TY - GEN

T1 - M,N-Adhesive Transformation Systems

AU - Habel, Annegret

AU - Plump, Detlef

PY - 2012

Y1 - 2012

N2 - The categorical framework of 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 M-adhesive transformation systems to M,N-adhesive transformation systems, where N is a class of morphisms containing the vertical morphisms in double-pushouts. We show that the category of partially labelled graphs is M,N-adhesive, where M and 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 M,N-adhesive systems.

AB - The categorical framework of 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 M-adhesive transformation systems to M,N-adhesive transformation systems, where N is a class of morphisms containing the vertical morphisms in double-pushouts. We show that the category of partially labelled graphs is M,N-adhesive, where M and 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 M,N-adhesive systems.

UR - http://www.cs.york.ac.uk/plasma/publications/pdf/HabelPlump.12a.pdf

U2 - 10.1007/978-3-642-33654-6_15

DO - 10.1007/978-3-642-33654-6_15

M3 - Conference contribution

SN - 978-3-642-33653-9

T3 - Lecture Notes in Computer Science

SP - 218

EP - 233

BT - Proc. 6th International Conference on Graph Transformations

A2 - Ehrig, Hartmut

A2 - Engels, Gregor

A2 - Kreowski, Hans-Joerg

A2 - Rozenberg, Grzegorz

PB - Springer

ER -