International Conference on Verification, Model Checking, and Abstract Interpretation

Verification, Model Checking, and Abstract Interpretation pp 455-475 | Cite as

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)

Abstract

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.

Notes

Acknowledgment

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

References

  1. 1.
    Abdulla, P.A.: Regular model checking. STTT 14(2), 109–118 (2012)CrossRefGoogle Scholar
  2. 2.
    Abdulla, P.A., Chen, Y.-F., Holík, L., Mayr, R., Vojnar, T.: When simulation meets antichains. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 158–174. Springer, Heidelberg (2010) CrossRefGoogle Scholar
  3. 3.
    Abdulla, P.A., Jonsson, B., Nilsson, M., d’Orso, J., Saksena, M.: Regular model checking for LTL(MSO). STTT 14(2), 223–241 (2012)CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Jonsson, B., Nilsson, M., Saksena, M.: A survey of regular model checking. In: Gardner, P., Yoshida, N. (eds.) CONCUR 2004. LNCS, vol. 3170, pp. 35–48. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  5. 5.
    Arenas, M., Barceló, P., Libkin, L.: Regular languages of nested words: fixed points, automata, and synchronization. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 888–900. Springer, Heidelberg (2007) CrossRefGoogle Scholar
  6. 6.
    Baier, C., Katoen, J.-P.: Principles of Model Checking. MIT Press, Cambridge (2008) MATHGoogle Scholar
  7. 7.
    Berre, D.L., Parrain, A.: The Sat4j library, release 2.2. JSAT 7(2–3), 56–59 (2010)Google Scholar
  8. 8.
    Blumensath, A.: Automatic structures. Master’s thesis, RWTH Aachen (1999)Google Scholar
  9. 9.
    Blumensath, A., Grädel, E.: Finite presentations of infinite structures: Automata and interpretations. Theor. Comput. Syst. 37(6), 641–674 (2004)MATHCrossRefGoogle Scholar
  10. 10.
    Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: The 40th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2013, Rome, Italy - January 23–25, 2013, pp. 457–468 (2013)Google Scholar
  11. 11.
    Cameron, P.J.: Permutation Groups. London Mathematical Society Student Texts. Cambridge University Press, Cambridge (1999)MATHCrossRefGoogle Scholar
  12. 12.
    Clarke, E.M., Jha, S., Enders, R., Filkorn, T.: Exploiting symmetry in temporal logic model checking. Formal Methods Syst. Des. 9(1/2), 77–104 (1996)CrossRefGoogle Scholar
  13. 13.
    Dill, D.L., Drexler, A.J., Hu, A.J., Yang, C.H.: Protocol verification as a hardware design aid. In: Proceedings 1991 IEEE International Conference on Computer Design: VLSI in Computer and Processors, ICCD 1992, Cambridge, MA, USA, October 11–14, 1992, pp. 522–525 (1992)Google Scholar
  14. 14.
    Donaldson, A.F.: Automatic Techniques for Detecting and Exploiting Symmetry in Model Checking. Ph.D. thesis, University of Glasgow (2007)Google Scholar
  15. 15.
    Donaldson, A.F., Miller, A.: Automatic symmetry detection for model checking using computational group theory. In: FM, pp. 631–631 (2005)Google Scholar
  16. 16.
    Donaldson, A.F., Miller, A.: Automatic symmetry detection for promela. J. Autom. Reasoning 41, 251–293 (2008)MATHCrossRefGoogle Scholar
  17. 17.
    Emerson, E.A., Kahlon, V.: Reducing model checking of the many to the few. In: Proceedings of the 17th International Conference on Automated Deduction, Pittsburgh, PA, USA, June 17–20, 2000, Automated Deduction - CADE-17, pp. 236–254 (2000)Google Scholar
  18. 18.
    Emerson, E.A., Namjoshi, K.S.: Reasoning about rings. In: POPL, 85–94, (1995)Google Scholar
  19. 19.
    Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Formal Methods Syst. Des. 9(1/2), 105–131 (1996)CrossRefGoogle Scholar
  20. 20.
    Gries, D.: The Science of Programming. Springer-Verlag (1981)Google Scholar
  21. 21.
    Herman, T.: Probabilistic self-stabilization. Inf. Process. Lett. 35(2), 63–67 (1990)MATHMathSciNetCrossRefGoogle Scholar
  22. 22.
    Ip, C.N., Dill, D.L.: Better verification through symmetry. Formal Methods Syst. Des. 9, 41–75 (1996)CrossRefGoogle Scholar
  23. 23.
    Israeli, A., Jalfon, M.: Token management schemes and random walks yield self-stabilizing mutual exclusion. In: PODC, pp. 119–131 (1990)Google Scholar
  24. 24.
    Jaghoori, M.M., Sirjani, M., Mousavi, M.R., Khamespanah, E., Movaghar, A.: Symmetry and partial order reduction techniques in model checking rebeca. Acta Inf. 47, 33–66 (2010)MATHMathSciNetCrossRefGoogle Scholar
  25. 25.
    Jaghoori, M.M., Sirjani, M., Mousavi, M.R.R., Movaghar, A.: Efficient symmetry reduction for an actor-based model. In: Chakraborty, G. (ed.) ICDCIT 2005. LNCS, vol. 3816, pp. 494–507. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  26. 26.
    Lehmann, D., Rabin, M.: On the advantage of free choice: A symmetric and fully distributed solution to the dining philosophers problem (extended abstract). In: Proceedings 8th Annual ACM Symposium on Principles of Programming Languages (POPL 1981), pp. 133–138 (1981)Google Scholar
  27. 27.
    Lin, A.W.: Accelerating tree-automatic relations. In: FSTTCS, pp. 313–324 (2012)Google Scholar
  28. 28.
    Lin, A.W., Nguyen, T.K., Rümmer, P., Sun, J.: Regular symmetry patterns (technical report). http://arxiv.org/abs/1510.08506 (cited in 2015)
  29. 29.
    Sistla, A.P., Gyuris, V., Emerson, E.A.: SMC: a symmetry-based model checker for verification of safety and liveness properties. ACM Trans. Softw. Eng. Method. 9, 133–166 (2000)CrossRefGoogle Scholar
  30. 30.
    Spermann, C., Leuschel, M.: ProB gets nauty: effective symmetry reduction for B and Z models. In: TASE, pp. 15–22 (2008)Google Scholar
  31. 31.
    Vojnar, T.: Cut-offs and automata in formal verification of infinite-state systems: Habilitation Thesis. Brno University of Technology, Faculty of Information Technology (2007)Google Scholar
  32. 32.
    Wahl, T., Donaldson, A.F.: Replication and abstraction: Symmetry in automated formal verification. Symmetry 2, 799–847 (2010)MathSciNetCrossRefGoogle Scholar
  33. 33.
    Zhang, S.J., Sun, J., Sun, C., Liu, Y., Ma, J., Dong, J.S.: Constraint-based automatic symmetry detection. In: ASE, pp. 15–25 (2013)Google Scholar

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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