Weihrauch reducibility
In computable analysis, Weihrauch reducibility is a notion of reducibility between multi-valued functions on represented spaces that roughly captures the uniform computational strength of computational problems. It was originally introduced by Klaus Weihrauch in an unpublished 1992 technical report.

Definition 

A represented space is a pair  of a set   and a surjective partial function .

Let  be represented spaces and let  be a partial multi-valued function. A realizer for  is a (possibly partial) function  such that, for every , . Intuitively, a realizer  for  behaves "just like " but it works on names. If  is a realizer for  we write .

Let  be represented spaces and let  be partial multi-valued functions. We say that  is Weihrauch reducible to , and write , if there are computable partial functions  such thatwhere  and  denotes the join in the Baire space. Very often, in the literature we find  written as a binary function, so to avoid the use of the join. In other words,  if there are two computable maps  such that the function  is a realizer for  whenever  is a solution for . The maps  are often called forward and backward functional respectively.

We say that  is strongly Weihrauch reducible to , and write , if the backward functional  does not have access to the original input. In symbols:

See also 
 Wadge reducibility

References 

Computable analysis