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A Parallel Relation-Based Algorithm for Symbolic Bisimulation Minimization

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Verification, Model Checking, and Abstract Interpretation (VMCAI 2019)

Abstract

Symbolic computation using BDDs and bisimulation minimization are alternative ways to cope with the state space explosion in model checking. The combination of both techniques opens up many parameters that can be tweaked for further optimization. Most importantly, the bisimulation can either be represented as equivalence classes or as a relation. While recent work argues that storing partitions is more efficient, we show that the relation-based approach is preferable. We do so by deriving a relation-based minimization algorithm based on new coarse-grained BDD operations. The implementation demonstrates that the relational approach uses fewer memory and performs better.

The second author is funded by the research program VENI with project number 639.021.649 of the Netherlands Organization for Scientific Research (NWO).

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References

  1. Baier, C., Katoen, J.: Principles of Model Checking. MIT Press, Cambridge (2008)

    MATH  Google Scholar 

  2. Blom, S., Orzan, S.: Distributed branching bisimulation reduction of state spaces. Electron. Notes Theor. Comput. Sci. 89(1), 99–113 (2003)

    Article  Google Scholar 

  3. Bouali, A., de Simone, R.: Symbolic bisimulation minimisation. In: von Bochmann, G., Probst, D.K. (eds.) CAV 1992. LNCS, vol. 663, pp. 96–108. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-56496-9_9

    Chapter  Google Scholar 

  4. Brace, K.S., Rudell, R.L., Bryant, R.E.: Efficient implementation of a BDD package. In: 27th ACM/IEEE Design Automation Conference, pp. 40–45 (1990)

    Google Scholar 

  5. Bryant, R.E.: Graph-based algorithms for boolean function manipulation. IEEE Trans. Comput. C–35(8), 677–691 (1986)

    Article  Google Scholar 

  6. Burch, J., Clarke, E., McMillan, K., Dill, D., Hwang, L.: Symbolic model checking: 1020 states and beyond. Inf. Comput. 98(2), 142–170 (1992)

    Article  Google Scholar 

  7. Ciardo, G., Lüttgen, G., Siminiceanu, R.: Saturation: an efficient iteration strategy for symbolic state—Space generation. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 328–342. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-45319-9_23

    Chapter  MATH  Google Scholar 

  8. Dalsgaard, A.E., Enevoldsen, S., Larsen, K.G., Srba, J.: Distributed computation of fixed points on dependency graphs. In: Fränzle, M., Kapur, D., Zhan, N. (eds.) SETTA 2016. LNCS, vol. 9984, pp. 197–212. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-47677-3_13

    Chapter  Google Scholar 

  9. De Nicola, R., Vaandrager, F.: Three logics for branching bisimulation. J. ACM (JACM) 42(2), 458–487 (1995)

    Article  MathSciNet  Google Scholar 

  10. van Dijk, T.: Sylvan: multi-core decision diagrams. Ph.D. thesis, University of Twente (2016). https://doi.org/10.3990/1.9789036541602

  11. van Dijk, T., van de Pol, J.: Multi-core symbolic bisimulation minimisation. Int. J. Softw. Tools Technol. Transf. 20(2), 157–177 (2018)

    Article  Google Scholar 

  12. van Dijk, T., van de Pol, J.C.: Lace: non-blocking split deque for work-stealing. In: Lopes, L., et al. (eds.) Euro-Par 2014. LNCS, vol. 8806, pp. 206–217. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-14313-2_18

    Chapter  Google Scholar 

  13. Fisler, K., Vardi, M.Y.: Bisimulation and model checking. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 338–342. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48153-2_29

    Chapter  Google Scholar 

  14. Fisler, K., Vardi, M.Y.: Bisimulation minimization in an automata-theoretic verification framework. In: Gopalakrishnan, G., Windley, P. (eds.) FMCAD 1998. LNCS, vol. 1522, pp. 115–132. Springer, Heidelberg (1998). https://doi.org/10.1007/3-540-49519-3_9

    Chapter  Google Scholar 

  15. Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. J. ACM (JACM) 32(1), 137–161 (1985)

    Article  MathSciNet  Google Scholar 

  16. Huth, M., Ryan, M.: Verification by model checking, chap. Logic in Computer Science, p. 241. Cambridge University Press, Cambridge (2004)

    Chapter  Google Scholar 

  17. Liu, X., Smolka, S.A.: Simple linear-time algorithms for minimal fixed points. In: Larsen, K.G., Skyum, S., Winskel, G. (eds.) ICALP 1998. LNCS, vol. 1443, pp. 53–66. Springer, Heidelberg (1998). https://doi.org/10.1007/BFb0055040

    Chapter  Google Scholar 

  18. Milner, R.: Communication and Concurrency. Prentice Hall, Upper Saddle River (1989)

    MATH  Google Scholar 

  19. Mumme, M., Ciardo, G.: An efficient fully symbolic bisimulation algorithm for non-deterministic systems. IJFCS 24(02), 263–282 (2013)

    MathSciNet  MATH  Google Scholar 

  20. Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987). https://doi.org/10.1137/0216062

    Article  MathSciNet  MATH  Google Scholar 

  21. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981). https://doi.org/10.1007/BFb0017309

    Chapter  Google Scholar 

  22. Shannon, C.E.: A symbolic analysis of relay and switching circuits. Electr. Eng. 57(12), 713–723 (1938). https://doi.org/10.1109/EE.1938.6431064

    Article  Google Scholar 

  23. Solé, M., Pastor, E.: Traversal techniques for concurrent systems. In: Aagaard, M.D., O’Leary, J.W. (eds.) FMCAD 2002. LNCS, vol. 2517, pp. 220–237. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-36126-X_14

    Chapter  Google Scholar 

  24. Van Dijk, T., Laarman, A., Van De Pol, J.: Multi-core BDD operations for symbolic reachability. Electron. Notes Theor. Comput. Sci. 296, 127–143 (2013)

    Article  Google Scholar 

  25. Wimmer, R., Herbstritt, M., Hermanns, H., Strampp, K., Becker, B.: Sigref – a symbolic bisimulation tool box. In: Graf, S., Zhang, W. (eds.) ATVA 2006. LNCS, vol. 4218, pp. 477–492. Springer, Heidelberg (2006). https://doi.org/10.1007/11901914_35

    Chapter  Google Scholar 

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Correspondence to Alfons Laarman .

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Huybers, R., Laarman, A. (2019). A Parallel Relation-Based Algorithm for Symbolic Bisimulation Minimization. In: Enea, C., Piskac, R. (eds) Verification, Model Checking, and Abstract Interpretation. VMCAI 2019. Lecture Notes in Computer Science(), vol 11388. Springer, Cham. https://doi.org/10.1007/978-3-030-11245-5_25

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  • DOI: https://doi.org/10.1007/978-3-030-11245-5_25

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