Parametric Identification of Temporal Properties

  • Eugene Asarin
  • Alexandre Donzé
  • Oded Maler
  • Dejan Nickovic
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7186)


Given a dense-time real-valued signal and a parameterized temporal logic formula with both magnitude and timing parameters, we compute the subset of the parameter space that renders the formula satisfied by the trace. We provide two preliminary implementations, one which follows the exact semantics and attempts to compute the validity domain by quantifier elimination in linear arithmetics and one which conducts adaptive search in the parameter space.


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  1. 1.
    Angluin, D., Smith, C.H.: Inductive inference: Theory and methods. ACM Comput. Surv. 15(3), 237–269 (1983)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Bishop, C.M.: Pattern Recognition and Machine Learning. Springer, Heidelberg (2006)zbMATHGoogle Scholar
  3. 3.
    Bozzelli, L., La Torre, S.: Decision Problems for Lower/Upper Bound Parametric Timed Automata. In: Arge, L., Cachin, C., Jurdziński, T., Tarlecki, A. (eds.) ICALP 2007. LNCS, vol. 4596, pp. 925–936. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  4. 4.
    Chan, W.: Temporal-Locig Queries. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 450–463. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  5. 5.
    Donzé, A.: Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  6. 6.
    Donzé, A., Clermont, G., Langmead, C.J.: Parameter synthesis in nonlinear dynamical systems: Application to systems biology. Journal of Computational Biology 17(3), 325–336 (2010)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Donzé, A., Krogh, B.H., Rajhans, A.: Parameter Synthesis for Hybrid Systems with an Application to Simulink Models. In: Majumdar, R., Tabuada, P. (eds.) HSCC 2009. LNCS, vol. 5469, pp. 165–179. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  8. 8.
    Donzé, A., Maler, O.: Robust Satisfaction of Temporal Logic over Real-Valued Signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  9. 9.
    Ehrgott, M.: Multicriteria optimization. Springer, Heidelberg (2005)zbMATHGoogle Scholar
  10. 10.
    Fages, F., Rizk, A.: From Model-Checking to Temporal Logic Constraint Solving. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 319–334. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410(42), 4262–4291 (2009)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Di Giampaolo, B., La Torre, S., Napoli, M.: Parametric Metric Interval Temporal Logic. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 249–260. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Jones, K.D., Konrad, V., Nickovic, D.: Analog property checkers: a ddr2 case study. Formal Methods in System Design 36(2), 114–130 (2010)zbMATHCrossRefGoogle Scholar
  14. 14.
    Lasaruk, A., Sturm, T.: Effective Quantifier Elimination for Presburger Arithmetic with Infinity. In: Gerdt, V.P., Mayr, E.W., Vorozhtsov, E.V. (eds.) CASC 2009. LNCS, vol. 5743, pp. 195–212. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  15. 15.
    Legriel, J., Le Guernic, C., Cotton, S., Maler, O.: Approximating the Pareto Front of Multi-criteria Optimization Problems. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 69–83. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  16. 16.
    Ljung, L.: System Identification - Theory For the User. Prentice Hall (1999)Google Scholar
  17. 17.
    Maler, O., Nickovic, D.: Monitoring Temporal Properties of Continuous Signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS 2004 and FTRTFT 2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  18. 18.
    Maler, O., Nickovic, D., Pnueli, A.: Checking Temporal Properties of Discrete, Timed and Continuous Behaviors. In: Avron, A., Dershowitz, N., Rabinovich, A. (eds.) Trakhtenbrot/Festschrift. LNCS, vol. 4800, pp. 475–505. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  19. 19.
    Monniaux, D.: A Quantifier Elimination Algorithm for Linear Real Arithmetic. In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 243–257. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  20. 20.
    Monniaux, D.: Automatic modular abstractions for linear constraints. In: POPL 2009, pp. 140–151. ACM (2009)Google Scholar
  21. 21.
    Nickovic, D., Maler, O.: AMT: A Property-Based Monitoring Tool for Analog Systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 304–319. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  22. 22.
    Pnueli, A.: The Temporal Semantics of Concurrent Programs. Theoretical Computer Science 13, 45–60 (1981)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: On a Continuous Degree of Satisfaction of Temporal Logic Formulae with Applications to Systems Biology. In: Heiner, M., Uhrmacher, A.M. (eds.) CMSB 2008. LNCS (LNBI), vol. 5307, pp. 251–268. Springer, Heidelberg (2008)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Eugene Asarin
    • 1
  • Alexandre Donzé
    • 2
  • Oded Maler
    • 2
  • Dejan Nickovic
    • 3
  1. 1.LIAFAUniversité Paris Diderot / CNRSParisFrance
  2. 2.VerimagUniversité Joseph Fourier / CNRSGiéresFrance
  3. 3.IST AustriaKlosterneuburgAustria

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