The computational complexity of certain graph grammars

Abstract

This paper contributes to the theory of graph grammars, studying the generated languages of graphs from the viewpoint of complexity theory. To this respect we naturally bridge the gap between graphs and strings. A string is identified with a graph which is an oriented chain, and conversely, a representation of a graph, e.g., by its adjacency matrix, is a well-structured string. Our main result states that context-free respectively monotone graph grammars in the approach developed by Nagl [5] precisely have the computational power of n²-space-bounded nondeterministic Turing machines, and for this result there is no difference between directed and undirected graphs respectively graph grammars.