Confluence of graph transformation revisited

  • Authors:
  • Detlef Plump

  • Affiliations:
  • Department of Computer Science, The University of York, York, United Kingdom

  • Venue:
  • Processes, Terms and Cycles
  • Year:
  • 2005

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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.