There is a variety of different approaches to the specification of software systems based on graph rewriting. In order to relate these and other state and/or rules based approaches algebra transformation systems have been introduced. They constitute a semantic domain that is independent of the way in which the rewriting of graphs or algebras is defined (implemented). Composition operations and refinement relations have been defined for algebra transformation systems that yield a comprehensive semantic specification framework in this way. Corresponding notions of rewriting, transformation system, composition and refinement in the different graph rewriting approaches can be compared with these semantic notions to relate them and exhibit their compatibility.
