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Confluence of Graph Rewriting with Interfaces

  • Filippo Bonchi
  • Fabio Gadducci
  • Aleks Kissinger
  • Paweł Sobociński
  • Fabio Zanasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10201)

Abstract

For terminating double-pushout (DPO) graph rewriting systems confluence is, in general, undecidable. We show that confluence is decidable for an extension of DPO rewriting to graphs with interfaces. This variant is important due to it being closely related to rewriting of string diagrams. We show that our result extends, under mild conditions, to decidability of confluence for terminating rewriting systems of string diagrams in symmetric monoidal categories.

Keywords

Confluence DPO rewriting systems Adhesive categories PROPs String diagrams 

Notes

Acknowledgment

Aleks Kissinger and Fabio Zanasi acknowledge support from the ERC under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ERC grant no. 320571. The work of Filippo Bonchi has been partly supported by the project ANR-16-CE25-0011 REPAS and Labex MILYON/ANR-10-LABX-0070. The work of Fabio Gadducci has been partly supported by the project PRA_2016_64 “Through the fog” funded by the University of Pisa.

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Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  • Filippo Bonchi
    • 1
  • Fabio Gadducci
    • 2
  • Aleks Kissinger
    • 3
  • Paweł Sobociński
    • 4
  • Fabio Zanasi
    • 5
  1. 1.CNRS, ENS de LyonLyonFrance
  2. 2.University of PisaPisaItaly
  3. 3.Radboud University NijmegenNijmegenThe Netherlands
  4. 4.University of SouthamptonSouthamptonUK
  5. 5.University College LondonLondonUK

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