A hierarchy of probabilistic system types
A hierarchy of probabilistic system types
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DOI：
10.1016/j.tcs.2004.07.019
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发表时间：
2004-10-25
影响因子：
1.1
通讯作者：
de Vink, E
中科院分区：
文献类型：
--
作者：
Bartels, F;Sokolova, A;de Vink, E
我们安排各类的概率系统在文献中研究的表现力层次结构。我们的表现力标准是存在一个系统的翻译，从较少的表达型到更多的表达型，保留和反映概率的双相似性。我们模型的不同系统类型的coalgebras合适的行为函子，并认为相应的coalgebras双相似性与概率双相似性的类，后者的概念已在文献中提出。余代数理论为我们建立层次结构所需的不同类和系统平移的表示提供了一个统一的框架。所有这些平移都以标准的方式从两个行为函子之间的自然变换中产生。这样的翻译一般保持共代数双相似性。我们利用一个新的结果，在温和的假设下的行为函子，一个系统的翻译引起的自然变换与内射组件也反映了双相似性。(C)2004 Elsevier B.V.保留所有权利。
We arrange various classes of probabilistic systems studied in the literature in an expressiveness hierarchy. Our expressiveness criterion is the existence of a system translation, from the less expressive type into the more expressive type, that preserves and reflects probabilistic bisimilarity. We model the different system types as coalgebras of suitable behaviour functors and argue that the corresponding coalgebraic bisimilarity coincides with probabilistic bisimilarity for the classes for which the latter notion has been proposed in the literature. The theory of coalgebras provides a unified framework for the presentation of the different classes and the system translations we needed to establish the hierarchy. All these translations arise in a standard way from natural transformations between the two behaviour functors involved. Such a translation generally preserves coalgebraic bisimilarity. We exploit a new result that, under mild assumptions on the behaviour functors, a system translation induced by a natural transformation with injective components also reflects bisimilarity. (C) 2004 Elsevier B.V. All rights reserved.