Abstract
Symmetry reduction is an established method for limiting the amount of states that have to be checked during exhaustive model checking. The idea is to only verify a single representative of every class of symmetric states. However, computing this representative can be non-trivial, especially for a language such as B with its involved data structures and operations. In this paper, we propose an alternate approach, called permutation flooding. It works by computing permutations of newly encountered states, and adding them to the state space. This turns out to be relatively unproblematic for B’s data structures and we have implemented the algorithm inside the ProB model checker. Empirical results confirm that this approach is effective in practice; speedups exceed an order of magnitude in some cases. The paper also contains correctness results of permutation flooding, which should also be applicable for classical symmetry reduction in B.
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References
Abrial, J.-R.: The B-Book. Cambridge University Press, Cambridge (1996)
Aloul, F.A., Ramani, A., Markov, I.L., Sakallah, K.A.: Solving difficult SAT instances in the presence of symmetry. In: DAC, pp. 731–736. ACM Press, New York (2002)
Aloul, F.A., Sakallah, K.A., Markov, I.L.: Efficient symmetry breaking for boolean satisfiability. IEEE Trans. Computers 55(5), 549–558 (2006)
Butler, M., Leuschel, M.: Combining CSP and B for specification and property verification. In: Fitzgerald, J.S., Hayes, I.J., Tarlecki, A. (eds.) FM 2005. LNCS, vol. 3582, pp. 221–236. Springer, Heidelberg (2005)
Clarke, E.M., Filkorn, T., Jha, S.: Exploiting symmetry in temporal logic model checking. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 450–462. Springer, Heidelberg (1993)
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (1999)
Crawford, J.M., Ginsberg, M.L., Luks, E.M., Roy, A.: Symmetry-breaking predicates for search problems. In: KR 1996, pp. 148–159 (1996)
Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting structure in symmetry detection for CNF. In: Malik, S., Fix, L., Kahng, A.B. (eds.) DAC, pp. 530–534. ACM Press, New York (2004)
Emerson, E.A., Sistla, A.P.: Symmetry and model checking. Formal Methods in System Design 9(1/2), 105–131 (1996)
Flannery, S.: In Code: A Mathematical Adventure. Profile Books Ltd (2001)
Ip, C.N., Dill, D.L.: Better verification through symmetry. In: Computer Hardware Description Languages and their Applications, pp. 97–111 (1993)
Kreher, D.L., Stinson, D.R.: Combinatorial Algorithms: Generation, Enumeration, Search. CRC Press, Boca Raton (1999)
Legeard, B., Peureux, F., Utting, M.: Automated boundary testing from Z and B. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME 2002. LNCS, vol. 2391, pp. 21–40. Springer, Heidelberg (2002)
Leuschel, M., Butler, M.: ProB: A model checker for B. In: Araki, K., Gnesi, S., Mandrioli, D. (eds.) FME 2003. LNCS, vol. 2805, pp. 855–874. Springer, Heidelberg (2003)
Leuschel, M., Butler, M.: Automatic refinement checking for B. In: Lau, K.-K., Banach, R. (eds.) ICFEM 2005. LNCS, vol. 3785, pp. 345–359. Springer, Heidelberg (2005)
McKay, B.: Nauty users guide, Available at: http://cs.anu.edu.au/people/bdm/nauty/
Sistla, A.P.: Employing symmetry reductions in model checking. Computer Languages, Systems & Structures 30(3-4), 99–137 (2004)
Sistla, A.P., Godefroid, P.: Symmetry and reduced symmetry in model checking. ACM Trans. Program. Lang. Syst. 26(4), 702–734 (2004)
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Leuschel, M., Butler, M., Spermann, C., Turner, E. (2006). Symmetry Reduction for B by Permutation Flooding. In: Julliand, J., Kouchnarenko, O. (eds) B 2007: Formal Specification and Development in B. B 2007. Lecture Notes in Computer Science, vol 4355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11955757_9
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DOI: https://doi.org/10.1007/11955757_9
Publisher Name: Springer, Berlin, Heidelberg
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