Graph expressions and graph rewritings View Full Text


Ontology type: schema:ScholarlyArticle     


Article Info

DATE

1987-12

AUTHORS

Michel Bauderon, Bruno Courcelle

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. More... »

PAGES

83-127

References to SciGraph publications

  • 1983. A survey of NLC grammars in CAAP'83
  • 1976. Algebraic Theories in NONE
  • 1975-12. Deriving graphs from graphs by applying a production in ACTA INFORMATICA
  • 1987. Some structural aspects of hypergraph languages generated by hyperedge replacement in STACS 87
  • 1985. Fundamentals of Algebraic Specification 1, Equations and Initial Semantics in NONE
  • 1981-12. Transformations of structures: An algebraic approach in MATHEMATICAL SYSTEMS THEORY
  • 1987. A representation of graphs by algebraic expressions and its use for graph rewriting systems in GRAPH-GRAMMARS AND THEIR APPLICATION TO COMPUTER SCIENCE
  • 1983. On context-free graph languages generated by edge replacement in GRAPH-GRAMMARS AND THEIR APPLICATION TO COMPUTER SCIENCE
  • 1979. Introduction to the algebraic theory of graph grammars (a survey) in GRAPH-GRAMMARS AND THEIR APPLICATION TO COMPUTER SCIENCE AND BIOLOGY
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/bf01692060

    DOI

    http://dx.doi.org/10.1007/bf01692060

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1013326091


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