Unfolding and Event Structure Semantics for Graph Grammars

We propose an unfolding semantics for graph transformation systems in the double-pushout (DPO) approach. Mimicking Winskel's construction for Petri nets, a graph grammar is unfolded into an acyclic branching structure, that is itself a (nondeterministic occurrence) graph grammar describing all the possible computations of the original grammar. The unfolding can be abstracted naturally to a prime algebraic domain and then to an event structure semantics. We show that such event structure coincides both with the one defined by Corradini et al. via a comma category construction on the category of concatenable derivation traces, and with the one proposed by Schied, based on a deterministic variant of the DPO approach. This results, besides confirming the appropriateness of our unfolding construction, unify the various event structure semantics for the DPO approach to graph transformation.