Mathematical systems theory

, Volume 20, Issue 1, pp 83–127 | Cite as

Graph expressions and graph rewritings

  • Michel Bauderon
  • Bruno Courcelle
Article

Abstract

We define an algebraic structure for the set of finite graphs, a notion of graph expression for defining them, and a complete set of equational rules for manipulating graph expressions. (By agraph we mean an oriented hypergraph, the hyperedges of which are labeled with symbols from a fixed finite ranked alphabet and that is equipped with a finite sequence of distinguished vertices). The notion of a context-free graph grammar is introduced (based on the substitution of a graph for a hyperedge in a graph). The notion of an equational set of graphs follows in a standard way from the algebraic structure. As in the case of context-free languages, a set of graphs is contextfree iff it is equational. By working at the level of expressions, we derive from the algebraic formalism a notion of graph rewriting which is as powerful as the usual one (based on a categorical approach) introduced by Ehrig, Pfender, and Schneider.

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Copyright information

© Springer-Verlag New York Inc 1987

Authors and Affiliations

  • Michel Bauderon
    • 1
  • Bruno Courcelle
    • 2
  1. 1.Département d'InformatiqueI.U.T.A, Université Bordeaux ITalenceFrance
  2. 2.Département d'Informatique, Formation associée au CNRSUniversité Bordeaux ITalenceFrance

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