Graph Grammars with Application Conditions

The algebraic approach of graph grammars is extended by a very general notion of application conditions which can be defined separately for each production. This extended approach is applied to a small library system in order to show the flexibility of this concept for the design of systems in computer science and related areas. In addition to the general concept we study some special cases of graph grammars with application conditions with respect to their generative power. Finally we state some facts how to extend known results in the algebraic theory of graph grammars to the case with application conditions.