Unfolding grammars in adhesive categories

  • Authors:
  • Paolo Baldan;Andrea Corradini;Tobias Heindel;Barbara König;Paweł Sobociński

  • Affiliations:
  • Dipartimento di Matematica Pura e Applicata, Università di Padova, Italy;Dipartimento di Informatica, Università di Pisa, Italy;Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Germany;Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Germany;ECS, University of Southampton, United Kingdom

  • Venue:
  • CALCO'09 Proceedings of the 3rd international conference on Algebra and coalgebra in computer science
  • Year:
  • 2009

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Abstract

We generalize the unfolding semantics, previously developed for concrete formalisms such as Petri nets and graph grammars, to the abstract setting of (single pushout) rewriting over adhesive categories. The unfolding construction is characterized as a coreflection, i.e. the unfolding functor arises as the right adjoint to the embedding of the category of occurrence grammars into the category of grammars. As the unfolding represents potentially infinite computations, we need to work in adhesive categories with "well-behaved" colimits of ω-chains of monomorphisms. Compared to previous work on the unfolding of Petri nets and graph grammars, our results apply to a wider class of systems, which is due to the use of a refined notion of grammar morphism.