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arXiv · 2203.01032

Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes

Roy Overbeek·Jörg Endrullis·Aloïs Rosset
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Abstract

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.

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Roy Overbeek, Jörg Endrullis, Aloïs Rosset. 2022-03-02. Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes. https://doi.org/10.1016/j.jlamp.2023.100873

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