Hypergraph Construction and Its Application to the Static Analysis of Concurrent Systems
We define a construction operation on hypergraphs based on a colimit and show that its expressiveness is equal to the graph expressions of Bauderon and Courcelle. We also demonstrate that by closing a set of rewrite rules under graph construction we obtain a notion of rewriting equivalent to the double-pushout approach of Ehrig. The usefulness of our approach for the compositional modelling of concurrent systems is then demonstrated by giving a semantics of process graphs-corresponding to a process calculus with mobility-and of Petri nets. Based on hypergraph construction, a method for the static analysis of process graphs, related to type systems, is introduced.
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