Mučnik reducibility

In computability theory, a set P of functions ${\displaystyle \mathbb {N} \rightarrow \mathbb {N} }$ is said to be Mučnik-reducible to another set Q of functions ${\displaystyle \mathbb {N} \rightarrow \mathbb {N} }$ when for every function g in Q, there exists a function f in P which is Turing-reducible to g.[1]

Unlike most reducibility relations in computability, Mučnik reducibility is not defined between functions ${\displaystyle \mathbb {N} \rightarrow \mathbb {N} }$ but between sets of such functions. These sets are called "mass problems" and can be viewed as problems with more than one solution. Informally, P is Mučnik-reducible to Q when any solution of Q can be used to compute some solution of P.[2]