Embedding theorems in the algebraic theory of graph grammars

  • Hartmut Ehrig
Section B Computation Theory in Category
Part of the Lecture Notes in Computer Science book series (LNCS, volume 56)


In the first section we start with an overview of basic constructions and results in the algebraic theory of graph grammars. The rest of the paper is devoted to two embedding theorems for graph grammars which are most important for several applications and implementation purposes: Locally defined derivation sequences can be extended to global ones provided that the embedding of the start graph of the local derivation is noncritical in a specific sense. This is shown for two different types of embeddings.


Implementation Purpose Colored Graph Algebraic Theory Graph Grammar Embed Theorem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /EK 76a/.
    Ehrig, H., Kreowski, H.-J.: Categorical Approach to Graphic Systems and Graph Grammars, Conf. Report Algebraic System Theory, Udine 1975, Springer Lect. Notes in Econ. Math. Syst. 131 (1976), 323–351Google Scholar
  2. /EK 76b/.
    Ehrig, H., Kreowski, H.-J.: Parallelism of Manipulations in Multidimensional Information Structures, Proc. Conf. Math. Foundations of Comp. Sci., Gdansk 1976, Springer Lect. Notes in Comp. Sci. 45 (1976), 284–293Google Scholar
  3. /EK76c/.
    Ehrig, H., Kreowski, H.-J.: Contributions to the Algebraic Theory of Graph Grammars, Forschungsbericht FB 20, TU Berlin, 76–22Google Scholar
  4. /EPS 73/.
    Ehrig, H., Pfender, M., Schneider, H.J.: GRAPH GRAMMARS: An Algebraic Approach, Proc. IEEE Conf. on Automata and Switching Theory, Iowa City 1973, 167–180Google Scholar
  5. /ER 76/.
    Ehrig, H., Rosen, B.K.: Commutativity of Independent Transformations on Complex Objects, IBM Research Report, RC 6251, Oct 1976Google Scholar
  6. /ER 77a/.
    Ehrig, H., Rosen, B.K.: The Mathematics of Record Handling, Proc. Conf. 4th ICALP, Turku 1977Google Scholar
  7. /ER 77b/.
    Ehrig, H., Rosen, B.K.: Rapid Evaluation of Recursively Defined Functions: An Application of Algebraic Graph Theory (in preparation)Google Scholar
  8. /ET 75a/.
    Ehrig, H., Tischer, K.W.: Graph Grammars and Applications to Specialization and Evolution in Biology, in Journ. Comp. Syst. Sci., vol 11, No 2 (1975), 212–236, also in Forschungsbericht FB 20, TU Berlin, 74–31Google Scholar
  9. /ET 75b/.
    Ehrig, H., Tischer, K.W.: Derivations of Stochastic Graphs, Proceedings Conference on Uniformly Structured Automata Theory and Logic, Tokyo 1975, 1–6Google Scholar
  10. /FG 74/.
    Furtado, A.L., Gotlieb, C.D.: Data Schemata Based on Directed Graphs, Techn. Report No 70, Dept. Comp. Sci., University of Toronto, 1974Google Scholar
  11. /FKZ 76/.
    Farrow, R., Kennedy, K., Zucconi, L.: Graph Grammars and Global Program Data Flow Analysis, Proc. 17th Ann. IEEE Symp. on Foundations of Comp. Sci., Houston, 1976Google Scholar
  12. /Fr 75/.
    Franck, R.: PLAN2D — Syntaxanalyse von Präzedenz-Graph-Grammatiken, Dissertation, Techn. Universität Berlin, FB 20, 1975Google Scholar
  13. /Gr 68/.
    Griffiths, T.V.: Some Remarks on Derivations in General Rewriting Systems, Information and Control 12, 1968, 27–54Google Scholar
  14. /LR 76/.
    Lindenmayer, A., Rozenberg, G. (Editors): Automata, Languages, Development, North-Holland, Amsterdam 1976Google Scholar
  15. /Kr 77/.
    Kreowski, H.-J.: Transformations of Derivation Sequences in Graph Grammars, this volumeGoogle Scholar
  16. /Ro 73/.
    Rosen, B.K.: Tree-Manipulating Systems and Church-Rosser Theorems, Journ. ACM 20, 1, 1973, 160–187Google Scholar
  17. /Ro 75a/.
    Rosen, B.K.: A Church-Rosser Theorem for Graph Grammars (announcement), SIGACT News 7, 3, 1975, 26–31Google Scholar
  18. /Ro 75b/.
    Rosen, B.K.: Deriving Graphs from Graphs by Applying a Production, Acta Informatica 4, 1975, 337–357Google Scholar
  19. /Sch 74/.
    Schneider, H.J.: Syntax-Directed Description of Incremental Compilers, Springer Lect. Notes in Comp. Sci. 26, 1974, 192–201Google Scholar
  20. /Sch 76/.
    Schneider, H.J.: Conceptual Data Base Description Using Graph Grammars, erscheint in: Proc. Workshop "Graphentheoretische Konzepte in der Informatik", Göttingen, 1976Google Scholar
  21. /SE 76/.
    Schneider, H.J., Ehrig, H.: Grammars on Partial Graphs, Acta Informatica 6, 297–316 (1976), also in Arbeitsberichte Inst. Math. Masch. Datenverarbeitung (Univ. Erlangen-Nürnberg) Bd. 8 (1975) Nr. 1, 64–91Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Hartmut Ehrig
    • 1
  1. 1.Fachbereich InformatikTechnische Universität Berlin1 Berlin 10

Personalised recommendations