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**Set theoretic approaches to graph grammars.**
*(English)*
Zbl 0643.68115

Graph-grammars and their application to computer science, 3rd Int. Workshop, Warrenton/Va. 1986, Lect. Notes Comput. Sci. 291, 41-54 (1987).

[For the entire collection see Zbl 0636.00013.]

This paper sketches the approaches of a certain branch of graph grammars mainly studied at Erlangen, Osnabrück, Koblenz and Aachen, West Germany. It is named set theoretic, or expression, or algorithmic approach of graph grammars, because its mathematical base is elementary set theory, expressions are used to denote embedding transformations, and the question of applicability and implementation always was regarded of equal importance as theoretical results.

The paper gives an introduction to this branch of graph grammars by introducing one representative, sketches the theoretical results, the different modifications introduced for applications, and the various fields of applications already studied. It concludes with an outline how graph grammars can be used f)x(1-x) and the behaviour of the associated S(\(\alpha)\) as \(\epsilon\searrow 0\). Finally we discuss how to apply these ideas to experimental time series and non-hyperbolic attractors.

This paper sketches the approaches of a certain branch of graph grammars mainly studied at Erlangen, Osnabrück, Koblenz and Aachen, West Germany. It is named set theoretic, or expression, or algorithmic approach of graph grammars, because its mathematical base is elementary set theory, expressions are used to denote embedding transformations, and the question of applicability and implementation always was regarded of equal importance as theoretical results.

The paper gives an introduction to this branch of graph grammars by introducing one representative, sketches the theoretical results, the different modifications introduced for applications, and the various fields of applications already studied. It concludes with an outline how graph grammars can be used f)x(1-x) and the behaviour of the associated S(\(\alpha)\) as \(\epsilon\searrow 0\). Finally we discuss how to apply these ideas to experimental time series and non-hyperbolic attractors.

### MSC:

68Q45 | Formal languages and automata |

68R10 | Graph theory (including graph drawing) in computer science |