Deriving bisimulation congruences in the DPO approach to graph rewriting with borrowed contexts

  • Authors:

  • Hartmut Ehrig;Barbara König

  • Affiliations:

  • Institut für Softwaretechnik und Theoretische Informatik, Technische Universität Berlin, Germany Email: ehrig@cs.tu-berlin.de;Institut für Informatik und interaktive Systeme, Universität Duisburg-Essen, 47048 Duisburg, Germany Email: barbara_koenig@uni-due.de

  • Venue:
  • Mathematical Structures in Computer Science
  • Year:
  • 2006

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Abstract

Motivated by recent work on the derivation of labelled transitions and bisimulation congruences from unlabelled reaction rules, we show how to address this problem in the DPO (double-pushout) approach to graph rewriting. Unlike the case with previous approaches, we consider graphs as objects, rather than arrows, of the category under consideration. This allows us to present a very simple way of deriving labelled transitions (called rewriting steps with borrowed context), which integrates smoothly with the DPO approach, has a very constructive nature and requires only a minimum of category theory. The core part of this paper is the proof that the bisimilarity based on graph rewriting with borrowed contexts is a congruence relation. We will also introduce some proof techniques and compare our approach with the derivation of labelled transitions via relative pushouts.