Graph Unification and Matching

A concept of graph unification and matching is introduced by using hyperedges as graph variables and hyperedge replacement as substitution mechanism. It is shown that a restricted form of graph unification corresponds to solving linear Diophantine equations, and hence is decidable. For graph matching, transformation rules are given which compute all (pure) solutions to a matching problem. The matching concept suggests a new graph rewriting approach which is very simple to describe and which generalizes the well-known double-pushout approach.

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