DPO transformation with open maps

Authors:
Reiko Heckel
Affiliations:
Department of Computer Science, University of Leicester, UK
Venue:
ICGT'12 Proceedings of the 6th international conference on Graph Transformations
Year:
2012

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Abstract

In graph transformation, a match just represents an occurrences of a rule's left-hand side in the host graph. This is expressed by a morphism preserving the graph structure. However, there are situations where occurrences are bound by additional constraints. These can either be implicit, such as the gluing conditions of the DPO, or explicit such as negative application conditions. In this paper we study another type of implicit condition based on the reflection of structure. Morphisms reflecting some of the structures of their targets are abstractly characterised as open maps in the sense of Joyal, Nielsen, and Winskel. We show that under certain restrictions on the rules, DPOs preserve open maps. We establish an encoding of open maps into negative application conditions and study concurrency properties of the new approach.