Graph Rewriting with Contextual Refinement

In the standard theory of graph transformation, a rule modifies only subgraphs of constant size and fixed shape. The rules supported by the graph-rewriting tool GRGEN are far more expressive: they may modify subgraphs of unbounded size and variable shape. Therefore properties like termination and confluence cannot be analyzed as for the standard case. In order to lift such results, we formalize the outstanding feature of GRGEN rules by using plain rules on two levels: schemata are rules with variables; they are refined with meta-rules, which are based on contextual hyperedge replacement, before they are used for rewriting. We show that every rule based on single pushouts, on neighborhood-controlled embedding, or on variable substitution can be modeled by a schema with appropriate meta-rules. It turns out that the question whether schemata may have overlapping refinements is not decidable.