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On context-free graph languages generated by edge replacement

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Graph-Grammars and Their Application to Computer Science (Graph Grammars 1982)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 153))

Abstract

Edge replacement systems provide a simple mechanism to generate graph languages. They generalize context-free (string) grammars to the case of graphs. This paper summarizes some recent results on graph languages generated by edge replacement. Especially, we show that our languages are fixed points of their productions (considered as equations) and that they can be generated by language operations (substitution and iteration) from finite graph languages.

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References

  1. Bird, R.: Programs and Machines, Wiley, New York (1976).

    Google Scholar 

  2. Claus, V., Ehrig, H., Rozenberg, G. (eds.): Graph-Grammars and their Application to Computer Science and Biology, Lect. Not. Comp. Sci.73 (1979)

    Google Scholar 

  3. Della Vigna, P., Ghezzi, C.: Context-free Graph Grammars, Inf.Contr. 37, 207–233 (1978)

    Google Scholar 

  4. Ehrig, H.: Introduction to the Algebraic Theory of Graph Grammars, Lect. Not. Comp. Sci. 73 (1979), 1–69

    Google Scholar 

  5. Farrow, R., Kennedy, K., Zucconi, L.: Graph Grammars and Global Program Data Flow Analysis; Proc. 17th Ann. Symp. on Found. of Comp. Sci., Houston (1976)

    Google Scholar 

  6. Ginsburg, S., Rice, G.: Two Families of Languages Related to ALGOL, Journ. ACM, vol. 9, 350–371 (1962)

    Google Scholar 

  7. Gruska, J.: A Characterization of Context-free Languages, Journ. Comp. Syst. Sci. 5, 353–364 (1971)

    Google Scholar 

  8. Janssens, D., Rozenberg, G.: On the structure of node-label-controlled graph grammars; Information Science 20, 191–216 (1980)

    Google Scholar 

  9. Kaul, M.: Private Communication, 1982

    Google Scholar 

  10. Kleene, S.C.: Introduction to Meta Mathematics, D. Von Nostrand, Inc., Princeton, N.J. (1952)

    Google Scholar 

  11. Kreowski, H.-J.: Manipulationen von Graphmanipulationen, Ph.D.Thesis, Techn. Univ. Berlin, Comp. Sci. Dept., 1977 (short version in LNCS 56 (1977), 275–286)

    Google Scholar 

  12. -: A Pumping Lemma for Context-free Graph Languages, Lect. Not. Comp. Sci. 73, (1979), 270–283

    Google Scholar 

  13. Manna, Z.: Mathematical Theory of Computation; McGraw-Hill, New York (1974)

    Google Scholar 

  14. Nagl, M.: A Tutorial and Bibliographical Survey on Graph Grammars, Lect. Not. Comp. Sci. 73 (1979), 70–126

    Google Scholar 

  15. Woods, W.A.: Transition Network Grammars for Natural Language Analysis, Comm. of the ACM 1970, 13(10), 591–606

    Google Scholar 

  16. Yntema, M.K.: Cap Expressions for Context-Free Languages, Inf. Contr. 18 (1971), 311–318

    Google Scholar 

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Hartmut Ehrig Manfred Nagl Grzegorz Rozenberg

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© 1983 Springer-Verlag Berlin Heidelberg

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Habel, A., Kreowski, H.J. (1983). On context-free graph languages generated by edge replacement. In: Ehrig, H., Nagl, M., Rozenberg, G. (eds) Graph-Grammars and Their Application to Computer Science. Graph Grammars 1982. Lecture Notes in Computer Science, vol 153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0000104

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  • DOI: https://doi.org/10.1007/BFb0000104

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12310-1

  • Online ISBN: 978-3-540-39897-4

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