Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: volume I. foundations
Handbook of graph grammars and computing by graph transformation: vol. 3: concurrency, parallelism, and distribution
Handbook of graph grammars and computing by graph transformation: vol. 2: applications, languages, and tools
Introduction to the Algebraic Theory of Graph Grammars (A Survey)
Proceedings of the International Workshop on Graph-Grammars and Their Application to Computer Science and Biology
Relabelling in Graph Transformation
ICGT '02 Proceedings of the First International Conference on Graph Transformation
Double-pushout graph transformation revisited
Mathematical Structures in Computer Science
Fundamentals of Algebraic Graph Transformation (Monographs in Theoretical Computer Science. An EATCS Series)
Correctness of high-level transformation systems relative to nested conditions†
Mathematical Structures in Computer Science
The Graph Programming Language GP
CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
On Term Graphs as an Adhesive Category
Electronic Notes in Theoretical Computer Science (ENTCS)
Hereditary pushouts reconsidered
ICGT'10 Proceedings of the 5th international conference on Graph transformations
Adhesivity is not enough: local church-rosser revisited
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Fundamenta Informaticae - Recent Developments in the Theory of Graph Transformation, 2010
A general attribution concept for models in M-adhesive transformation systems
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
A general attribution concept for models in M-adhesive transformation systems
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
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The categorical framework of $\mathcal M$-adhesive transformation systems does not cover graph transformation with relabelling. Rules that relabel nodes are natural for computing with graphs, however, and are commonly used in graph transformation languages. In this paper, we generalise $\mathcal M$-adhesive transformation systems to $\mathcal M,\mathcal N$-adhesive transformation systems, where $\mathcal N$ is a class of morphisms containing the vertical morphisms in double-pushouts. We show that the category of partially labelled graphs is $\mathcal M,\mathcal N$-adhesive, where $\mathcal M$ and $\mathcal N$ are the classes of injective and injective, undefinedness-preserving graph morphisms, respectively. We obtain the Local Church-Rosser Theorem and the Parallelism Theorem for graph transformation with relabelling and application conditions as instances of results which we prove at the abstract level of $\mathcal M,\mathcal N$-adhesive systems.