Abstract
It is shown that it is undecidable in general whether a terminating graph rewriting system is confluent or not—in contrast to the situation for term and string rewriting systems. Critical pairs are introduced to hypergraph rewriting, a generalisation of graph rewriting, where it turns out that the mere existence of common reducts for all critical pairs of a graph rewriting system does not imply local confluence. A Critical Pair Lemma for hypergraph rewriting is then established which guarantees local confluence if each critical pair of a system has joining derivations that are compatible in that they map certain nodes to the same nodes in the common reduct.
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Plump, D. (2005). Confluence of Graph Transformation Revisited. In: Middeldorp, A., van Oostrom, V., van Raamsdonk, F., de Vrijer, R. (eds) Processes, Terms and Cycles: Steps on the Road to Infinity. Lecture Notes in Computer Science, vol 3838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11601548_16
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