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An algebraic formalism for graphs

  • Michel Bauderon
  • Bruno Courcelle
Graphs And Grammars
Part of the Lecture Notes in Computer Science book series (LNCS, volume 214)

Abstract

We provide an algebraic structure for the set of finite graphs, whence a notion of graph expression for defining them and a complete set of equational rules for manipulating expressions.

By working at the level of expressions, one derives from this algebraic formalism a notion of graph rewriting which is as powerful and conceptually simpler than the usual categorical approach of Ehrig and alii.

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6. References

  1. [BC85]
    BAUDERON M., COURCELLE B., Graph expressions and graph rewritings, (Report 8525, University Bordeaux I, Dept Maths Info 1985)Google Scholar
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    COURCELLE B., Equivalences and transformations of regular systems. Applications to recursive program schemes and grammars, To appear in Theor. Comp. Sci. (Report 8521, University Bordeaux I, Dept Maths Info 1985)Google Scholar
  3. [Eh79]
    EHRIG H., Introduction to the algebraic theory of graphs, Lect. Notes in Comp. Sci. 73 Springer 1979 1–69Google Scholar
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    EHRIG H., KREOWSKI H-J., Push-out properties: An analysis of gluing constructions for graphs, Math. Nachr. 91 (1979) 135–149Google Scholar
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    EHRIG H., KREOWSKI H-J., MAGGIOLO-SCHETTINI A., ROSEN B R., WINKOWSKI J., Transformations of structures: An algebraic approach, Math. Systems Theory 14 (1981) 305–334Google Scholar
  6. [HK83]
    HABEL A., KREOWSKI H-J., On context free graphs languages generated by edge replacement, Lect. Notes in Comp. Sci. 153 Springer 1983, 143–158Google Scholar
  7. [Ra84]
    RAOULT J.C., On graphs rewritings, Theor. Comp. Sci. 32 (1984) 114–128Google Scholar

Copyright information

© Springer-Verlag 1986

Authors and Affiliations

  • Michel Bauderon
    • 1
  • Bruno Courcelle
    • 1
  1. 1.Département de Mathématiques et d'Informatique Formation associée au CNRSUniversité de Bordeaux ITalenceFrance

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