Advertisement

On polynomial time graph grammars

  • Franz J. Brandenburg
Contributed Papers Graph Grammars
Part of the Lecture Notes in Computer Science book series (LNCS, volume 294)

Abstract

The complexity of node rewriting graph grammars is investigated, i.e. the membership problem for sets of graphs L(G) generated by directed, node and edge label controlled graph grammars G. We improve known results on the membership problem and comprise them into the following sharp characterization of the P vs. NP borderline, which is an "if and only if" result.

∀G: (fCR ∧ connected ∧ bounded degree) then L(G) is in P.

∃G: not (fCR ∧ connected ∧ bounded degree) and L(G) is NP hard.

Here, fCR means that the graph grammar G has the finite Church Rosser property, and connected and bounded degree means that the graphs in the generated language L(G) are connected and of bounded degree.

Keywords

Polynomial Time Edge Label Node Label Derivation Tree Graph Grammar 
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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    IJ.J. Aalbersberg, A. Ehrenfeucht and G. Rozenberg, "On the membership problem for regular DNLC grammars". Discrete Applied Mathematics 13 (1986), 79–85.Google Scholar
  2. [2]
    IJ.J. Aalbersberg, J. Engelfriet and G. Rozenberg, "The complexity of regular DNLC graph languages". Report 86-03, Rijksuniversiteit Leiden (1986).Google Scholar
  3. [3]
    R.V. Book, "On the complexity of formal grammars", Acta Informatica, Vol.9 (1978), 171–182Google Scholar
  4. [4]
    F. J. Brandenburg, "On the complexity of the membership problem of graph grammars", in: Proceedings of the Workshop on Graphtheoretic Concepts in Computer Science 83, M. Nagl and J. Perl, eds., Tauner-Verlag Linz (1983), 40–49.Google Scholar
  5. [5]
    E. Dahlhaus and M. Warmuth, "Membership for growing context sensitive grammars is polynomial", Lecture Notes in Computer Science 214 (1986), 85–99.Google Scholar
  6. [6]
    H. Ehrig, A. Rosenfeld and G Rozenberg (eds.), Proc. 3rd Intern. Workshop on Graph Grammars and their Application to Computer Science (1986), Lecture Notes in Computer Science (to appear).Google Scholar
  7. [7]
    J. Engelfriet, G. Leih and G. Rozenberg, "APEX graph grammars and attribute grammars", Report 87-04, Rijksuniversiteit Leiden (1987).Google Scholar
  8. [8]
    A. Ehrenfeucht, M. Main and G. Rozenberg, "Restrictions on NLC graph grammars", Theoret. Comput. Sci 31 (1984), 211–223.Google Scholar
  9. [9]
    M.R. Garey and D.S. Johnson, "Computers and Intractability — A Guide to the Theory of NP Completeness", Freeman, San Francisco (1979).Google Scholar
  10. [11]
    D.Janssens, "Node label controlled graph grammers",Ph. D. thesis, University of Antwerp, (1983).Google Scholar
  11. [12]
    D. Janssens and G. Rozenberg, "On the structure of node label controlled graph languages", Information Sciences 20 (1980), 191–216.Google Scholar
  12. [13]
    D. Janssens and G. Rozenberg, "Restrictions, extensions, and variations of NLC grammars", Information Sciences 20 (1980), 217–244.Google Scholar
  13. [14]
    D. Janssens and G. Rozenberg, "A characterization of context-free string languages by directed node-label controlled graph grammars", Acta Informatica 16 (1981), 63–85.Google Scholar
  14. [15]
    D. Janssens and G. Rozenberg, "Graph grammars with neighbourhood-controlled embedding", Theoret. Comput. Sci. 21 (1982), 55–74.Google Scholar
  15. [16]
    D. Janssens, G. Rozenberg, R. Verraedt, "On sequential and parallel node-rewriting graph grammars", Computer Graphics and Image Processing 18 (1982), 279–304.Google Scholar
  16. [17]
    M. Kaul, "Syntaxanalyse von Graphen bei Präzedenz-Graph-Grammatiken", Technical Report MIP 8610, Universität Passau, (1986).Google Scholar
  17. [18]
    K.J. Lange and E. Welzl, "String grammars with disconnecting or a basic root of the difficulty in graph grammar parsing", Discrete Applied Mathematics 16, 1987, 17–30.Google Scholar
  18. [19]
    M. Nagl, "Graph-Grammatiken Theorie, Implementierung, Anwendungen", Vieweg Verlag, Braunschweig (1979).Google Scholar
  19. [20]
    G. Rozenberg and E. Welzl, "Boundary NLC graph grammars — basic definitions, normal forms, and complexity", Inform. and Control 69 (1986), 136–167.Google Scholar
  20. [21]
    R. Schuster, "Graphgrammatiken und Grapheinbettungen: Algorithmen und Komplexität" Dissertation, Universität Passau, (1987).Google Scholar
  21. [22]
    A. O. Slisenko, "Context-free grammars as a tool for describing polynomial-time subclasses of hard problems", Inform. Process. Letters 14 (1982), 52–56.Google Scholar
  22. [23]
    J.D. Ullman, "Computational Aspects of VLSI", Computer Science Press (1984).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • Franz J. Brandenburg
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassauFederal Republic of Germany

Personalised recommendations