Regular Symmetry Patterns

  • Anthony W. Lin
  • Truong Khanh Nguyen
  • Philipp Rümmer
  • Jun Sun
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9583)


Symmetry reduction is a well-known approach for alleviating the state explosion problem in model checking. Automatically identifying symmetries in concurrent systems, however, is computationally expensive. We propose a symbolic framework for capturing symmetry patterns in parameterised systems (i.e. an infinite family of finite-state systems): two regular word transducers to represent, respectively, parameterised systems and symmetry patterns. The framework subsumes various types of “symmetry relations” ranging from weaker notions (e.g. simulation preorders) to the strongest notion (i.e. isomorphisms). Our framework enjoys two algorithmic properties: (1) symmetry verification: given a transducer, we can automatically check whether it is a symmetry pattern of a given system, and (2) symmetry synthesis: we can automatically generate a symmetry pattern for a given system in the form of a transducer. Furthermore, our symbolic language allows additional constraints that the symmetry patterns need to satisfy to be easily incorporated in the verification/synthesis. We show how these properties can help identify symmetry patterns in examples like dining philosopher protocols, self-stabilising protocols, and prioritised resource-allocator protocol. In some cases (e.g. Gries’s coffee can problem), our technique automatically synthesises a safety-preserving finite approximant, which can then be verified for safety solely using a finite-state model checker.


Permutation Group Concurrent System Pushdown Automaton Symmetry Pattern Regular Relation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



Lin is supported by Yale-NUS Grants, Rümmer by the Swedish Research Council. We thank Marty Weissman for a fruitful discussion.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Anthony W. Lin
    • 1
  • Truong Khanh Nguyen
    • 2
  • Philipp Rümmer
    • 3
  • Jun Sun
    • 4
  1. 1.Yale-NUS CollegeSingaporeSingapore
  2. 2.AutodeskSingaporeSingapore
  3. 3.Uppsala UniversityUppsalaSweden
  4. 4.Singapore University of Design and TechnologySingaporeSingapore

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