Using Statistical Model Checking for Measuring Systems

  • Radu Grosu
  • Doron Peled
  • C. R. Ramakrishnan
  • Scott A. Smolka
  • Scott D. Stoller
  • Junxing Yang
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8803)


State spaces represent the way a system evolves through its different possible executions. Automatic verification techniques are used to check whether the system satisfies certain properties, expressed using automata or logic-based formalisms. This provides a Boolean indication of the system’s fitness. It is sometimes desirable to obtain other indications, measuring e.g., duration, energy or probability. Certain measurements are inherently harder than others. This can be explained by appealing to the difference in complexity of checking CTL and LTL properties. While the former can be done in time linear in the size of the property, the latter is PSPACE in the size of the property; hence practical algorithms take exponential time. While the CTL-type of properties measure specifications that are based on adjacency of states (up to a fixpoint calculation), LTL properties have the flavor of expecting some multiple complicated requirements from each execution sequence. In order to quickly measure LTL-style properties from a structure, we use a form of statistical model checking; we exploit the fact that LTL-style properties on a path behave like CTL-style properties on a structure. We then use CTL-based measuring on paths, and generalize the measurement results to the full structure using optimal Monte Carlo estimation techniques. To experimentally validate our framework, we present measurements for a flocking model of bird-like agents.


Monte Carlo Model Check Temporal Logic Linear Temporal Logic Quantitative Property 
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.


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  1. 1.
    Chatterjee, K., Doyen, L., Henzinger, T.A.: Expressiveness and closure properties for quantitative languages. Logical Methods in Computer Science 6(3) (2010)Google Scholar
  2. 2.
    Conley, J.F.: Evolving boids: Using a genetic algorithm to develop boid behaviors. In: Proceedings of the 8th International Conference on GeoComputation (GeoComputation 2005) (2005),
  3. 3.
    Cucker, F., Dong, J.G.: A general collision-avoiding flocking framework. IEEE Trans. on Automatic Control 56(5), 1124–1129 (2011)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Cucker, F., Smale, S.: Emergent behavior in flocks. IEEE Trans. on Automatic Control 52(5), 852–862 (2007)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Dagum, P., Karp, R., Luby, M., Ross, S.: An optimal algorithm for Monte Carlo estimation. SIAM Journal on Computing 29(5), 1484–1496 (2000)MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Emerson, E.A., Clarke, E.M.: Characterizing correctness properties of parallel programs using fixpoints. In: de Bakker, J.W., van Leeuwen, J. (eds.) ICALP 1980. LNCS, vol. 85, pp. 169–181. Springer, Heidelberg (1980)CrossRefGoogle Scholar
  7. 7.
    Finkbeiner, B., Sankaranarayanan, S., Sipma, H.: Collecting statistics over runtime executions. Formal Methods in System Design 27(3), 253–274 (2005)CrossRefzbMATHGoogle Scholar
  8. 8.
    Gerth, R., Peled, D., Vardi, M.Y., Wolper, P.: Simple on-the-fly automatic verification of linear temporal logic. In: PSTV, pp. 3–18 (1995)Google Scholar
  9. 9.
    Grosu, R., Smolka, S.: Quantitative model checking. In: Proc. of the 1st International Symposium on Leveraging Applications of Formal Methods (ISOLA 2004), Paphos, Cyprus, pp. 165–174 (November 2004)Google Scholar
  10. 10.
    Grosu, R., Peled, D., Ramakrishnan, C.R., Smolka, S.A., Stoller, S.D., Yang, J.: Compositional branching-time measurements. In: Bensalem, S., Lakhneck, Y., Legay, A. (eds.) From Programs to Systems. LNCS, vol. 8415, pp. 118–128. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  11. 11.
    Hérault, T., Lassaigne, R., Magniette, F., Peyronnet, S.: Approximate probabilistic model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 73–84. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  12. 12.
    Karp, R., Luby, M., Madras, N.: Monte-Carlo approximation algorithms for enumeration problems. Journal of Algorithms 10, 429–448 (1989)MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Latvala, T., Biere, A., Heljanko, K., Junttila, T.A.: Simple bounded LTL model checking. In: Hu, A.J., Martin, A.K. (eds.) FMCAD 2004. LNCS, vol. 3312, pp. 186–200. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Legay, A., Delahaye, B., Bensalem, S.: Statistical model checking: An overview. In: Barringer, H., et al. (eds.) RV 2010. LNCS, vol. 6418, pp. 122–135. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  15. 15.
    Olfati-Saber, R.: Flocking for multi-agent dynamic systems: Algorithms and theory. IEEE Trans. on Automatic Control 51(3), 401–420 (2006)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Penczek, W., Wozna, B., Zbrzezny, A.: Bounded model checking for the universal fragment of ctl. Fundam. Inf. 51(1), 135–156 (2002)MathSciNetzbMATHGoogle Scholar
  17. 17.
    Pnueli, A.: The temporal logic of programs. In: FOCS, pp. 46–57 (1977)Google Scholar
  18. 18.
    Pnueli, A., Zaks, A.: PSL model checking and run-time verification via testers. In: Misra, J., Nipkow, T., Sekerinski, E. (eds.) FM 2006. LNCS, vol. 4085, pp. 573–586. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  19. 19.
    Reynolds, C.W.: Flocks, herds and schools: A distributed behavioral model. In: Proceedings of the 14th Annual Conference on Computer Graphics and Interactive Techniques (SIGGRAPH 1987), pp. 25–34. ACM (1987)Google Scholar
  20. 20.
    Stonedahl, F., Wilensky, U.: Finding forms of flocking: Evolutionary search in ABM parameter-spaces. In: Bosse, T., Geller, A., Jonker, C.M. (eds.) MABS 2010. LNCS, vol. 6532, pp. 61–75. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Vicsek, T., Czirók, A., Ben-Jacob, E., Cohen, I., Shochet, O.: Novel type of phase transition in a system of self-driven particles. Physical Review Letters 75, 1226–1229 (1995)CrossRefGoogle Scholar
  22. 22.
    Younes, H.K.L.: Verification and Planning for Stochastic Processes. Ph.D. thesis, Carnegie Mellon (2005)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Radu Grosu
    • 1
  • Doron Peled
    • 2
  • C. R. Ramakrishnan
    • 3
  • Scott A. Smolka
    • 3
  • Scott D. Stoller
    • 3
  • Junxing Yang
    • 3
  1. 1.Vienna University of TechnologyAustria
  2. 2.Department of Computer ScienceBar Ilan UniversityIsrael
  3. 3.Department of Computer ScienceStony Brook UniversityUSA

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