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Parallel Parameter Synthesis for Multi-affine Hybrid Systems from Hybrid CTL Specifications

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Computational Methods in Systems Biology (CMSB 2020)

Part of the book series: Lecture Notes in Computer Science ((LNBI,volume 12314))

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Abstract

We consider the parameter synthesis problem for multi-affine hybrid systems and properties specified using a hybrid extension of CTL (HCTL). The goal is to determine the sets of parameter valuations for which the given hybrid system satisfies the desired HCTL property. As our main contribution, we propose a shared-memory parallel algorithm which efficiently computes such parameter valuation sets. We combine a rectangular discretisation of the continuous dynamics with the discrete transitions of the hybrid system to obtain a single over-approximating semi-symbolic transition system. Such system can be then analysed using a fixed-point parameter synthesis algorithm to obtain all satisfying parametrisations. We evaluate the scalability of the method and demonstrate its applicability in a biological case study.

L. Brim–This work has been supported by the Czech Science Foundation grant No. 18-00178S.

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References

  1. André, É.: IMITATOR: a tool for synthesizing constraints on timing bounds of timed automata. In: Leucker, M., Morgan, C. (eds.) ICTAC 2009. LNCS, vol. 5684, pp. 336–342. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03466-4_22

    Chapter  Google Scholar 

  2. Arellano, G., et al.: “Antelope”: a hybrid-logic model checker for branching-time Boolean GRN analysis. BMC Bioinform. 12(1), 490 (2011)

    Article  Google Scholar 

  3. Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: On the robustness of temporal properties for stochastic models. In: Dang, T., Piazza, C. (eds.) Proceedings Second International Workshop on Hybrid Systems and Biology, HSB 2013, Taormina, Italy, 2nd September 2013. EPTCS, vol. 125, pp. 3–19 (2013)

    Google Scholar 

  4. Batt, G., Belta, C., Weiss, R.: Model checking genetic regulatory networks with parameter uncertainty. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 61–75. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71493-4_8

    Chapter  Google Scholar 

  5. Belta, C.: On controlling aircraft and underwater vehicles. In: Proceedings of the IEEE International Conference on Robotics and Automation, vol. 5, pp. 4905–4910 (2004)

    Google Scholar 

  6. Belta, C., Habets, L.: Controlling a class of nonlinear systems on rectangles. IEEE Trans. Autom. Control 51(11), 1749–1759 (2006)

    Article  MathSciNet  Google Scholar 

  7. Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: A model checking approach to discrete bifurcation analysis. In: Fitzgerald, J., Heitmeyer, C., Gnesi, S., Philippou, A. (eds.) FM 2016. LNCS, vol. 9995, pp. 85–101. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-48989-6_6

    Chapter  Google Scholar 

  8. Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: Parallel SMT-based parameter synthesis with application to piecewise multi-affine systems. In: Artho, C., Legay, A., Peled, D. (eds.) ATVA 2016. LNCS, vol. 9938, pp. 192–208. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-46520-3_13

    Chapter  MATH  Google Scholar 

  9. Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: Pithya: a parallel tool for parameter synthesis of piecewise multi-affine dynamical systems. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 591–598. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_29

    Chapter  Google Scholar 

  10. Beneš, N., Brim, L., Pastva, S., Šafránek, D.: Parallel parameter synthesis algorithm for hybrid CTL. Sci. Comput. Program. 185, 102321 (2019)

    Article  Google Scholar 

  11. Beneš, N., Brim, L., Demko, M., Pastva, S., Šafránek, D.: Pithya: a parallel tool for parameter synthesis of piecewise multi-affine dynamical systems. Int. J. Struct. Stab. Dyn. (2017)

    Google Scholar 

  12. Bogomolov, S., Schilling, C., Bartocci, E., Batt, G., Kong, H., Grosu, R.: Abstraction-based parameter synthesis for multiaffine systems. Hardw. Softw.: Verif. Test. 11, 19–35 (2015)

    Google Scholar 

  13. Bortolussi, L., Milios, D., Sanguinetti, G.: U-Check: model checking and parameter synthesis under uncertainty. In: Campos, J., Haverkort, B.R. (eds.) QEST 2015. LNCS, vol. 9259, pp. 89–104. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-22264-6_6

    Chapter  Google Scholar 

  14. Bortolussi, L., Policriti, A.: Hybrid systems and biology. In: Bernardo, M., Degano, P., Zavattaro, G. (eds.) SFM 2008. LNCS, vol. 5016, pp. 424–448. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-68894-5_12

    Chapter  Google Scholar 

  15. Bortolussi, L., Sanguinetti, G.: Smoothed model checking for uncertain continuous time Markov chains. CoRR abs/1402.1450 (2014)

    Google Scholar 

  16. Brim, L., Češka, M., Demko, M., Pastva, S., Šafránek, D.: Parameter synthesis by parallel coloured CTL model checking. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 251–263. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23401-4_21

    Chapter  Google Scholar 

  17. Calzone, L., Fages, F., Soliman, S.: BIOCHAM: an environment for modeling biological systems and formalizing experimental knowledge. Bioinformatics 22(14), 1805–1807 (2006)

    Article  Google Scholar 

  18. Chiang, H.K., Fages, F., Jiang, J.R., Soliman, S.: Hybrid simulations of heterogeneous biochemical models in SBML. ACM Trans. Model. Comput. Simul. 25(2), 14:1–14:22 (2015)

