Mučnik reducibility

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

Unlike most reducibility relations in computability, Mučnik reducibility is not defined between functions $$\mathbb{N} \rarr \mathbb{N}$$ 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.