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Graph expressions and graph rewritings

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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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This work has been supported by the PRC “Mathématiques et Informatique”. Reprints can be requested from B. Courcelle by electronic mail at the following address (UUCP network): mcvax!inria!geocub!courcell.

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Bauderon, M., Courcelle, B. Graph expressions and graph rewritings. Math. Systems Theory 20, 83–127 (1987). https://doi.org/10.1007/BF01692060

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