Parallel Independence in Hierarchical Graph Transformation

Hierarchical graph transformation as defined in [1, 2] extends double-pushout graph transformation in the spirit of term rewriting: Graphs are provided with hierarchical structure, and transformation rules are equipped with graph variables. In this paper we analyze conditions under which diverging transformation steps H ⇐ G ⇒ H ′ can be joined by subsequent transformation sequences H ∗ ⇒ M ∗ ⇐ H ′. Conditions for joinability have been found for graph transformation (called parallel independence) and for term rewriting (known as non-critical overlap). Both conditions carry over to hierarchical graph transformation. Moreover, the more general structure of hierarchical graphs and of transformation rules leads to a refined condition, termed fragmented parallel independence, which subsumes both parallel independence and non-critical overlap as special cases.