A representation of graphs by algebraic expressions and its use for graph rewriting systems

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


We define a set of operations on graphs and an algebraic notation for finite graphs. A complete axiomatization of the equivalence of graph expressions by equational rules is given. Graph rewriting systems can be defined as rewriting systems on graph expressions. This new definition is equivalent to the classical one using double push-outs.


Many-sorted algebra graph expression graph rewriting system graph-grammar 


  1. [1]
    ARNOLD A., DAUCHET M., Théorie des magmoïdes, RAIRO Informatique théorique 12 (1978) 235–257.Google Scholar
  2. [2]
    BAUDERON M., COURCELLE B., Graph expressions and graph rewritings, Report I-8623, 1986, to appear in Math. Systems Theory (Also L.N.C.S. Vol.214 pp.74–84, Springer 1986).Google Scholar
  3. [3]
    BLOOM S., ESIK Z., Axiomatizing schemes and their behaviors, J.C.S.S. vol. 31 no3 (1985) pp 375–393.Google Scholar
  4. [4]
    COURCELLE B., Fundamental properties of infinite trees, Theor.Comp. Sci. 25(1983) 95–169.CrossRefGoogle Scholar
  5. [5]
    COURCELLE B., Equivalences and transformations of regular systems. Applications to recursive program schemes and grammars, Theor.Comp.Sci. 46 (1986), 1–122.CrossRefGoogle Scholar
  6. [6]
    COURCELLE B., Recognizability and second order definability for sets of finite graphs, Research report 8634 Bordeaux I University, 1986.Google Scholar
  7. [7]
    COURCELLE B., On context-free sets of graphs and their monadic second-order theory, this volume.Google Scholar
  8. [8]
    EHRIG H., Introduction to the algebraic theory of graphs Lect. Notes in Comp. Sci. 73, Springer 1979, 1–69.Google Scholar
  9. [9]
    EHRIG H. (ed.) Proceedings 1st International workshop on graph grammars, L.N.C.S. vol. 73, 1979.Google Scholar
  10. [10]
    EHRIG H. (ed.), Proceedings 2nd International workshop on graph grammars, L.N.C.S. vol. 153, 1983.Google Scholar
  11. [11]
    EHRIG H., KREOWSKI H.J., MAGGIOLO-SCHETTINI A., ROSEN B. WINKOWSKI J., Transformations of structures: An algebraic approach, Math. Systems Theory 14 (1981) 305–334.CrossRefGoogle Scholar
  12. [12]
    EHRIG H., MAHR B., Fundamental of algebraic specifications 1, EATCS monograph vol.6, Springer-Verlag 1985.Google Scholar
  13. [13]
    EHRIG H., PFENDER M., SCHNEIDER H., Graph grammars: an algebraic approach, Proc. 14th IEEE Symp. on Switching and automata theory, Iowa City, 1973 p. 167–180.Google Scholar
  14. [14]
    ELGOT C., Monadic computation and iterative algebraic theories, Proc. Logic Colloq. 73, North Holland, Pub. Co. Amsterdam 1975, 175–230.Google Scholar
  15. [15]
    GINSBURG S., RICE, H., Two families of languages related to ALGOL, JACM 9 (1962) 350–371.Google Scholar
  16. [16]
    HABEL A. and KREOWSKI H.J, On context-free graph languages generated by edge replacements, Lec.Notes Comp.Sci. 153, Springer 1983, pp 143–158.Google Scholar
  17. [17]
    HABEL A. and KREOWSKI H.J, Some structural aspects of hypergraph languages generated by hyperedge replacements, Preprint, October 1985. Proc. STACS 1987. L.N.C.S. vol.247.Google Scholar
  18. [18]
    HUET G., OPPEN D., Equations and rewrite rules, a survey, in "Formal languages, Perspectives and open problems" R.Book ed. Academic Press 1980.Google Scholar
  19. [19]
    JANSSENS D., ROZENBERG G., Neighborhood uniform NLC grammars, Computer vision, graphics and image processing 35 (1986) 131–151.Google Scholar
  20. [20]
    MEZEI J., WRIGHT J., Algebraic automata and context-free sets, Information and control 11 (1967) 3–29.CrossRefGoogle Scholar
  21. [21]
    NAGL M., Bibliography on graph-rewriting systems (graph grammars), Lec.Notes Comp.Sci. 153 Springer 1983, pp. 415–448.Google Scholar
  22. [22]
    PETROV S., Graph grammars and automata (survey), Automation and Remote Control 39 (1978) 1034–1050.Google Scholar
  23. [23]
    RAOULT J.C., On graphs rewritings, Theor.Comp.Sci. 32 (1984) 1–24.Google Scholar
  24. [24]
    ROSEN B., Deriving graphs from graphs by applying a production, Acta Informatica 4 (1975) 337–357.CrossRefGoogle Scholar
  25. [25]
    ROZENBERG G, D. JANSSENS, A survey of NLC grammars, in Proc. CAAP' 83 L'Aquila, Lect. Notes in Comp. Sci. 159, Springer 1983, 114–128.Google Scholar
  26. [26]
    ROZENBERG G., WELZL E., BNLC grammars: graph theoretic closure properties, Acta Informatica 23 (1986) 289–309CrossRefGoogle Scholar
  27. [27]
    SCHMECK H., Algebraic characterization of reducible flow-charts, Journ. of Comp. and Syst. Sci. 27,2 (1983) 165–199.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1987

Authors and Affiliations

  • Bruno Courcelle
    • 1
  1. 1.Bordeaux 1 University Mathematiques Et InformatiqueTalenceFrance

Personalised recommendations