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Graph expressions and graph rewritings. (English) Zbl 0641.68115
Summary: 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 a graph 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 context-free 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.

MSC:
68Q45 Formal languages and automata
Software:
ALGOL 60
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