A construction of free dcpo-cones

IF 0.4 4区计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS

Mathematical Structures in Computer Science Pub Date : 2024-01-10 DOI:10.1017/s0960129523000427

Yuxu Chen, Hui Kou, Zhenchao Lyu, Xiaolin Xie

引用次数: 0

Abstract

We give a construction of the free dcpo-cone over any dcpo. There are two steps for getting this result. Firstly, we extend the notion of power domain to directed spaces which are equivalent to Abstract Image $T_0$ monotone-determined spaces introduced by Erné, and we construct the probabilistic powerspace of the monotone determined space, which is defined as a free monotone determined cone. Secondly, we take D-completion of the free monotone determined cone over the dcpo with its Scott topology. In addition, we show that generally the valuation power domain of any dcpo is not the free dcpo-cone.

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自由圆锥体的构造

我们给出了任意 dcpo 上自由 dcpo 锥体的构造。得到这个结果有两个步骤。首先，我们把幂域的概念扩展到有向空间，有向空间等价于厄内引入的 $T_0$ 单调确定空间，我们构造单调确定空间的概率幂空间，它被定义为自由单调确定锥。其次，我们用斯科特拓扑对 dcpo 上的自由单调确定锥进行 D-补全。此外，我们还证明，一般来说，任何 dcpo 的估值力域都不是自由 dcpo 锥。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Mathematical Structures in Computer Science 工程技术-计算机：理论方法

CiteScore

1.50

自引率

0.00%

发文量

审稿时长

12 months

期刊介绍： Mathematical Structures in Computer Science is a journal of theoretical computer science which focuses on the application of ideas from the structural side of mathematics and mathematical logic to computer science. The journal aims to bridge the gap between theoretical contributions and software design, publishing original papers of a high standard and broad surveys with original perspectives in all areas of computing, provided that ideas or results from logic, algebra, geometry, category theory or other areas of logic and mathematics form a basis for the work. The journal welcomes applications to computing based on the use of specific mathematical structures (e.g. topological and order-theoretic structures) as well as on proof-theoretic notions or results.