Up-to techniques for behavioural metrics via fibrations

IF 0.4 4区 计算机科学 Q4 COMPUTER SCIENCE, THEORY & METHODS Mathematical Structures in Computer Science Pub Date : 2023-04-01 DOI:10.1017/s0960129523000166
Filippo Bonchi, Barbara König, Daniela Petrisan
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引用次数: 2

Abstract

Abstract Up-to techniques are a well-known method for enhancing coinductive proofs of behavioural equivalences. We introduce up-to techniques for behavioural metrics between systems modelled as coalgebras, and we provide abstract results to prove their soundness in a compositional way. In order to obtain a general framework, we need a systematic way to lift functors: we show that the Wasserstein lifting of a functor, introduced in a previous work, corresponds to a change of base in a fibrational sense. This observation enables us to reuse existing results about soundness of up-to techniques in a fibrational setting. We focus on the fibrations of predicates and relations valued in a quantale. To illustrate our approach, we provide an example on distances between regular languages.
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通过振动进行行为度量的最新技术
Up-to技术是一种众所周知的增强行为等价的共归纳证明的方法。我们介绍了行为度量系统之间建模为共代数的最新技术,我们提供了抽象的结果来证明它们在组合方式上的合理性。为了得到一个一般的框架,我们需要一个系统的方法来提升函子:我们证明了在之前的工作中引入的函子的Wasserstein提升,对应于纤维意义上的基的变化。这一观察结果使我们能够重复利用现有的结果,关于在颤振设置的健全技术。我们关注的是量值中谓词和关系的颤动。为了说明我们的方法,我们提供了一个关于常规语言之间距离的示例。
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来源期刊
Mathematical Structures in Computer Science
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
30
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.
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