Abstract
We shall show how the kind of graph grammars invented by Göttler [8, 9, 10] can be defined in categorical terms. Derivations can then be carried out in the framework of [6]. This translation enables us to review the definitions which were given with implementations in mind. Furthermore it may suggest a way to add expressive power to the algebraic approach. And, hopefully, some theorems carry over between the algebraic approach and special cases (notably NLC [12, 16] or NCE graph grammars [13]) of the operational graph grammars considered in this paper.
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References
K. Barthelmann. Graphgrammatikalische Hilfsmittel zur Beschreibung verteilter Systeme. Dissertation, IMMD2, Universität Erlangen-Nürnberg, 1990 (to appear).
P. Böhm, H.-R. Fonio, and A. Habel. Amalgamation of graph transformations with applications to synchronization. In TAPSOFT, volume 185, pages 267–283, 1985.
P. Böhm, H.-R. Fonio, and A. Habel. Amalgamation of graph transformations: A synchronization mechanism. Journal of Computer and System Sciences, 34:377–408, 1987.
H. Ehrig. Introduction to the algebraic theory of graph grammars. Lecture Notes in Computer Science, 73:1–69, 1979.
H. Ehrig. Tutorial introduction to the algebraic approach of graph grammars. Lecture Notes in Computer Science, 291:3–14, 1987.
H. Ehrig, M. Pfender, and H.J. Schneider. Graph-grammars: An algebraic approach. In Proc. of the IEEE Conf. on Automata and Switching Theory, Iowa City, pages 167–180, 1973.
H. Ehrig and B. K. Rosen. Parallelism and concurrency of graph manipulations. Theoretical Computer Science, 11:247–275, 1980.
H. Göttler. Zweistufige Graphmanipulationssysteme für die Semantik von Programmiersprachen. Arbeitsbericht (Dissertation) 10, 12, IMMD2, Universität Erlangen-Nürnberg, 1977.
H. Göttler. Semantical description by two-level graph-grammars for quasihierarchical graphs. In Proc. WG78 ‘Graphs, Data Structures, Algorithms'. Hanser-Verlag, 1979.
H. Göttler. Graphgrammatiken in der Softwaretechnik (Theorie und Anwendungen). Springer-Verlag, 1988.
L. Hess and B. H. Mayoh. Graph grammars for knowledge representation. DAIMI PB — 304, Computer Science Department, Aarhus University, 1990.
D. Janssens and G. Rozenberg. On the structure of node-label controlled graph languages and restrictions, extensions and variations of NLC grammars. Information Sciences, 20:191–244, 1980.
D. Janssens and G. Rozenberg. Graph grammars with neighbourhood-controlled embedding. Theoretical Computer Science, 21:55–74, 1982.
M. Nagl. Formale Sprachen von markierten Graphen. Arbeitsbericht (Dissertation) 7, 4, IMMD2, Universität Erlangen-Nürnberg, 1974.
M. Nagl. Graph-Grammatiken (Theorie, Implementierung, Anwendungen). Vieweg-Verlag, 1979. Habilitation.
G. Rozenberg. An introduction to the NLC way of rewriting graphs. Lecture Notes in Computer Science, 291:55–66, 1987.
D. E. Rydeheard and R. M. Burstall. Computational Category Theory. Prentice-Hall, 1988.
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Barthelmann, K. (1991). Describing Göttler's operational graph grammars with pushouts. In: Ehrig, H., Kreowski, HJ., Rozenberg, G. (eds) Graph Grammars and Their Application to Computer Science. Graph Grammars 1990. Lecture Notes in Computer Science, vol 532. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0017384
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DOI: https://doi.org/10.1007/BFb0017384
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