Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes
arXiv:2203.01032 · doi:10.1016/j.jlamp.2023.100873
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.
This article significantly extends and improves arXiv:2010.08230. 36 pages