On the Definition of Parallel Independence in the Algebraic Approaches to Graph Transformation
On the Definition of Parallel Independence in the Algebraic Approaches to Graph Transformation
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关于图变换代数方法中并行独立性的定义
DOI：
10.1007/978-3-319-50230-4_8
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发表时间：
2016
期刊：
影响因子：
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通讯作者：
A. Corradini
中科院分区：
文献类型：
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作者：
A. Corradini
变换步骤之间的并行独立性是图变换的代数方法的基本且易于理解的概念，并且通常保证两个步骤可以以任何顺序应用以获得相同的结果图，直到同构。这个概念已经被重新定义为几个代数方法作为一个经典的“代数”条件的变化，要求每个匹配的态射分解通过其他变换步骤的上下文图。然而，看看一些经典的论文双推出的方法，人们发现，原来的平行独立性的定义是制定在集理论方面，要求在主机图的两个左手边的图像的交集包含在两个接口图的交集。这个定义之间的关系和标准的代数一个讨论在这个立场文件中，无论是在左线性和非左线性规则的情况下。
Parallel independence between transformation steps is a basic and well-understood notion of the algebraic approaches to graph transformation, and typically guarantees that the two steps can be applied in any order obtaining the same resulting graph, up to isomorphism. The concept has been redefined for several algebraic approaches as variations of a classical “algebraic” condition, requiring that each matching morphism factorizes through the context graphs of the other transformation step. However, looking at some classical papers on the double-pushout approach, one finds that the original definition of parallel independence was formulated in set-theoretical terms, requiring that the intersection of the images of the two left-hand sides in the host graph is contained in the intersection of the two interface graphs. The relationship between this definition and the standard algebraic one is discussed in this position paper, both in the case of left-linear and non-left-linear rules.