Skip to main content
SpringerLink
Log in

On the generative power of sequential and parallel programmed graph grammars

Zur generativen Mächtigkeit von sequentiellen und parallelen programmierten Graph-Grammatiken

  • Published:
Computing Aims and scope Submit manuscript

Abstract

Programmed graph grammars are formally introduced and their generative power is investigated. Programmed graph grammars differ from other approaches to graph grammars in the so-called control diagram which controls the application order of productions. Restricting the form of the productions of a programmed graph grammar we get several classes of graph languages. These are compared mutually as well as with the hierarchy introduced by Nagl [18]. For unrestricted and monotone productions corresponding classes of graph languages coincide, while the class of context free programmed graph languages is properly contained in the class of context free graph languages in the sense of [18].

Zusammenfassung

Programmierte Graph-Grammatiken werden formal definiert und bezüglich ihrer generativen Mächtigkeit untersucht. Programmierte Graph-Grammatiken unterscheiden sich von anderen Graph-Grammatik-Ansätzen durch das sogenannte Kontrolldiagramm, welches die Reihenfolge steuert, in der Produktionen angewendet werden. Durch Einschränkung der Gestalt der Produktionen erhält man verschiedene Klassen von Graph-Sprachen. Diese werden untereinander sowie mit der von Nagl [18] eingeführten Hierarchie verglichen. Im Falle von uneingeschränkten und monotonen Produktionen fallen einander entsprechende Klassen von Graph-Sprachen zusammen, während die Klasse der kontextfreien programmierten Graph-Sprachen echt enthalten ist in der Klasse der kontextfreien Graph-Sprachen nach [18].

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bartini, C.: Rewriting systems as a tool for relational data base design. Lect. Notes Comp. Sci.73, 139–154 (1979).

    Google Scholar 

  2. Brendel, W., Bunke, H., Nagl, M.: Syntaxgesteuerte Programmierung und inkrementelle Compilation. Informatik-Fachberichte10, 57–74 (1977).

    Google Scholar 

  3. Bunke, H.: Sequentielle und parallele Graph-Grammatiken. Arbeitsbericht des IMMD Erlangen12, 3 (1979).

    Google Scholar 

  4. Culik, K., II, Lindenmayer, A.: Parallel rewriting on graphs and multidimensional development. Int. Journ. of Gen. Syst.3, 53–66 (1976).

    Google Scholar 

  5. Denert, E., Franck, R., Streng, W.: PLAN2D-Toward a twodimensional programming language. Lect. Notes Comp. Sci.26, 202–213 (1975).

    Google Scholar 

  6. Della Vigna, P., Ghezzi, C.: Context-free graph grammars. Inf. Contr.37, 207–233 (1978).

    Google Scholar 

  7. Ehrig, H.: Embedding theorems in the algebraic theory of graph-grammars. Lect. Notes Comp. Sci.56, 245–255 (1977).

    Google Scholar 

  8. Ehrig, H.: Introduction to the algebraic theory of graph grammars. Lect. Notes Comp. Sci.73, 1–69 (1979).

    Google Scholar 

  9. Ehrig, H., Kreowski, H.-J.: Parallel graph grammars, in: Automata, Languages, Development (Lindenmayer, A., Rozenberg, G., eds.), pp. 425–442. Amsterdam: North-Holland 1976.

    Google Scholar 

  10. Ehrig, H., Pfender, H., Schneider, H.J.: Graph grammars: an algebraic approach. Proc., 14th Annual Conf. Switching a. Automata Theory, pp. 167–180 (1973).

  11. Furtado, A. L.: Transformation of data base structures. Lect. Notes Comp. Sci.73, 224–236 (1979).

    Google Scholar 

  12. Göttler, H.: Semantical description by two-level graph-grammars for quasihierarchical graphs. Applied Comp. Sci.13, 207–226 (1979).

    Google Scholar 

  13. Grötsch, E., Nagl, M.: Explicit versus implicit parallel rewriting on graphs. Lect. Notes Comp. Sci.73, 237–254 (1979).

    Google Scholar 

  14. Kreowski, H.-J.: A pumping lemma for context-free graph languages. Lect. Notes Comp. Sci.73, 270–283 (1979).

    Google Scholar 

  15. Levy, L. S., Yueh, K.: On labelled graph grammars. Computing20, 109–125 (1978).

    Google Scholar 

  16. Montanari, U. G.: Separable graphs, planar graphs and web grammars. Inf. Contr.16, 243–267 (1970).

    Google Scholar 

  17. Nagl, M.: On the relation between graph grammars and graph Lindenmayer-systems. Lect. Notes Comp. Sci.56, 142–151 (1977).

    Google Scholar 

  18. Nagl, M.: Formal languages of labelled graphs. Computing16, 113–137 (1976).

    Google Scholar 

  19. Nagl, M.: A tutorial and bibliographical survey on graph grammars. Lect. Notes Comp. Sci.73, 70–126 (1979).

    Google Scholar 

  20. Nagl, M.: Graph-Grammatiken: Theorie, Anwendungen, Implementierung. Wiesbaden: Vieweg-Verlag 1979.

    Google Scholar 

  21. Pavlidis, T.: Linear and context-free graph-grammars. JACM19, 11–23 (1972).

    Google Scholar 

  22. Pfaltz, J. L., Rosenfeld, A.: Web grammars. Proc. 1 st Int. Joint Conf. Art. Intell., Washington, 609–619 (1969).

  23. Pratt, T.: Pair graphs, graph languages and string-to-graph translations. Journ. Comp. Syst. Sci.5, 560–595 (1971).

    Google Scholar 

  24. Rosenfeld, A.: Isotonic grammars, parallel grammars, and picture grammars. Mach. Intell.6, 281–294 (1971).

    Google Scholar 

  25. Rosenkrantz, D. J.: Programmed grammars and classes of formal languages. JACM16, 107–131 (1969).

    Google Scholar 

  26. Schneider, H. J.: A necessary and sufficient condition for Chomsky-productions over partially ordered symbol sets. Lect. Notes in Econ. and Math. Syst.78, 90–98 (1972).

    Google Scholar 

  27. Schneider, H. J.: Conceptual data base description using graph grammars. Applied Comp. Sci.13, 77–98 (1979).

    Google Scholar 

  28. Schneider, H. J.: Graph grammars. Lect. Notes Comp. Sci.56, 314–331 (1977).

    Google Scholar 

  29. Schneider, H. J., Ehrig, H.: Grammars on partial graphs. Acta Informatica6, 297–316 (1976).

    Google Scholar 

  30. Timmesfeld, K. H., et al.: PEARL — a proposal for a process- and experiment automation realtime language. Tech. Report KFK-PDV 1, Gesellschaft für Kernforschung, Karlsruhe, 1973.

    Google Scholar 

  31. Uesu, T.: A system of graph grammars which generates all recursively enumerable sets of labelled graphs. Tsukuba Journ. Math.2, 11–26 (1978).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Lehrstuhl für Informatik 5 (Mustererkennung), IMMD, Universität Erlangen-Nürnberg, Martensstrasse 3, D-8520, Erlangen, Federal Republic of Germany

    H. Bunke

Authors
  1. H. Bunke
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bunke, H. On the generative power of sequential and parallel programmed graph grammars. Computing 29, 89–112 (1982). https://doi.org/10.1007/BF02249935

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02249935

AMS Subject Classifications

Key words

Search

Navigation