Double-pushout rewriting is an established categorical approach to the rule-based transformation of graphs and graph-like objects. One of its standard results is the construction of concurrent rules and the Concurrency Theorem pertaining to it: The sequential application of two rules can equivalently be replaced by the application of a concurrent rule and vice versa. We extend and generalize this result by introducing generalized concurrent rules (GCRs). Their distinguishing property is that they allow identifying and preserving elements that are deleted by their first underlying rule and created by the second one. We position this new kind of composition of rules among the existing ones and obtain a Generalized Concurrency Theorem for it. We conduct our work in the same generic framework in which the Concurrency Theorem has been presented, namely double-pushout rewriting in M-adhesive categories via rules equipped with application conditions.

中文翻译：

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双推出重写的通用并发规则构造

双推出重写是一种成熟的分类方法，用于基于规则的图形和类似图形的对象转换。它的标准结果之一是并发规则的构建以及与之相关的并发性定理：两个规则的顺序应用可以等效地由并发规则的应用来替代，反之亦然。我们通过引入广义并发规则（GCR）扩展和推广此结果。它们的显着特性是，它们允许标识和保留被第一个基础规则删除并由第二个基础规则创建的元素。我们将这种新型的规则组合放置在现有规则中，并为其获得广义并发定理。我们在提出并发定理的通用框架中进行工作，