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Theory of Constraints and Application Conditions: From Graphs to High-Level Structures

Ehrig H., Ehrig K., Habel A., Pennemann K-H.

Fundamenta Informaticae

2006

Vol. 74, nr 1

135-166

Graph constraints and application conditions are most important for graph grammars and transformation systems in a large variety of application areas. Although different approaches have been presented in the literature already there is no adequate theory up to now which can be applied to different kinds of graphs and high-level structures. In this paper, we introduce a general notion of graph constraints and application conditions and show under what conditions the basic results can be extended from graph transformation to high-level replacement systems. In fact, we use the new framework of adhesive HLR categories recently introduced as combination of HLR systems and adhesive categories. Our main results are the transformation of graph constraints into right application conditions and the transformation from right to left application conditions in this new framework. The transformations are illustrated by a railroad control system with rail net constraints and application conditions.