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.

[1] It was originally introduced by Klaus Weihrauch in an unpublished 1992 technical report.

[2] A represented space is a pair

, δ )

and a surjective partial function

δ :⊂

δ

δ

be represented spaces and let

be a partial multi-valued function.

is a (possibly partial) function

δ

Intuitively, a realizer

" but it works on names.

be represented spaces and let

be partial multi-valued functions.

is Weihrauch reducible to

, if there are computable partial functions

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.

[citation needed] In other words,

if there are two computable maps

are often called forward and backward functional respectively.

is strongly Weihrauch reducible to

, if the backward functional

does not have access to the original input.

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