使用PBPO+进行图重写与重新标记：拟拓扑斯的一种统一理论
Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes
AI总结：
本文提出PBPO+方法，通过强匹配增强对模式嵌入的控制，证明其可统一PBPO、AGREE和DPO，并适用于带标签图和属性图的重写。
摘要：
我们扩展了用于图重写的强大的拉回-推出（PBPO）方法，加入了强匹配。我们的方法称为PBPO+，允许对模式在宿主图中的嵌入进行更多控制，这对于一大类重写系统很重要。我们认为，通过证明PBPO+可以定义由PBPO、AGREE和DPO可定义的重写关系的严格超集，PBPO+可以被视为拟拓扑斯一般设定下的一种统一理论。此外，我们通过在标签集上引入格结构并要求图态射保持序，表明PBPO+非常适合重写带标签图和某些类别的属性图。
英文摘要：
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called PBPO+, allows more control over the embedding of the pattern in the host graph, which is important for a large class of rewrite systems. We argue that PBPO+ can be considered a unifying theory in the general setting of quasitoposes, by demonstrating that PBPO+ can define a strict superset of the rewrite relations definable by PBPO, AGREE and DPO. Additionally, we show that PBPO+ is well suited for rewriting labeled graphs and some classes of attributed graphs, by introducing a lattice structure on the label set and requiring graph morphisms to be order-preserving.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
