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Graph-Rewriting Petri Nets

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Book cover Graph Transformation (ICGT 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10887))

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Abstract

Controlled graph rewriting enhances expressiveness of plain graph-rewriting systems (i.e., sets of graph-rewriting rules) by introducing additional constructs for explicitly controlling graph-rewriting rule applications. In this regard, a formal semantic foundation for controlled graph rewriting is inevitable as a reliable basis for tool-based specification and automated analysis of graph-based algorithms. Although several promising attempts have been proposed in the literature, a comprehensive theory of controlled graph rewriting capturing semantic subtleties of advanced control constructs provided by practical tools is still an open challenge. In this paper, we propose graph-rewriting Petri nets (GPN) as a novel foundation for unifying control-flow and rule-application semantics of controlled graph rewriting. GPN instantiate coloured Petri nets with categorical DPO-based graph-rewriting theory where token colours denote typed graphs and graph morphisms and transitions define templates for guarded graph-rewriting rule applications. Hence, GPN enjoy the rich body of specification and analysis techniques of Petri nets including inherent notions of concurrency. To demonstrate expressiveness of GPN, we present a case study by means of a topology-control algorithm for wireless sensor networks.

This work has been partially funded by the German Research Foundation (DFG) as part of project A1 within CRC1053–MAKI.

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Authors and Affiliations

  1. Real-Time Systems Lab, TU Darmstadt, Darmstadt, Germany

    Géza Kulcsár, Malte Lochau & Andy Schürr

Authors
  1. Géza Kulcsár
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  2. Malte Lochau
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  3. Andy Schürr
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Correspondence to Géza Kulcsár .

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Editors and Affiliations

  1. University of Potsdam, Potsdam, Germany

    Leen Lambers

  2. University of Victoria, Victoria, British Columbia, Canada

    Jens Weber

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Kulcsár, G., Lochau, M., Schürr, A. (2018). Graph-Rewriting Petri Nets. In: Lambers, L., Weber, J. (eds) Graph Transformation. ICGT 2018. Lecture Notes in Computer Science(), vol 10887. Springer, Cham. https://doi.org/10.1007/978-3-319-92991-0_6

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  • DOI: https://doi.org/10.1007/978-3-319-92991-0_6

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  • Publisher Name: Springer, Cham

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