Abstract
For the definition of parallel rewriting systems on graphs there are two different classes of approaches in literature which we call explicit and implicit in the following. In explicit approaches besides replacement rules governing which graph is to be replaced by which one, connection rules are introduced which define the connections between the inserted graphs. In implicit systems, graph replacement rules have a third component, called connection transformation, which provides for connecting the edges. Common to all parallel rewriting systems is that in any direct derivation step the whole host graph is rewritten. In the following several explicit and implicit approaches are compared with respect to their generative power. This leads to a hierarchy of graph languages generated by parallel graph rewriting systems.
This is a preview of subscription content, log in via an institution.
Preview
Unable to display preview. Download preview PDF.
References
CULIK, K. II/LINDENMAYER, A.: Parallel Rewriting on Graphs and Multidimensional Development, Techn. Report CS-74-22, University of Waterloo, Canada (1974).
CULIK, K. II/LINDENMAYER, A.: Parallel Graph Generating and Graph Recurrence Systems for Multi-dimensional Development, Int. J. General Systems 3, 53–66 (1976).
EHRIG, H./KREOWSKI, H.J.: Parallel Graph Grammars, in/LiRb76/, 425–442 (1976).
EHRIG, H./ROZENBERG, G.: Some Definitional Suggestions for Parallel Graph Grammars, in /LiRb76/, 443–468 (1976).
GRÖTSCH, E.: Vergleichende Studie über parallele Ersetzung markierter Graphen, Arbeitsber. d. Inst. f. Math. Masch. u. Datenverarb. 9, 6, 1–152, University of Erlangen (1976).
GRÖTSCH, E./NAGL, M.: Comparison between Explicit and Implicit Graph L-Systems, Arbeitsber. d. Inst. f. Math. Masch. u. Datenverarb. 10, 8, 5–23, University of Erlangen (1977).
LINDENMAYER, A./ROZENBERG, G. (Eds.): Automata, Languages, Development, Amsterdam: North Holland (1976).
MAYOH, B.H.: Multidimensional Lindenmayer Organisms, Lect. Notes Comp. Sci. 15, 302–326, Berlin: Springer Verlag (1974).
MAYOH, B.H.: Another Model for the Development of Multidimensional Organisms, in /LiRb76/, 469–486 (1976).
NAGL, M.: On a Generalization of Lindenmayer-Systems to Labelled Graphs, in /LiRb76/, 487–508 (1976).
NAGL, M.: Graph Rewriting Systems and their Application in Biology, Lecture Notes in Biomathematics 11, 135–156 (1976).
NAGL, M.: On the Relation between Graph Grammars and Graph L-Systems, Lect. Notes Comp. Sci. 56, 142–151, Berlin: Springer-Verlag (1977).
NAGL, M.: Graph-Ersetzungssysteme: Theorie, Anwendungen, Implementierung, Habilitationsschrift, University of Erlangen (1978).
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1979 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grötsch, E., Nagl, M. (1979). Explicit versus implicit parallel rewriting on graphs. In: Claus, V., Ehrig, H., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science and Biology. Graph Grammars 1978. Lecture Notes in Computer Science, vol 73. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0025724
Download citation
DOI: https://doi.org/10.1007/BFb0025724
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-09525-5
Online ISBN: 978-3-540-35091-0
eBook Packages: Springer Book Archive