In computability theory, a set P of functions ℕ → ℕ is said to be Mučnik-reducible to another set Q of functions ℕ → 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 ℕ → 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]
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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