Introducing symmetry to graph rewriting systems with process abstraction

Taichi Tomioka*, Yutaro Tsunekawa, Kazunori Ueda

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution


Symmetry reduction in model checking is a technique for reducing state spaces by exploiting the inherent symmetry of models, i.e., the interchangeability of their subcomponents. Model abstraction, which abstracts away the details of models, often strengthens the symmetry of the models. Graph rewriting systems allow us to express models in such a way that inherent symmetry manifests itself with graph isomorphism of states. In graph rewriting, the synergistic effect of symmetry reduction and model abstraction is obtained under graph isomorphism. This paper proposes a method for abstracting programs described in a hierarchical graph rewriting language LMNtal. The method automatically finds and abstracts away subgraphs of a graph rewriting system that are irrelevant to the results of model checking. The whole framework is developed within the syntax and the formal semantics of the modeling language LMNtal without introducing new domains or languages. We show that the proposed abstraction method combined with symmetry reduction reduces state spaces while preserving the soundness of model checking. We implemented the method on SLIM, an implementation of LMNtal with an LTL model checker, tested it with various concurrent algorithms, and confirmed that it automatically reduces the number of states by successfully extracting the symmetry of models.

Original languageEnglish
Title of host publicationGraph Transformation - 12th International Conference, ICGT 2019, Held as Part of STAF 2019, Proceedings
EditorsEsther Guerra, Fernando Orejas
PublisherSpringer Verlag
Number of pages18
ISBN (Print)9783030236106
Publication statusPublished - 2019
Event12th International Conference on Graph Transformation, ICGT 2019, Held as part of STAF 2019 - Eindhoven, Netherlands
Duration: 2019 Jul 152019 Jul 16

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11629 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference12th International Conference on Graph Transformation, ICGT 2019, Held as part of STAF 2019


  • Abstraction
  • Graph rewriting systems
  • LMNtal
  • Model checking
  • Symmetry reduction

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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