Checking Bisimilarity for Attributed Graph Transformation

  • Fernando Orejas
  • Artur Boronat
  • Ulrike Golas
  • Nikos Mylonakis
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7794)

Abstract

Borrowed context graph transformation is a technique developed by Ehrig and Koenig to define bisimilarity congruences from reduction semantics defined by graph transformation. This means that, for instance, this technique can be used for defining bisimilarity congruences for process calculi whose operational semantics can be defined by graph transformation. Moreover, given a set of graph transformation rules, the technique can be used for checking bisimilarity of two given graphs. Unfortunately, we can not use this ideas to check if attributed graphs are bisimilar, i.e. graphs whose nodes or edges are labelled with values from some given data algebra and where graph transformation involves computation on that algebra. The problem is that, in the case of attributed graphs, borrowed context transformation may be infinitely branching. In this paper, based on borrowed context transformation of what we call symbolic graphs, we present a sound and relatively complete inference system for checking bisimilarity of attributed graphs. In particular, this means that, if using our inference system we are able to prove that two graphs are bisimilar then they are indeed bisimilar. Conversely, two graphs are not bisimilar if and only if we can find a proof saying so, provided that we are able to prove some formulas over the given data algebra. Moreover, since the proof system is complex to use, we also present a tableau method based on the inference system that is also sound and relatively complete.

Keywords

Attributed graph transformation symbolic graph transformation borrowed contexts bisimilarity 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Fernando Orejas
    • 1
  • Artur Boronat
    • 1
    • 2
  • Ulrike Golas
    • 3
  • Nikos Mylonakis
    • 1
  1. 1.Universitat Politècnica de CatalunyaSpain
  2. 2.University of LeicesterUK
  3. 3.Konrad-Zuse-Zentrum für Informationstechnik BerlinGermany

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