Brattka, Vasco and Pauly, Arno - On the algebraic structure of Weihrauch degrees

lmcs:3854 - Logical Methods in Computer Science, October 25, 2018, Volume 14, Issue 4
On the algebraic structure of Weihrauch degrees

Authors: Brattka, Vasco and Pauly, Arno

We introduce two new operations (compositional products and implication) on Weihrauch degrees, and investigate the overall algebraic structure. The validity of the various distributivity laws is studied and forms the basis for a comparison with similar structures such as residuated lattices and concurrent Kleene algebras. Introducing the notion of an ideal with respect to the compositional product, we can consider suitable quotients of the Weihrauch degrees. We also prove some specific characterizations using the implication. In order to introduce and study compositional products and implications, we introduce and study a function space of multi-valued continuous functions. This space turns out to be particularly well-behaved for effectively traceable spaces that are closely related to admissibly represented spaces.


Source : oai:arXiv.org:1604.08348
DOI : 10.23638/LMCS-14(4:4)2018
Volume: Volume 14, Issue 4
Section: Computability and logic
Published on: October 25, 2018
Submitted on: August 10, 2017
Keywords: Computer Science - Logic in Computer Science,Mathematics - Logic


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