Medvedev reducibility

In computability theory, a set P of functions ${\displaystyle \mathbb {N} \rightarrow \mathbb {N} }$ is said to be Medvedev-reducible to another set Q of functions ${\displaystyle \mathbb {N} \rightarrow \mathbb {N} }$ when there exists an oracle Turing machine that 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, that compute functions from P.^[2]