Grammatical inference based on hyperedge replacement

  • Eric Jeltsch
  • Hans-Jörg Kreowski
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 532)


In this paper, a grammatical-inference algorithm is developed with finite sets of sample graphs as inputs and hyperedge-replacement grammars as outputs. In particular, the languages generated by inferred grammars contain the input samples. Essentially, the inference procedure iterates the application of an operation which decomposes hyperedge-replacement rules according to edge-disjoint coverings of the right-hand sides of the rules. The main result is a characterization of the inferred grammars as “samples-composing” meaning that each sample can be derived and each rule contributes to the generation of samples in a certain way.


grammatical inference hyperedge-replacement graph grammars 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Ba 74]
    J. M. Barzdin: Finite Automata: Synthesis and Behaviour, North-Holland, 1974.Google Scholar
  2. [Ba 83]
    B. Bartsch-Spörl: Grammatical Inference of Graph-Grammars for Syntactic Pattern Recognition, Lect. Not. Comp. Sci. 153, 1–7, 1983.Google Scholar
  3. [BC 87]
    M. Bauderon, B. Courcelle: Graph Expressions and Graph Rewriting, Math. Systems Theory 20, 83–127, 1987.CrossRefGoogle Scholar
  4. [Co 87]
    B. Courcelle: On Context-Free Sets of Graphs and Their Monadic Second-Order Theory, Lect. Not. Comp. Sci. 291, 133–146, 1987.Google Scholar
  5. [Co 90]
    B. Courcelle: The Monadic Second-Order Logic of Graphs I Recognizable Sets of Finite Graphs, Information and Computation 85, 12–75, 1990.CrossRefGoogle Scholar
  6. [CRA 76]
    C. Cook, A. Rosenfeld, A. Aronson: Grammatical Inference by Hill Climbing, Informational Sciences 10, 59–80, 1976.Google Scholar
  7. [Fu 82]
    K.S. Fu: Syntactic Pattern Recognition and Applications, Prentice-Hall, Englewood-Cliffs, N.J., 1982.Google Scholar
  8. [FB 75]
    K.S. Fu, T.K. Booth: Grammatical Inference: Introduction and Survey Part I and II, IEEE-Trans. Syst. Man and Cyber. 5, 95–111 and 409–423, 1975.Google Scholar
  9. [Go 67]
    E. M. Gold: Language Identification in the Limit, Information and Control 10, 447–474, 1967.CrossRefGoogle Scholar
  10. [GT 78]
    R.C. Gonzalez, M.G. Thomason: Syntactic Pattern Recognition, Addison-Wesley, Reading, Massachusetts, 1978.Google Scholar
  11. [Ha 89]
    A. Habel: Hyperedge Replacement: Grammars and Languages, Ph. D. Thesis, Fachbereich Mathematik und Informatik, Universität Bremen, April 1989.Google Scholar
  12. [HK 87a]
    A. Habel, H.-J. Kreowski: May We Introduce to You: Hyperedge Replacement, Lect. Not. Comp. Sci. 291, 15–26, 1987.Google Scholar
  13. [HK 87b]
    A. Habel, H.-J. Kreowski: Some Structural Aspects of Hypergraph Languages Generated by Hyperedge Replacement, Lect. Not. Comp. Sci. 247, 207–219, 1987.Google Scholar
  14. [HK 89]
    A. Habel, H.-J. Kreowski: Filtering Hyperedge-Replacement Languages Trough Compatible Properties, Lect. Not. Comp. Sci. 411, 107–120, 1989.Google Scholar
  15. [HKV 89]
    A. Habel, H.-J. Kreowski, W. Vogler: Metatheorems for Decision Problems on Hyperedge Replacement Graph Languages, Acta Informatica 26, 657–677, 1989.CrossRefGoogle Scholar
  16. [JB 81]
    K. P. Jantke, H.-R. Beick: Combining Postulates of Naturalness in Inductive Inference, EIK 17, 465–484, 1981.Google Scholar
  17. [JL 87]
    H. Jürgensen, A. Lindenmayer: Inference Algorithms for Developmental Systems with Cell Lineages, Bulletin of Mathematical Biology 49, Nr.1, 93–123, 1987.CrossRefGoogle Scholar
  18. [LW 88]
    T. Lengauer, E. Wanke: Efficient Analysis of Graph Properties on Context-Free Graph Languages, Lect. Not. Comp. Sci. 317, 379–393, 1988.Google Scholar
  19. [Ta 88]
    Y. Takada: Grammatical Inference for Even Linear Languages Based on Control Sets, In: Proceedings of the ECAI 88, München, 375–377, 1988.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1991

Authors and Affiliations

  • Eric Jeltsch
    • 1
  • Hans-Jörg Kreowski
    • 1
  1. 1.Fachbereich Mathematik und InformatikUniversität BremenBremen 33

Personalised recommendations