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Analysing oscillatory trends of discrete-state stochastic processes through HASL statistical model checking

  • Paolo BallariniEmail author
SMC

Abstract

The application of formal methods to the analysis of stochastic oscillators has been at the focus of several research works in recent times. In this paper, we provide insights on the application of an expressive temporal logic formalism, namely the hybrid automata stochastic logic (HASL), to that issue. We show how one can take advantage of the expressive power of the HASL logic to define and assess relevant characteristics of (stochastic) oscillators.

Keywords

Statistical model checking Hybrid automata stochastic logic Oscillation analysis Confidence-interval estimates Discrete event stochastic processes 

References

  1. 1.
    Ajmone Marsan, M., Balbo, G., Conte, G., Donatelli, S., Franceschinis, G.: Modelling with Generalized Stochastic Petri Nets. Wiley, London (1995)zbMATHGoogle Scholar
  2. 2.
    Alur, R., Courcoubetis, C., Dill, D.: Model-checking for probabilistic real-time systems. In: ICALP’91, LNCS 510 (1991)Google Scholar
  3. 3.
    Andrei, O., Calder, M.: Trend-based analysis of a population model of the akap scaffold protein. Trans. Compt. Syst. Biol. 14, 1–25 (2012)CrossRefGoogle Scholar
  4. 4.
    Baier, C., Haverkort, B., Hermanns, H., Katoen, J.-P.: Model-checking algorithms for CTMCs. IEEE Trans. Softw. Eng. 29(6), 524–541 (2003)Google Scholar
  5. 5.
    Ballarini, P., Djafri, H., Duflot, M., Haddad, S., Pekergin, N.: COSMOS: A statistical model checker for the hybrid automata stochastic logic. In: Proceedings of the 8th international conference on quantitative evaluation of systems (QEST’11), pp. 143–144. IEEE Computer Society Press (2011)Google Scholar
  6. 6.
    Ballarini, P., Djafri, H., Duflot, M., Haddad, S., Pekergin, N.: HASL: an expressive language for statistical verification of stochastic models. In: Proceedings of Valuetools (2011)Google Scholar
  7. 7.
    Ballarini, P., Guerriero, M.: Query-based verification of qualitative trends and oscillations in biochemical systems. Theor. Comput. Sci. 411(20), 2019–2036 (2010)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Bulychev, P.E., David, A., Larsen, K.G., Mikucionis, M., Poulsen, D.B., Legay, A., Wang, Z.: Uppaal-SMC: statistical model checking for priced timed automata. In: Proceedings 10th workshop on quantitative aspects of programming languages and systems, volume 85 of EPTCS, pp. 1–16 (2012)Google Scholar
  9. 9.
    Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Quantitative model checking of CTMC against timed automata specifications. In: Proceedings of LICS’09 (2009)Google Scholar
  10. 10.
    CosyVerif home page. http://www.cosyverif.org
  11. 11.
  12. 12.
    David, A., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Runtime verification of biological systems. ISoLA 1, 388–404 (2012)Google Scholar
  13. 13.
    Donatelli, S., Haddad, S., Sproston, J.: Model checking timed and stochastic properties with \(CSL^{TA}\). IEEE Trans. Softw. Eng., 35, 224–240 (2009)Google Scholar
  14. 14.
    Glynn, P.W.: On the role of generalized semi-Markov processes in simulation output analysis. In: Proceedings of conference winter simulation (1983)Google Scholar
  15. 15.
    Herault, T., Lassaigne, R., Peyronnet, S.: APMC 3.0: Approximate verification of discrete and continuous time Markov chains. In: Proceedings of QEST’06 (2006)Google Scholar
  16. 16.
    Ihekwaba, A., Sedwards, S.: Communicating oscillatory networks: frequency domain analysis. BMC Syst. Biol. 5(1), 203 (2011)CrossRefGoogle Scholar
  17. 17.
    Jégourel, C., Legay, A., Sedwards, S.: A platform for high performance statistical model checking-plasma. In: TACAS, Volume 7214 of Lecture Notes in Computer Science, pp. 498–503 (2012)Google Scholar
  18. 18.
    Júlvez, J., Kwiatkowska, M., Norman, G., Parker, D.: Evaluation of sustained stochastic oscillations by means of a system of differential equations. Int. J. Comput Appl. (IJCA) 19(2), 101–111 (2012)Google Scholar
  19. 19.
    Katoen, J.P., Zapreev, I.S.: Simulation-based CTMC model checking: an empirical evaluation. In: Proceedings of QEST’09 (2009)Google Scholar
  20. 20.
    Knuth, D.E.: The Art of Computer Programming, Volume 2 (3rd Ed.): Seminumerical Algorithms. Addison-Wesley Longman Publishing Co., Inc, Boston (1997)Google Scholar
  21. 21.
    Kwiatkowska, M., Norman, G., Parker, D.: Stochastic model checking. In: Formal Methods for the Design of Computer, Communication and Software Systems: Performance Evaluation, volume 4486 of LNCS, pp. 220–270, Springer, Berlin (2007)Google Scholar
  22. 22.
  23. 23.
    Sen, K., Viswanathan, M., Agha, G.: VESTA: A statistical model-checker and analyzer for probabilistic systems. In: Proceedings of QEST’05 (2005)Google Scholar
  24. 24.
    Spieler, D. : Model checking of oscillatory and noisy periodic behavior in markovian population models. Master’s thesis, Saarland University (2009)Google Scholar
  25. 25.
    Spieler, D.: Characterizing oscillatory and noisy periodic behavior in markov population models. In: Proceedings of QEST’13 (2013)Google Scholar
  26. 26.
    Vilar, J., Kueh, H.-Y., Barkai, N., Leibler, S.: Mechanisms of noise-resistance in genetic oscillators. Proc. Natl. Acad. Sci. USA 99(9), 5988–5992 (2002)CrossRefGoogle Scholar
  27. 27.
    Ymer, H.L. Younes.: A statistical model checker. In: Computer Aided Verification, pp. 429–433, Springer, Berlin (2005)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.Centrale SupélecChâtenay-MalabryFrance

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