Abstract
Generic representatives have been proposed for the effective combination of symmetry reduction and symbolic representation with BDDs in non-probabilistic model checking. This approach involves the translation of a symmetric source program into a reduced program, in which counters are used to generically represent states of the original model. Symmetric properties of the original program can also be translated, and checked directly over the reduced program. We extend this approach to apply to probabilistic systems with Markov decision process or discrete time Markov chain semantics, represented as MTBDDs. We have implemented a prototype tool, GRIP, which converts a symmetric PRISM program and PCTL property into reduced form. Model checking results for the original program can then be inferred by applying PRISM, unchanged, to the smaller model underlying the reduced program. We present encouraging experimental results for two case studies.
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References
Baier, C., Ciesinski, F., Größer, M.: ProbMela and verification of Markov decision processes. SIGMETRICS Performance Evaluation Review 32(4), 22–27 (2005)
Baier, C., Kwiatkowska, M.: Model checking for a probabilistic branching time logic with fairness. Distributed Computing 11, 125–155 (1998)
Barner, S., Grumberg, O.: Combining symmetry reduction and under-approximation for symbolic model checking. Formal Methods in System Design 27(1–2), 29–66 (2005)
Bosnacki, D., Dams, D., Holenderski, L.: Symmetric spin. International Journal on Software Tools for Technology Transfer 4(1), 65–80 (2002)
Clarke, E.M., Emerson, E.A., Jha, S., Sistla, A.P.: Symmetry reductions in model checking. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 147–158. Springer, Heidelberg (1998)
Clarke, E.M., Enders, R., Filkhorn, T., Jha, S.: Exploiting symmetry in temporal logic model checking. Formal Methods in System Design 9(1–2), 77–104 (1996)
Dolev, S., Israeli, A., Moran, S.: Analysing expected time by scheduler-luck games. IEEE Transactions on Software Engineering 21(5), 429–439 (1995)
Donaldson, A.F., Miller, A.: Symmetry reduction for probabilistic systems. In: Proc. 12th Workshop on Automated Reasoning, pp. 17–18 (2005)
Donaldson, A.F., Miller, A.: Exact and approximate strategies for symmetry reduction in model checking. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 541–556. Springer, Heidelberg (2006)
Emerson, E.A., Sistla, A.P.: Utilizing symmetry when model-checking under fairness assumptions: an automata-theoretic approach. ACM Transactions on Programming Languages and Systems 19(4), 617–638 (1997)
Emerson, E.A., Trefler, R.J.: From asymmetry to full symmetry: new techniques for symmetry reduction in model checking. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 142–156. Springer, Heidelberg (1999)
Emerson, E.A., Wahl, T.: On combining symmetry reduction and symbolic representation for efficient model checking. In: Geist, D., Tronci, E. (eds.) CHARME 2003. LNCS, vol. 2860, pp. 216–230. Springer, Heidelberg (2003)
Emerson, E.A., Wahl, T.: Dynamic symmetry reduction. In: Halbwachs, N., Zuck, L.D. (eds.) TACAS 2005. LNCS, vol. 3440, pp. 382–396. Springer, Heidelberg (2005)
Emerson, E.A., Wahl, T.: Efficient reduction techniques for systems with many components. Electronic Notes in Theoretical Computer Science 130, 379–399 (2005)
Gagnon, E., Hendren, L.J.: SableCC, an object-oriented compiler framework. In: TOOLS 1998, pp. 140–154. IEEE Computer Society Press, Los Alamitos (1998)
GRIP website, http://www.dcs.gla.ac.uk/people/personal/ally/grip/
Hansson, H., Jonsson, B.: A logic for reasoning about time and reliability. Formal Aspects of Computing 6(4), 512–535 (1994)
Hinton, A., Kwiatkowska, M., Norman, G., Parker, D.: PRISM: a tool for automatic verification of probabilistic systems. In: Hermanns, H., Palsberg, J. (eds.) TACAS 2006. LNCS, vol. 3920, pp. 441–444. Springer, Heidelberg (2006)
Ip, C.N., Dill, D.L.: Better verification through symmetry. Formal Methods in System Design 9(1/2), 41–75 (1996)
Kwiatkowska, M., Norman, G., Parker, D.: Symmetry reduction for probabilistic model checking. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144. Springer, Heidelberg (2006)
Larsen, K., Skou, A.: Bisimulation through probabilistic testing. Information and Computation 94, 1–28 (1991)
Miller, A., Donaldson, A., Calder, M.: Symmetry in temporal logic model checking. Computing Surveys (to appear, 2006)
PRISM website, http://www.cs.bham.ac.uk/~dxp/prism/
Pnueli, A., Zuck, L.: Verification of multiprocess probabilistic protocols. Distributed Computing 1(1), 53–72 (1986)
Rutten, J.J.M.M., Kwiatkowska, M., Norman, G., Parker, D.: Mathematical Techniques for Analyzing Concurrent and Probabilistic Systems. CRM Monograph Series, vol. 23. American Mathematical Society (2004)
Segala, R., Lynch, N.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)
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Donaldson, A.F., Miller, A. (2006). Symmetry Reduction for Probabilistic Model Checking Using Generic Representatives. In: Graf, S., Zhang, W. (eds) Automated Technology for Verification and Analysis. ATVA 2006. Lecture Notes in Computer Science, vol 4218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901914_4
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DOI: https://doi.org/10.1007/11901914_4
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