Graph rewriting and relabeling with PBPO+: A unifying theory for quasitoposes

Roy Overbeek; Jörg Endrullis; Aloïs Rosset

doi:10.1016/j.jlamp.2023.100873

Graph rewriting and relabeling with PBPO⁺: A unifying theory for quasitoposes

Roy Overbeek^*
, Jörg Endrullis
, Aloïs Rosset

^*Corresponding author for this work

Research output: Contribution to Journal › Article › Academic › peer-review

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.

Original language	English
Article number	100873
Pages (from-to)	1-25
Number of pages	25
Journal	Journal of Logical and Algebraic Methods in Programming
Volume	133
Early online date	6 Apr 2023
DOIs	https://doi.org/10.1016/j.jlamp.2023.100873
Publication status	Published - Jun 2023

Bibliographical note

Funding Information:
The authors received funding from the Netherlands Organisation for Scientific Research (NWO) under the Innovational Research Incentives Scheme Vidi (project. No. VI.Vidi.192.004 ).

Publisher Copyright:
© 2023 The Authors

Funding

The authors received funding from the Netherlands Organisation for Scientific Research (NWO) under the Innovational Research Incentives Scheme Vidi (project. No. VI.Vidi.192.004 ).

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10.1016/j.jlamp.2023.100873

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Cite this

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title = "Graph rewriting and relabeling with PBPO+: A unifying theory for quasitoposes",

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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