Explicit versus implicit parallel rewriting on graphs

Abstract

For the definition of parallel rewriting systems on graphs there are two different classes of approaches in literature which we call explicit and implicit in the following. In explicit approaches besides replacement rules governing which graph is to be replaced by which one, connection rules are introduced which define the connections between the inserted graphs. In implicit systems, graph replacement rules have a third component, called connection transformation, which provides for connecting the edges. Common to all parallel rewriting systems is that in any direct derivation step the whole host graph is rewritten. In the following several explicit and implicit approaches are compared with respect to their generative power. This leads to a hierarchy of graph languages generated by parallel graph rewriting systems.