Graph Rewriting and Relabeling with PBPO+

TL;DR

This paper introduces extbackslash pbpostrong, an extension of the PBPO approach for graph rewriting that offers enhanced control over pattern embedding, especially for labeled and attributed graphs, using lattice structures and order-preserving morphisms.

Contribution

The paper presents extbackslash pbpostrong, a novel graph rewriting method that improves control and generality over pattern embedding compared to existing relabeling techniques.

Findings

extbackslash pbpostrong effectively handles labeled and attributed graphs.

The approach is simpler and more general than existing relabeling methods.

It employs lattice structures and order-preserving morphisms for enhanced control.

Abstract

We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting with strong matching. Our approach, called \pbpostrong, exerts more control over the embedding of the pattern in the host graph, which is important for a large class of graph rewrite systems. In addition, we show that \pbpostrong is well-suited for rewriting labeled graphs and certain classes of attributed graphs. For this purpose, we employ a lattice structure on the label set and use order-preserving graph morphisms. We argue that our approach is simpler and more general than related relabeling approaches in the literature.