    Google Scholar 

  19. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_15

    Chapter  Google Scholar 

  20. Clarke Jr., E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT Press, Cambridge (1999)

    MATH  Google Scholar 

  21. Demko, M., Beneš, N., Brim, L., Pastva, S., Šafránek, D.: High-performance symbolic parameter synthesis of biological models: a case study. In: Bartocci, E., Lio, P., Paoletti, N. (eds.) CMSB 2016. LNCS, vol. 9859, pp. 82–97. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45177-0_6

    Chapter  Google Scholar 

  22. 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). https://doi.org/10.1007/978-3-642-14295-6_17

    Chapter  Google Scholar 

  23. Donzé, A., Krogh, B., 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). https://doi.org/10.1007/978-3-642-00602-9_12

    Chapter  MATH  Google Scholar 

  24. 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). https://doi.org/10.1007/978-3-642-04244-7_26

    Chapter  Google Scholar 

  25. 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). https://doi.org/10.1007/978-3-540-78929-1_14

    Chapter  MATH  Google Scholar 

  26. Frehse, G., et al.: SpaceEx: scalable verification of hybrid systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 379–395. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_30

    Chapter  Google Scholar 

  27. Fribourg, L., Kühne, U.: Parametric verification and test coverage for hybrid automata using the inverse method. In: Delzanno, G., Potapov, I. (eds.) RP 2011. LNCS, vol. 6945, pp. 191–204. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24288-5_17

    Chapter  Google Scholar 

  28. Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT solver for nonlinear theories over the reals. In: Automated Deduction - CADE-24, pp. 208–214 (2013)

    Google Scholar 

  29. Grosu, R., et al.: From cardiac cells to genetic regulatory networks. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 396–411. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22110-1_31

    Chapter  Google Scholar 

  30. Henzinger, T.A.: The theory of hybrid automata. In: Proceedings 11th Annual IEEE Symposium on Logic in Computer Science, pp. 278–292, July 1996

    Google Scholar 

  31. Islam, M.A., et al.: Bifurcation analysis of cardiac alternans using \(\delta \)-decidability. In: Bartocci, E., Lio, P., Paoletti, N. (eds.) CMSB 2016. LNCS, vol. 9859, pp. 132–146. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-45177-0_9

    Chapter  Google Scholar 

  32. de Jong, H.: Modeling and simulation of genetic regulatory systems: a literature review. J. Comput. Biol. 9(1), 67–103 (2002)

    Article  MathSciNet  Google Scholar 

  33. Kong, S., Gao, S., Chen, W., Clarke, E.: dReach: \(\delta \)-reachability analysis for hybrid systems. In: Baier, C., Tinelli, C. (eds.) TACAS 2015. LNCS, vol. 9035, pp. 200–205. Springer, Heidelberg (2015). https://doi.org/10.1007/978-3-662-46681-0_15

    Chapter  Google Scholar 

  34. Lincoln, P., Tiwari, A.: Symbolic systems biology: hybrid modeling and analysis of biological networks. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 660–672. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-24743-2_44

    Chapter  MATH  Google Scholar 

  35. Liu, B., Kong, S., Gao, S., Zuliani, P., Clarke, E.M.: Parameter synthesis for cardiac cell hybrid models using \(\delta \)–decisions. In: Mendes, P., Dada, J.O., Smallbone, K. (eds.) CMSB 2014. LNCS, vol. 8859, pp. 99–113. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-12982-2_8

    Chapter  Google Scholar 

  36. Liu, L., Bockmayr, A.: Formalizing metabolic-regulatory networks by hybrid automata. bioRxiv (2019)

    Google Scholar 

  37. Liu, X., Stechlinski, P.: Infectious Disease Modeling. Springer, Cham (2020). https://doi.org/10.1007/978-3-319-53208-0

    Book  MATH  Google Scholar 

  38. Rizk, A., Batt, G., Fages, F., Soliman, S.: Continuous valuations of temporal logic specifications with applications to parameter optimization and robustness measures. Theor. Comput. Sci. 412(26), 2827–2839 (2011). Foundations of Formal Reconstruction of Biochemical Networks

    Google Scholar 

  39. Stéphanou, A., Volpert, V.: Hybrid modelling in biology: a classification review. Math. Model. Nat. Phenom. 11(1), 37–48 (2016)

    Article  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Faculty of Informatics, Masaryk University, Brno, Czech Republic

    Eva Šmijáková, Samuel Pastva, David Šafránek & Luboš Brim

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  1. Eva Šmijáková
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  2. Samuel Pastva
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Correspondence to David Šafránek .

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Editors and Affiliations

  1. Department of Computer Science, University of Oxford, Oxford, UK

    Alessandro Abate

  2. Department of Computer and Information Science, University of Konstanz, Konstanz, Germany

    Tatjana Petrov

  3. Department of Computer Science, Saarland University, Saarbrücken, Germany

    Verena Wolf

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Šmijáková, E., Pastva, S., Šafránek, D., Brim, L. (2020). Parallel Parameter Synthesis for Multi-affine Hybrid Systems from Hybrid CTL Specifications. In: Abate, A., Petrov, T., Wolf, V. (eds) Computational Methods in Systems Biology. CMSB 2020. Lecture Notes in Computer Science(), vol 12314. Springer, Cham. https://doi.org/10.1007/978-3-030-60327-4_15

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  • DOI: https://doi.org/10.1007/978-3-030-60327-4_15

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