# On the relation between graph grammars and graph L-systems

## Abstract

Sequential graph rewriting systems called graph or web grammars have been extensively studied within the last years, while parallel graph rewriting systems, named graph L-systems, are a very recent topic of research. In the following a relation between two representatives of these graph rewriting models is given: [CF]=[PEGL], where [CF] is the class of context free graph languages in [12], and [PEGL] is the class of propagating extended graph L-languages given in [13]. The validity of this relation in the graph case, opposite to the string case, is due to the fact that graphs derived in both rewriting systems have nonterminal edges. These edges may occur in the derivation of a graph belonging to the language of such a system, but not in the graph itself. Furthermore, the sequential mechanism is very powerful with respect to the transformation of the embeddings of the replaced graphs, and the parallel mechanism is very general with respect to the transformation of the connections from mother nodes to daughter graphs. These tools allow to simulate a sequential derivation step by two parallel ones and, vice versa, to simulate a parallel derivation step by a sequence of sequential steps.

## Keywords

Edge Label Node Label Derivation Step Graph Grammar Connection Structure## Preview

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