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Graph transformation formalisms have proven to be suitable tools for the modelling of chemical reactions. They are well established in theoretical studies and increasingly also in practical applications in chemistry. The latter is made…
Sesqui-pushout (SqPO) rewriting is a variant of transformations of graph-like and other types of structures that fit into the framework of adhesive categories where deletion in unknown context may be implemented. We provide the first…
Graph polynomials encode fundamental combinatorial invariants of graphs. Their computation is investigated using tree and path decomposition frameworks, with formal definitions of treewidth, k-trees, and pathwidth establishing the…
Recently, transformer architectures for graphs emerged as an alternative to established techniques for machine learning with graphs, such as (message-passing) graph neural networks. So far, they have shown promising empirical results, e.g.,…
Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a…
Reaction mechanisms are often presented as sequences of elementary steps, such as codified by arrow pushing. We propose an approach for representing such mechanisms using graph transformation. In this framework, each elementary step is a…
In this paper, we study the ideas of composition and decomposition in the context of vector spaces, graphs and matroids. For vector spaces $\V_{AB},$ treated as collection of row vectors, with specified column set $A\uplus B,$ we define…
Sesqui-pushout (SqPO) rewriting along non-linear rules and for monic matches is well-known to permit the modeling of fusing and cloning of vertices and edges, yet to date, no construction of a suitable concurrency theorem was available. The…
Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified…
In this paper, we study how graph transformations based on sesqui-pushout rewriting can be reversed and how the composition of rewrites can be constructed. We illustrate how such reversibility and composition can be used to design an audit…
We extend the notion of compositional associative rewriting as recently studied in the rule algebra framework literature to the setting of rewriting rules with conditions. Our methodology is category-theoretical in nature, where the…
Graph transformation systems have the potential to be realistic models of chemistry, provided a comprehensive collection of reaction rules can be extracted from the body of chemical knowledge. A first key step for rule learning is the…
In this article, we establish a mathematical framework that utilizes concepts from graph theory to formalize the parity transformation, an encoding strategy for compiling optimization problems on quantum devices. We introduce the…
Graph transformation is the rule-based modification of graphs, and is a discipline dating back to the 1970s. The declarative nature of graph rewriting rules comes at a cost. In general, to match the left-hand graph of a fixed rule within a…
We present a new, high-level approach for the specification of model-to-model transformations based on declarative patterns. These are (atomic or composite) constraints on triple graphs declaring the allowed or forbidden relationships…
Many applications of graph transformation require rules that change a graph without introducing new consistency violations. When designing such rules, it is natural to think about the desired outcome state, i.e., the desired effect, rather…
We tackle the problem of attributed graph transformations and propose a new algorithmic approach for defining parallel graph transformations allowing overlaps. We start by introducing some abstract operations over graph structures. Then, we…
Graphs are a natural representation for systems based on relations between connected entities. Combinatorial optimization problems, which arise when considering an objective function related to a process of interest on discrete structures,…
Graph compression is a data analysis technique that consists in the replacement of parts of a graph by more general structural patterns in order to reduce its description length. It notably provides interesting exploration tools for the…
Proposing an effective and flexible matrix to represent a graph is a fundamental challenge that has been explored from multiple perspectives, e.g., filtering in Graph Fourier Transforms. In this work, we develop a novel and general…