Algebraic Approaches to Graph Transformation, Part II: Single Pushout Approach and Comparison with Double Pushout Approach

The algebraic approaches to graph transformation are based on the concept of gluing of graphs corresponding to pushouts in suitable categories of graphs and graph morphisms. This allows one to give not only an explicit algebraic or set theoretical description of the constructions but also to use concepts and results from category theory in order to build up a rich theory and to give elegant proofs even in complex situations. In the previous chapter we have presented an overview of the basic notions and problems common to the two algebraic approaches the double pushout DPO approach and the single pushout SPO approach and their solutions in the DPO approach. In this chapter we introduce the SPO approach to graph transformation and some of its main results. We study application conditions for graph productions and the transformation of more general structures than graphs in the SPO approach where similar generalizations have been or could be studied also in the DPO approach. Finally we present a detailed comparison of the DPO and the SPO approach especially concerning the solutions to the problems discussed for both approaches in the previous chapter.