一句话：在 Weihrauch 度上引入复合乘积与蕴涵，系统刻画其代数结构、分配律、理想与商。
本文研究 Weihrauch 度的代数结构。作者在 Weihrauch 度上引入两种新运算：复合乘积与蕴涵，并考察由此构成的整体代数结构。文中系统检验各类分配律是否成立，以此与剩余格、并发 Kleene 代数等已知结构进行比较。通过定义关于复合乘积的理想，作者得到 Weihrauch 度的合适商结构，并利用蕴涵证明若干具体刻画。为引入和研究这些运算，论文还定义并研究多值连续函数的函数空间；该空间对于与可容许表示空间密切相关的有效可追踪空间表现出良好性质。
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.
@article{paperbot367,
title = {On the algebraic structure of Weihrauch degrees},
author = {Vasco Brattka and Arno Pauly},
journal = {Logical Methods in Computer Science},
volume = {Volume 14, Issue 4},
number = {Computability and logic},
year = {2018},
doi = {10.23638/lmcs-14(4:4)2018}
}