Is parallelism already concurrency? Part 1: Derivations in graph grammars

The aim of this paper is to outline the support the theory of graph grammars offers to deal with parallelism and concurrency. The considerations in Part 1 are based on derivations in graph grammars (using a simple, but general framework). Sequentialization and parallelization of derivation steps are studied. From the point of view of concurrency, these constructions induce an equivalence on derivations. It turns out that each equivalence class is uniquely represented by a canonical derivation, which is minimal with respect to a delay index. Part 2 deals with a kind of non-sequential processes in graph grammars (overcoming the sequentiality of derivations).