Practical applications of precedence graph grammars

  • Manfred Kaul
Part II Technical Contributions
Part of the Lecture Notes in Computer Science book series (LNCS, volume 291)


Precedence graph grammars are of major interest in all those applications of graph grammars, where highly efficient parsers are needed. Up to now there are no other graph parsers with the same performance. Due to the fact, that even regular graph grammars with very restricted embedding relations have a NP-complete membership problem, different kinds than Chomsky-like restrictions have to be imposed on graph grammars. We start with contextfree graph grammars and introduce precedence relations. By demanding conflictfreeness, unique invertibility and some further, more technical constraints, precedence graph grammars are introduced with an O(n2) — membership problem, where n ist the number of nodes of the input graph.Precedence graph grammars are unambiguous, which is especially important for semantic evaluation of the derivation trees. In this paper we show, that in spite of all constraints the proposed graph grammar class has interesting generative power, concerning applications in such areas as e.g. dynamic data structures, program graphs, data and control flow graphs and syntactic pattern recognition. For the last topic an error correcting facility incorporated into the precedence graph parser is of special interest. In general inexact graph matching is NP-complete. In this paper we present a method, that increases the time complexity of our parser only by a factor of n. At last, our method is demonstrated with an example from syntactic pattern recognition.

Key words

graph grammar contextfree membership problem graph parser precedence relations parallel parsing hierarchical graph model inexact graph matching similarity of graphs error distance between graphs 


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10. References

  1. [AaRoEh 86]
    Aalbersberg, I.J./G. Rozenberg/A. Ehrenfeucht: On the membership problem for regular DNLC grammars; Discr. Appl. Math. 13, (1986) 79–85CrossRefGoogle Scholar
  2. [AhUl 72]
    A.V. Aho/J.D. Ullman: The Theory of Parsing, Translation, and Compiling; I,II, Prentice-Hall, Englewood Cliffs, NJ (1972)Google Scholar
  3. [Bab 79]
    J.P. Babinov: Class of generalized context-sensitive prcedence languages; Progr.Comput. Software 5 (1979) 117–126Google Scholar
  4. [BuAl 83]
    H. Bunke/G. Allermann: Inexact Graph Matching for Structural Pattern Recognition; Pat.Rec.Let. 1 (1983) 245–253CrossRefGoogle Scholar
  5. [ClEhRo 79]
    V. Claus/H. Ehrig/G. Rozenberg: Graph-Grammars and Their Application to Computer Science and Biology; 1st Int. Workshop, LNCS 73, Springer (1979)Google Scholar
  6. [EhNaRo 83]
    H. Ehrig/M. Nagl/G. Rozenberg(Eds.): Graph-Grammars and Their Application to Computer Science, 2nd Int. Workshop, LNCS 153, Springer (1983)Google Scholar
  7. [Fra 78]
    R. Franck: A Class of Linearly Parsable Graph Grammars, Acta Inform. 10(1978)175–201CrossRefGoogle Scholar
  8. [Fu 82]
    K.S. Fu: Syntactic Pattern Recognition; Prentice-Hall, Englewood Cliffs, NJ (1982)Google Scholar
  9. [GaJo 79]
    M.R. Garey/D.S. Johnson: Computers and Intractability; A Guide to the Theory of NP-Completeness; Freeman, San Francisco(1979)Google Scholar
  10. [Har 69]
    F. Harary: Graph Theory; Addison-Wesley Publ. Comp., Reading Mass. (1969)Google Scholar
  11. [Har 78]
    M. Harrison: Introduction to Formal Language Theory; Addison-Wesley Publ. Comp., Reading Mass. (1978)Google Scholar
  12. [Has 74]
    R. Haskell: Symmetrical precedence relations on general phrase structure grammars; Comp. Journ. 17 (1974) 234–241CrossRefGoogle Scholar
  13. [JaRo 80]
    D. Janssens/G. Rozenberg: On the structure of Node Label Controlled Graph Languages; Inform.Sci. 20 (1980) 191–216Google Scholar
  14. [Ka 86]
    M.Kaul: Syntaxanalyse von Graphen bei Präzedenz-Graph-Grammatiken; Techn. Report MIP-8610, Uni. Passau, West-GermanyGoogle Scholar
  15. [Knu 68]
    D.E.Knuth: Semantic of Context-free Languages; Math. Syst. Theo. (1968)Google Scholar
  16. [LeNa 84]
    C.Lewerentz/M.Nagl: A Formal Specification Language for Software Systems Defined by Graph Grammars; in U.Pape (Ed.):Proc. WG'84, Workshop on Graphtheor. Conc. in Computer Science, June 13–15, Berlin (1984)Google Scholar
  17. [Lud 81]
    H. Ludwigs: Properties of Ordered Graph Grammars; in: H.Noltemeier(Ed.): Graphtheoretic Concepts in Comp. Science; LNCS 100, Springer (1981) 70–79Google Scholar
  18. [Nag 79]
    M. Nagl: Graph-Grammatiken — Theorie, Implementierung, Anwendung; Vieweg, Braunschweig (1979)Google Scholar
  19. [Nag 82]
    M.Nagao: Control Strategies in Pattern Analysis; Proc. Pat. Rec. Vol. I, 6th Int. Conf., Munich 1982 (1982) 996–1006Google Scholar
  20. [Rf 82]
    A.Rosenfeld: Image Analysis: Progress, Problems, and Prospects; Proc. Pat. Rec. Vol. I, 6th Int. Conf., Munich 1982 (1982) 7–15Google Scholar
  21. [Sch 87]
    A. Schütte: Spezifikation und Generierung von Übersetzern für Graph-Sprachen durch attributierte Graph-Grammatiken; Dissertation, Express Edition (Reihe Informatik), Berlin 1987.Google Scholar
  22. [ShHa 81]
    L.G.Shapiro/R.M.Haralick: Structural Descriptions and Inexact Matching;IEEE Trans. Pat. Ana. PAMI-3, No. 5 (1981)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Manfred Kaul
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität PassauPassauWest-Germany

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