** Dominique Duval
**

** Algebraic graph rewriting
**

Graphs are used to describe a wide range of situations.
When system states are represented by graphs, it is
natural to use rules that transform graphs to describe the system evolution.
The algebraic approaches to graph transformation are based on the fact that
the categorical notions of pushout and pullback provide a good
description of the simplest transformations.
Then the challenge is to generalize them in a proper way for expressing
a diversity of transformations on a diversity of graphs.
The algebraic approaches to graph transformation include
the *double-pushout* (DPO), the *single-pushout* (SPO),
the *sesqui-pushout* (SqPO),
which subsumes the DPO and SPO in most situations,
as well as the *double-pullback* (DPB).

In 2014 we extended the SqPO approach to *attributed* graphs,
which play an important role in model-driven design and programming.
In 2015 we proposed the AGREE approach
(for *Algebraic Graph Rewriting with controllEd Embedding*),
which can simulate the SqPO rewriting and which allows non-local
transformations.
In 2016 we went one step further in understanding how pushout-based and
pullback-based algebraic approaches may collaborate.
In 2018 we introduced a new categorical condition of parallel independence
and we proved its equivalence with two other conditions proposed in the
literature.

See my Publications with Andrea Corradini, Michael Löwe, Rachid Echahed, Frédéric Prost and Leila Ribeiro and the references in these papers.