In computability theory, a set P of functions ℕ → ℕ is said to be Medvedev-reducible to another set Q of functions ℕ → ℕ when there exists an oracle Turing machine which computes some function of P whenever it is given some function from Q as an oracle.[1]
Medvedev reducibility is a uniform variant of Mučnik reducibility, requiring a single oracle machine that can compute some function of P given any oracle from Q, instead of a family of oracle machines, one per oracle from Q, which compute functions from P.[2]
See also
editReferences
edit- ^ Hinman, Peter G. (2012). "A survey of Mučnik and Medvedev degrees". Bulletin of Symbolic Logic. 18 (2): 161–229.
- ^ Simpson, Stephen G. "Mass Problems and Degrees of Unsolvability" (PDF). Retrieved 2024-06-10.
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