Parameter Synthesis Through Temporal Logic Specifications

Part of the Lecture Notes in Computer Science book series (LNCS, volume 9109)

Abstract

Parameters are often used to tune mathematical models and capture nondeterminism and uncertainty in physical and engineering systems. This paper is concerned with parametric nonlinear dynamical systems and the problem of determining the parameter values that are consistent with some expected properties. In our previous works, we proposed a parameter synthesis algorithm limited to safety properties and demonstrated its applications for biological systems. Here we consider more general properties specified by a fragment of STL (Signal Temporal Logic), which allows us to deal with complex behavioral patterns that biological processes exhibit. We propose an algorithm for parameter synthesis w.r.t. a property specified using the considered logic. It exploits reachable set computations and forward refinements. We instantiate our algorithm in the case of polynomial dynamical systems exploiting Bernstein coefficients and we illustrate it on an epidemic model.

Keywords

Parameter synthesis STL Biological systems Reachability 

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References

  1. 1.
    Pnueli, A.: The temporal logic of programs. In: Symposium on Foundations of Computer Science, SFCS, pp. 46–57. IEEE (1977)Google Scholar
  2. 2.
    Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT press (1999)Google Scholar
  3. 3.
    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
  4. 4.
    Maler, O., Nickovic, D., Pnueli, A.: Checking temporal properties of discrete, timed and continuous behaviors. Pillars of Computer Science, 475–505 (2008)Google Scholar
  5. 5.
    Jones, K.D., Konrad, V., Nickovic, D.: Analog property checkers: a DDR2 case study. Formal Methods in System Design 36(2), 114–130 (2010)CrossRefMATHGoogle Scholar
  6. 6.
    Jin, X., Donzé, A., Deshmukh, J.V., Seshia, S.A.: Mining requirements from closed-loop control models. In: Proc. of International Conference on Hybrid Systems: Computation and Control, HSCC, pp. 43–52. ACM (2013)Google Scholar
  7. 7.
    Donzé, A., Fanchon, E., Gattepaille, L.M., Maler, O., Tracqui, P.: Robustness analysis and behavior discrimination in enzymatic reaction networks. PLOS One 6(9), e24246 (2011)Google Scholar
  8. 8.
    Stoma, S., Donzé, A., Bertaux, F., Maler, O., Batt, G.: STL-based Analysis of TRAIL-induced Apoptosis Challenges the Notion of Type I/Type II Cell Line Classification. PLoS Computational Biology 9(5), e1003056 (2013)Google Scholar
  9. 9.
    Asarin, E., Donzé, A., Maler, O., Nickovic, D.: Parametric identification of temporal properties. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 147–160. Springer, Heidelberg (2012)CrossRefGoogle Scholar
  10. 10.
    Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410(42), 4262–4291 (2009)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Bartocci, E., Bortolussi, L., Nenzi, L.: On the robustness of temporal properties for stochastic models. In: Hybrid Systems and Biology, HSB. EPTCS, vol. 125, pp. 3–19 (2013)Google Scholar
  12. 12.
    Chen, X., Ábrahám, E., Sankaranarayanan, S.: Flow*: An analyzer for non-linear hybrid systems. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 258–263. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  13. 13.
    Gao, S., Kong, S., Chen, W., Clarke, E.M.: Delta-complete analysis for bounded reachability of hybrid systems. CoRR abs/1404.7171 (2014)Google Scholar
  14. 14.
    Testylier, R., Dang, T.: NLTOOLBOX: A library for reachability computation of nonlinear dynamical systems. In: Van Hung, D., Ogawa, M. (eds.) ATVA 2013. LNCS, vol. 8172, pp. 469–473. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  15. 15.
    Donzé, A., Ferrère, T., Maler, O.: Efficient robust monitoring for STL. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 264–279. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  16. 16.
    De Giacomo, G., Vardi, M.Y.: Linear temporal logic and linear dynamic logic on finite traces. In: Proc. of Intenrational Joint Conference on Artificial Intelligence, IJCAI, IJCAI/AAAI (2013)Google Scholar
  17. 17.
