偶图及其应用研究综述

Survey on Bigraph and Its Applications

偶图是由Robin Milner在2001年提出的一种基于图形的形式化理论模型,试图为普适计算提供一个设计、模拟和分析的平台以及为现有的进程代数提供一个统一的可扩展的框架.介绍了偶图的基本概念,揭示了偶图的数学基础——预范畴、范畴、s-范畴、对称偏幺半范畴之间的关系,对偶图的代数系统进行总结,简化了偶图的离散范式的表述形式,并给予证明.综述了偶图的发展及其应用概况.对偶图范畴的定义、商变换等基本理论中存在的一些问题提出讨论,指出偶图范畴应该属于小范畴而不是大范畴,并给出商变换得出的大范畴转换为小范畴的方法.最后简述了偶图模型的扩展、应用的拓广.

Bigraph was proposed by Robin Milner in 2001 as a formal theoretical model based on graphs in attempt to provide a design, simulation and analysis platform for ubiquitous computing and present a unified, extensible framework for the existing process algebra. In this paper first introduces the basic concepts of bigraph and reveals relationships among precategory, category, s-category and symmetric partial monoidal category which form the mathematical basis of bigraph, and then summarizes bigraphical algebra system while providing a simplified representation of the discrete normal form in bigraph with a proof. Next, it discusses some questions related to the definition of bigraphical categories and quotient translations after making a survey of the development of bigraph and its applications. This study argues that bigraphical category should be small category other than large category. Moreover, the paper illustrates how to convert the large category derived by quotient to small category. Finally, it outlines the extensions of bigraphical models and their applications.