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Applied Categorical Structures

, Volume 16, Issue 3, pp 389–419 | Cite as

Subobject Transformation Systems

  • Andrea CorradiniEmail author
  • Frank Hermann
  • Paweł Sobociński
Article

Abstract

Subobject transformation systems STS are proposed as a novel formal framework for the analysis of derivations of transformation systems based on the algebraic, double-pushout (DPO) approach. They can be considered as a simplified variant of DPO rewriting, acting in the distributive lattice of subobjects of a given object of an adhesive category. This setting allows a direct analysis of all possible notions of dependency between any two productions without requiring an explicit match. In particular, several equivalent characterizations of independence of productions are proposed, as well as a local Church–Rosser theorem in the setting of STS. Finally, we show how any derivation tree in an ordinary DPO grammar leads to an STS via a suitable construction and show that relational reasoning in the resulting STS is sound and complete with respect to the independence in the original derivation tree.

Keywords

Graph transformation systems Adhesive categories Occurrence grammars 

Mathematics Subject Classifications (2000)

18B35 68Q10 68Q42 

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Copyright information

© Springer Science+Business Media B.V. 2008

Authors and Affiliations

  • Andrea Corradini
    • 1
    Email author
  • Frank Hermann
    • 2
  • Paweł Sobociński
    • 3
  1. 1.Dipartimento di InformaticaUniversità di PisaPisaItaly
  2. 2.Department of Electrical Engineering and Computer ScienceTechnical University of BerlinBerlinGermany
  3. 3.ECSUniversity of SouthamptonSouthamptonUK

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