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Confluence up to Garbage in Graph Transformation
arXiv - CS - Logic in Computer Science Pub Date : 2021-01-06 , DOI: arxiv-2101.01842
Graham Campbell, Detlef Plump

The transformation of graphs and graph-like structures is ubiquitous in computer science. When a system is described by graph-transformation rules, it is often desirable that the rules are both terminating and confluent so that rule applications in an arbitrary order produce unique resulting graphs. However, there are application scenarios where the rules are not globally confluent but confluent on a subclass of graphs that are of interest. In other words, non-resolvable conflicts can only occur on graphs that are considered as "garbage". In this paper, we introduce the notion of confluence up to garbage and generalise Plump's critical pair lemma for double-pushout graph transformation, providing a sufficient condition for confluence up to garbage by non-garbage critical pair analysis. We apply our results in two case studies about efficient language recognition: we present backtracking-free graph reduction systems which recognise a class of flow diagrams and a class of labelled series-parallel graphs, respectively. Both systems are non-confluent but confluent up to garbage. We also give a critical pair condition for subcommutativity up to garbage which, together with closedness, implies confluence up to garbage even in non-terminating systems.

中文翻译:

图转换中的垃圾融合

图和类图结构的转换在计算机科学中无处不在。当用图变换规则描述系统时,通常希望规则既终止又融合,以便规则应用以任意顺序生成唯一的结果图。但是,在某些应用场景中,规则不是全局融合的,而是融合在感兴趣的图的子类上。换句话说,不可解决的冲突只能在被视为“垃圾”的图上发生。在本文中,我们介绍了汇合到垃圾的概念,并推广了Plump的关键对引理对双推出图的转换,通过非垃圾关键对分析为汇合到垃圾提供了充分的条件。我们将结果应用到有关有效语言识别的两个案例研究中:我们提供了无回溯图缩减系统,它们分别识别一类流程图和一类标记的串并联图。两种系统都不融合,但融合到垃圾中。我们还给出了直至垃圾的子交换性的关键对条件,再加上封闭性,即使在非终止系统中,也暗示了垃圾的汇合。
更新日期:2021-01-07
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