationships between reduction and continuity. Solovay reduction is a variation of Turing reduction based on the distance of two real numbers. We characterize Solovay reduction by the existence of a certain real function that is computable (in the sense of computable analysis) and Lipschitz continuous. We ask whether there exists a reducibility concept that corresponds to Hölder continuity. The answer is affirmative. We introduce quasi Solovay reduction and characterize this new reduction via Hölder continuity. In addition, we separate it from Solovay reduction and Turing reduction and investigate the relationships between complete sets and partial randomness.