English

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

Logic in Computer Science 2023-05-26 v3

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.

Keywords

Cite

@article{arxiv.2203.01032,
  title  = {Graph Rewriting and Relabeling with PBPO+: A Unifying Theory for Quasitoposes},
  author = {Roy Overbeek and Jörg Endrullis and Aloïs Rosset},
  journal= {arXiv preprint arXiv:2203.01032},
  year   = {2023}
}

Comments

This article significantly extends and improves arXiv:2010.08230. 36 pages