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Well-Structured Graph Transformation Systems with Negative Application Conditions

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Book cover Graph Transformations (ICGT 2012)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7562))

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Abstract

Given a transition system and a partial order on its states, the coverability problem is the question to decide whether a state can be reached that is larger than some given state. For graphs, a typical such partial order is the minor ordering, which allows to specify “bad graphs” as those graphs having a given graph as a minor. Well-structuredness of the transition system enables a finite representation of upward-closed sets and gives rise to a backward search algorithm for deciding coverability.

It is known that graph tranformation systems without negative application conditions form well-structured transition systems (WSTS) if the minor ordering is used and certain condition on the rules are satisfied. We study graph transformation systems with negative application conditions and show under which conditions they are well-structured and are hence amenable to a backwards search decision procedure for checking coverability.

Research partially supported by DFG project GaReV.

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Author information

Authors and Affiliations

  1. Abteilung für Informatik und Angewandte Kognitionswissenschaft, Universität Duisburg-Essen, Germany

    Barbara König & Jan Stückrath

Authors
  1. Barbara König
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  2. Jan Stückrath
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Editor information

Editors and Affiliations

  1. Technical University of Berlin, Franklinstr. 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  2. University of Paderborn, Zukunftsmeile 1, 33102, Paderborn, Germany

    Gregor Engels

  3. Department of Computer Science, University of Bremen, P.O. Box 33 04 40, 28334, Bremen, Germany

    Hans-Jörg Kreowski

  4. Leiden Center for Natural Computing, Leiden University, LCNC - LIACS, Niels Bohrweg 1, 2333 CA, Leiden, The Netherlands

    Grzegorz Rozenberg

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König, B., Stückrath, J. (2012). Well-Structured Graph Transformation Systems with Negative Application Conditions. In: Ehrig, H., Engels, G., Kreowski, HJ., Rozenberg, G. (eds) Graph Transformations. ICGT 2012. Lecture Notes in Computer Science, vol 7562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33654-6_6

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  • DOI: https://doi.org/10.1007/978-3-642-33654-6_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-33653-9

  • Online ISBN: 978-3-642-33654-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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