    Dreossi, T., Dang, T.: Parameter synthesis for polynomial biological models. In: Proc. of International Conference on Hybrid Systems: Computation and Control, HSCC, pp. 233–242. ACM (2014)Google Scholar
  18. 18.
    Dang, T., Dreossi, T., Piazza, C.: Parameter synthesis using parallelotopic enclosure and applications to epidemic models (2014), http://www-verimag.imag.fr/~dreossi/docs/papers/hsb_2014.pdf
  19. 19.
    Asarin, E., Bournez, O., Dang, T., Maler, O.: Approximate reachability analysis of piecewise-linear dynamical systems. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, pp. 20–31. Springer, Heidelberg (2000)CrossRefGoogle Scholar
  20. 20.
    Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  21. 21.
    Bauer, C., Frink, A., Kreckel, R.: Introduction to the GiNaC framework for symbolic computation within the C++ programming language. Journal of Symbolic Computation 33(1), 1–12 (2002)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Chowell, G., Hengartner, N.W., Castillo-Chavez, C., Fenimore, P.W., Hyman, J.: The basic reproductive number of Ebola and the effects of public health measures: the cases of Congo and Uganda. Journal of Theoretical Biology 229(1), 119–126 (2004)CrossRefMathSciNetGoogle Scholar
  23. 23.
    Allen, L.J.: Some discrete-time SI, SIR, and SIS epidemic models. Mathematical Biosciences 124(1), 83–105 (1994)CrossRefMATHGoogle Scholar
  24. 24.
    Zhou, X., Li, X., Wang, W.-S.: Bifurcations for a deterministic sir epidemic model in discrete time. Advances in Difference Equations 2014(1), 1–16 (2014)CrossRefGoogle Scholar
  25. 25.
    Barnat, J., Brim, L., Krejci, A., Streck, A., Safranek, D., Vejnar, M., Vejpustek, T.: On parameter synthesis by parallel model checking. IEEE/ACM Trans. Comput. Biol. Bioinformatics 9(3), 693–705 (2012)CrossRefGoogle Scholar
  26. 26.
    Gallet, E., Manceny, M., Le Gall, P., Ballarini, P.: An LTL Model Checking Approach for Biological Parameter Inference. In: Merz, S., Pang, J. (eds.) ICFEM 2014. LNCS, vol. 8829, pp. 155–170. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  27. 27.
    Rizk, A., Batt, G., Fages, F., Soliman, S.: Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures. Theoretical Computer Science 412(26), 2827–2839 (2011)CrossRefMATHMathSciNetGoogle Scholar
  28. 28.
    Gratie, D.-E., Iancu, B., Petre, I.: ODE Analysis of Biological Systems. In: Bernardo, M., de Vink, E., Di Pierro, A., Wiklicky, H. (eds.) SFM 2013. LNCS, vol. 7938, pp. 29–62. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  29. 29.
    Češka, M., Dannenberg, F., Kwiatkowska, M., Paoletti, N.: Precise parameter synthesis for stochastic biochemical systems. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 86–98. Springer, Heidelberg (2014)CrossRefGoogle Scholar
  30. 30.
    Dreossi, T., Dang, T.: Falsifying oscillation properties of parametric biological models. In: Hybrid Systems and Biology, HSB. EPTCS, vol. 125, pp. 53–67 (2013)Google Scholar
  31. 31.
    Frehse, G., Jha, S.K., Krogh, B.H.: A counterexample-guided approach to parameter synthesis for linear hybrid automata. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 187–200. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  32. 32.
    André, É., Soulat, R.: Synthesis of timing parameters satisfying safety properties. In: Delzanno, G., Potapov, I. (eds.) RP 2011. LNCS, vol. 6945, pp. 31–44. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  33. 33.
    Yordanov, B., Belta, C.: Parameter synthesis for piecewise affine systems from temporal logic specifications. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 542–555. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  34. 34.
    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
  35. 35.
    Sankaranarayanan, S., Miller, C., Raghunathan, R., Ravanbakhsh, H., Fainekos, G.: A model-based approach to synthesizing insulin infusion pump usage parameters for diabetic patients. In: Proc. of Annual Allerton Conference on Communication, Control, and Computing. IEEE (2012)Google Scholar
  36. 36.
    Frehse, G., Le Guernic, C., Donzé, A., Cotton, S., Ray, R., Lebeltel, O., Ripado, R., Girard, A., Dang, T., Maler, O.: SpaceEx: Scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.VERIMAGGieresFrance
  2. 2.University of UdineUdineItaly

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