Skip to main content
SpringerLink
Log in
Book cover

International Symposium on Formal Methods

FM 2015: FM 2015: Formal Methods pp 213–230Cite as

Parameter Synthesis Through Temporal Logic Specifications

  • Conference paper

Part of the book series: Lecture Notes in Computer Science ((LNPSE,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.

This work has been partially supported by GNCS-INDAM project “Algoritmica per il model checking e la sintesi di sistemi safety-critical”.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Pnueli, A.: The temporal logic of programs. In: Symposium on Foundations of Computer Science, SFCS, pp. 46–57. IEEE (1977)

    Google Scholar 

  2. Clarke, E.M., Grumberg, O., Peled, D.: Model checking. MIT press (1999)

    Google Scholar 

  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)

    Chapter  Google Scholar 

  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. Jones, K.D., Konrad, V., Nickovic, D.: Analog property checkers: a DDR2 case study. Formal Methods in System Design 36(2), 114–130 (2010)

    Article  MATH  Google Scholar 

  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. 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. 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. 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)

    Chapter  Google Scholar 

  10. Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theoretical Computer Science 410(42), 4262–4291 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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. 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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  23. Allen, L.J.: Some discrete-time SI, SIR, and SIS epidemic models. Mathematical Biosciences 124(1), 83–105 (1994)

    Article  MATH  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. VERIMAG, 2 avenue de Vignate, 38610, Gieres, France

    Thao Dang & Tommaso Dreossi

  2. University of Udine, via delle Scienze, 206, 33100, Udine, Italy

    Tommaso Dreossi & Carla Piazza

Authors
  1. Thao Dang
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tommaso Dreossi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Carla Piazza
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Thao Dang .

Editor information

Editors and Affiliations

  1. Microsoft Research, Redmond, Washington, USA

    Nikolaj Bjørner

  2. Centrum voor Wiskunde en Informatica, Amsterdam, The Netherlands

    Frank de Boer

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Dang, T., Dreossi, T., Piazza, C. (2015). Parameter Synthesis Through Temporal Logic Specifications. In: Bjørner, N., de Boer, F. (eds) FM 2015: Formal Methods. FM 2015. Lecture Notes in Computer Science(), vol 9109. Springer, Cham. https://doi.org/10.1007/978-3-319-19249-9_14

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-19249-9_14

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-19248-2

  • Online ISBN: 978-3-319-19249-9

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation