Double-Pushout Approach with Injective Matching

We investigate and compare four variants of the doublepushout approach to graph transformation. Besides the traditional approach with arbitrary matching and injective right-hand morphisms, we consider three variations by employing injective matching and/or arbitrary right-hand morphisms in rules. For each of the three variations, we clarify whether the well-known commutativity theorems are still valid and–where this is not the case–give modified results. In particular, for the most general approach with injective matching and arbitrary righthand morphisms, we establish sequential and parallel commutativity by appropriately strengthening sequential and parallel independence. We also show that injective matching provides additional expressiveness in two respects, viz. for generating graph languages by grammars without nonterminals and for computing graph functions by convergent graph transformation systems.