ON THE ALGEBRAIC STRUCTURE OF WEIHRAUCH DEGREES
ON THE ALGEBRAIC STRUCTURE OF WEIHRAUCH DEGREES
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DOI：
10.23638/lmcs-14(4:4)2018
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发表时间：
2018-01-01
影响因子：
0.6
通讯作者：
Pauly, Arno
中科院分区：
文献类型：
--
作者：
Brattka, Vasco;Pauly, Arno
我们引入了两种关于Wehrauch度的新运算(组合乘积和蕴涵)，并研究了它的整体代数结构。研究了各种分配律的有效性，并为与类似结构如剩余格和并发Kleene代数进行比较奠定了基础。引入关于成分积的理想的概念，我们可以考虑魏劳赫度的适当商。我们还利用蕴涵证明了一些具体的刻画。为了引入和研究合成积和蕴涵，我们引入并研究了一类多值连续函数的函数空间。事实证明，对于与可认可的表示空间密切相关的有效可追踪空间来说，这个空间表现得特别好。
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.