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On hyperedge replacement and BNLC graph grammars

  • Graph Grammars: Theory And Application
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Graph-Theoretic Concepts in Computer Science (WG 1989)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 411))

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Abstract

It is shown that up to vertex labelling BNLC grammars of bounded nonterminal degree generate the same languages of simple graphs as hyperedge replacement grammars. This does not hold if the vertex labelling is taken into account. Vice versa hyperedge replacement grammars generate the same languages of simple graphs as BNLC grammars of bounded nonterminal degree. Furthermore the generation of loops and multiple edges by hyperedege replacement grammars is discussed.

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References

  1. Arnborg, S.; Corneil, D.G.; Proskurowski, A.: Complexity of Finding Embeddings in a k-Tree. SIAM J. Alg. and Discr. Methods 8 (1987) 277–284

    Google Scholar 

  2. Arnborg, S.; Lagergreen, J.; Seese, D.: Problems Easy for Tree-Decomposable Graphs. In: T.Lepistö et al.(eds.): Automata, Languages and Programming. Proc. 15th ICALP, Tampere, 1988, Springer, Lect. Notes Comp. Sci. 317 (1988) 38–51

    Google Scholar 

  3. Bauderon, M.; Courcelle, B.: Graph Expressions and Graph Rewritings. Math. Systems Theory 20 (1987) 83–127

    Article  Google Scholar 

  4. Claus, V.; Ehrig, H.; Rozenberg, G. (eds.): Graph-Grammars and Their Application to Computer Science and Biology. Springer, 1979, LNCS 73

    Google Scholar 

  5. Courcelle, B.: The Monadic Second-Order Theory of Graphs I: Recognizable Sets of Finite Graphs. To appear in Information and Computation

    Google Scholar 

  6. Courcelle, B.: An Axiomatic Definition of Context-Free Rewriting and its Application to NLC Graph Grammars. Theor. Comp. Sci. 55 (1987)

    Google Scholar 

  7. Ehrenfeucht, A.; Main, M.G.; Rozenberg, G.: Restrictions on NLC Grammars. Theor. Comp. Sci. 31 (1984) 211–223

    Article  Google Scholar 

  8. Ehrig, H.; Nagl, M.; Rozenberg, G. (eds.): Graph Grammars and Their Application to Computer Science. Springer, 1983, Lect. Notes Comp. Sci. 153

    Google Scholar 

  9. Ehrig, H.; Nagl, M.; Rozenberg, G.; Rosenfeld, A. (eds.): Graph-Grammars and Their Application to Computer Science. Springer, 1987, Lect. Notes Comp. Sci. 291

    Google Scholar 

  10. Engelfriet, J.; Leih, G.; Rozenberg, G.: Apex Graph Grammars. In [ENR] 167–185

    Google Scholar 

  11. Engelfriet, J.; Rozenberg, G.: A Comparison of Boundary Graph Grammars and Context-Free Hypergraph Grammars. Dept. of Comp. Sci., Leiden University, 1988

    Google Scholar 

  12. Habel, A.: Hyperedge Replacement: Grammars and Languages. Diss. Uni. Bremen, FB Mathem./Inform., 1988

    Google Scholar 

  13. Habel, A.; Kreowski, H.-J.: Characteristics of Graph Languages Generated by Edge Replacement. Uni. Bremen, FB Mathem./Inform. Report No. 3/85, 1985; also: Theor. Comp. Sci. 51 (1987) 81–115

    Article  Google Scholar 

  14. Habel, A.; Kreowski, H.-J.: Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement. Techn. Report Nr. 12, TU Berlin, Uni. Bremen, 1985; extended Abstract in: F.J. Brandenburg et al. (eds.): STACS '87, Proc. of the 4th Annual Symposium on Theor. Aspects of Comp. Sci., Passau, 1987, Lect. Notes Comp. Sci. 247 (1987) 207–219

    Google Scholar 

  15. Lautemann, C.: Efficient Algorithms on Graphs Represented by Decomposition Trees, Uni. Bremen, FB Mathem./Inform., Bericht 6/87, 1987; also in: M. Dauchet; M. Nivat (eds.): CAAP '88, Lect. Notes Comp. Sci. 299 (1988) 28–39

    Google Scholar 

  16. Lautemann, C.: Efficient Algorithms on Context-Free Languages. In: T. Lepistö et al.(eds.): Automata, Languages and Programming. Proc. 15th ICALP, Tampere, 1988, Springer, Lect. Notes Comp. Sci. 317 (1988) 362–378

    Google Scholar 

  17. Pfaltz, J.; Rosenfeld, A.: Web Grammars. Proc. Int. Joint Conf. Art. Intell. Washington, 1969, 609–619

    Google Scholar 

  18. Robertson, N.; Seymour, P.D.: Graph Minors. II. Algorithmic Aspects of Tree Width. J. Algorithms 7 (1986) 309–322

    Article  Google Scholar 

  19. Rozenberg, G.; Welzl, E.: Boundary NLC Graph Grammars — Basic Definitions, Normal Forms and Complexity. Inf. and Control 69 (1986) 136–167

    Article  Google Scholar 

  20. Rozenberg, G.; Welzl, E.: Combinatorial Properties of Boundary NLC Graph Languages. Discr. Appl. Math. 16 (1987) 59–73

    Article  Google Scholar 

  21. Rozenberg, G.; Welzl, E.: Graph Theoretic Closure Properties of the Family of Boundary NLC Graph Languages. Acta Informatica 23 (1986) 289–309

    Article  Google Scholar 

  22. Schneider, H.J.: Chomsky-Systems for Partial Orderings (in German). Technical Report / MMD-3-3, University of Erlangen, 1970

    Google Scholar 

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Manfred Nagl

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© 1990 Springer-Verlag Berlin Heidelberg

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Vogler, W. (1990). On hyperedge replacement and BNLC graph grammars. In: Nagl, M. (eds) Graph-Theoretic Concepts in Computer Science. WG 1989. Lecture Notes in Computer Science, vol 411. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52292-1_6

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  • DOI: https://doi.org/10.1007/3-540-52292-1_6

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52292-8

  • Online ISBN: 978-3-540-46950-6

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