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Concurrent Graph and Term Graph Rewriting
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Formal Verification of Graph Grammars using Mathematical Induction
Electronic Notes in Theoretical Computer Science (ENTCS)
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CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
Unfolding-based diagnosis of systems with an evolving topology
Information and Computation
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ICGT'10 Proceedings of the 5th international conference on Graph transformations
Verification of graph grammars using a logical approach
Science of Computer Programming
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Several attempts have been made of extending to graph grammars the unfolding semantics originally developed by Winskel for (safe) Petri nets, but only partial results were obtained. In this paper, we fully extend Winskel's approach to single-pushout grammars providing them with a categorical concurrent semantics expressed as a coreflection between the category of (semi-weighted) graph grammars and the category of prime algebraic domains, which factorises through the category of occurrence grammars and the category of asymmetric event structures. For general, possibly nonsemi-weighted single-pushout grammars, we define an analogous functorial concurrent semantics, which, however, is not characterised as an adjunction. Similar results can be obtained for double-pushout graph grammars, under the assumptions that nodes are never deleted.