Graph Rewriting and Relabeling with PBPO+ (Extended Version)
release_y6ycrfwvive2xaclphaidfi45y
by
Roy Overbeek, Jörg Endrullis
2020
Abstract
We extend the powerful Pullback-Pushout (PBPO) approach for graph rewriting
with strong matching. Our approach, called PBPO+, exerts more control over the
embedding of the pattern in the host graph, which is important for a large
class of graph rewrite systems.
We show that PBPO+ 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 graph morphisms that respect the partial order on the
labels. We argue that our approach is both simpler and more general than
related approaches in the literature.
Finally, we demonstrate that PBPO+ allows for an elegant modeling of linear
term rewriting systems, such as string rewriting systems. This modeling
preserves termination as a global system property without having to restrict
the shape of the graphs.
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