Algebraic Approach to Single-Pushout Graph Transformation

The single-pushout approach to graph transformation interprets a double-pushout transformation rule of the classical algebraic approach which consists of two rotul graph morphisms as a single particll morphism from the left-to the right-hand side. The notion of a double-pushout diagram for the transformation process can then be substituted by a single-pushout diagram in an appropriate category of partial morphisms. It can be shown that this kind of transformation generalizes the double-pushout framework. Hence. the classical approach can be seen as a special (and very important) case of the new concept. It can be reobtained from the single-pushout approach by imposing an application condition on the redices which formulates the gluing conditions in the new setting. On the other hand, single-pushout transformations are always possible even if the gluing conditions for the redex are violated. The simpler structure of a direct transformation (one pushout diagram instead of two) simplifies many proofs. Hence, the whole theory for double-pushout transformations including sequential composition, parallel composition, and amalgamation can be reformulated and generalized in the new framework. Some constructions provide new effects and properties which are discussed in detail.