Adhesivity Is Not Enough: Local Church-Rosser Revisited

  • Paolo Baldan
  • Fabio Gadducci
  • Pawel Sobociński
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6907)


Adhesive categories provide an abstract setting for the double-pushout approach to rewriting, generalising classical approaches to graph transformation. Fundamental results about parallelism and confluence, including the local Church-Rosser theorem, can be proven in adhesive categories, provided that one restricts to linear rules. We identify a class of categories, including most adhesive categories used in rewriting, where those same results can be proven in the presence of rules that are merely left-linear, i.e., rules which can merge different parts of a rewritten object. Such rules naturally emerge, e.g., when using graphical encodings for modelling the operational semantics of process calculi.


Adhesive and extensive categories double-pushout rewriting local Church-Rosser property parallel and sequential independence 


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Copyright information

© Springer-Verlag GmbH Berlin Heidelberg 2011

Authors and Affiliations

  • Paolo Baldan
    • 1
  • Fabio Gadducci
    • 2
  • Pawel Sobociński
    • 3
  1. 1.Dipartimento di Matematica Pura e ApplicataUniversità di PadovaItaly
  2. 2.Dipartimento di InformaticaUniversità di PisaItaly
  3. 3.School of Electronics and Computer ScienceUniversity of SouthamptonEngland

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