Skip to main content
SpringerLink
Log in
Book cover

International Conference on Integrated Formal Methods

IFM 2019: Integrated Formal Methods pp 27–45Cite as

Accelerating Parameter Synthesis Using Semi-algebraic Constraints

  • Conference paper
  • First Online:

  • 769 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 11918))

Abstract

We propose a novel approach to parameter synthesis for parametrised Kripke structures and CTL specifications. In our method, we suppose the parametrisations form a semi-algebraic set and we utilise a symbolic representation using the so-called cylindrical algebraic decomposition of corresponding multivariate polynomials. Specifically, we propose a new data structure allowing to compute and efficiently manipulate such representations. The new method is significantly faster than our previous method based on SMT. We apply the method to a set of rational dynamical systems representing complex biological mechanisms with non-linear behaviour.

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

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 EPUB and 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

References

  1. Arney, D., Pajic, M., Goldman, J.M., Lee, I., Mangharam, R., Sokolsky, O.: Toward patient safety in closed-loop medical device systems. In: ICCPS 10, pp. 139–148. ACM (2010). https://doi.org/10.1145/1795194.1795214

  2. Arnon, D.S., Collins, G.E., McCallum, S.: Cylindrical algebraic decomposition I: the basic algorithm. SIAM J. Comput. 13(4), 865–877 (1984)

    Article  MathSciNet  Google Scholar 

  3. Asarin, E., Dang, T., Girard, A.: Hybridization methods for the analysis of nonlinear systems. Acta Informatica 43, 451–476 (2007)

    Article  MathSciNet  Google Scholar 

  4. Barnat, J., et al.: On parameter synthesis by parallel model checking. IEEE/ACM Trans. Comput. Biol. Bioinf. 9(3), 693–705 (2012)

    Article  MathSciNet  Google Scholar 

  5. Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: System design of stochastic models using robustness of temporal properties. TCS 587, 3–25 (2015)

    Article  MathSciNet  Google Scholar 

  6. Batt, G., Page, M., Cantone, I., Goessler, G., Monteiro, P., de Jong, H.: Efficient parameter search for qualitative models of regulatory networks using symbolic model checking. Bioinformatics 26(18), i603–i610 (2010)

    Article  Google Scholar 

  7. Batt, G., Yordanov, B., Weiss, R., Belta, C.: Robustness analysis and tuning of synthetic gene networks. Bioinformatics 23(18), 2415–2422 (2007)

    Article  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  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. Bérard, B., Haddad, S., Picaronny, C., El Din, M.S., Sassolas, M.: Polynomial interrupt timed automata. In: Bojańczyk, M., Lasota, S., Potapov, I. (eds.) RP 2015. LNCS, vol. 9328, pp. 20–32. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-24537-9_3

    Chapter  Google Scholar 

  11. Bogomolov, S., Schilling, C., Bartocci, E., Batt, G., Kong, H., Grosu, R.: Abstraction-based parameter synthesis for multiaffine systems. In: Piterman, N. (ed.) HVC 2015. LNCS, vol. 9434, pp. 19–35. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26287-1_2

    Chapter  Google Scholar 

  12. Brim, L., Dluhoš, P., Šafránek, D., Vejpustek, T.: STL*: extending signal temporal logic with signal-value freezing operator. Inf. Comput. 236, 52–67 (2014). Special Issue on Hybrid Systems and Biology

    Article  MathSciNet  Google Scholar 

  13. Brim, L., Demko, M., Pastva, S., Šafránek, D.: High-performance discrete bifurcation analysis for piecewise-affine dynamical systems. In: Abate, A., Šafránek, D. (eds.) HSB 2015. LNCS, vol. 9271, pp. 58–74. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-26916-0_4

    Chapter  MATH  Google Scholar 

  14. Brim, L., Češka, M., Dražan, S., Šafránek, D.: Exploring parameter space of stochastic biochemical systems using quantitative model checking. In: Sharygina, N., Veith, H. (eds.) CAV 2013. LNCS, vol. 8044, pp. 107–123. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-39799-8_7

    Chapter  Google Scholar 

  15. Brown, C.W.: QEPCAD B: a program for computing with semi-algebraic sets using CADs. ACM SIGSAM Bull. 37(4), 97–108 (2003)

    Article  Google Scholar 

  16. Chen, C., Davenport, J.H., Moreno Maza, M., Xia, B., Xiao, R.: Computing with semi-algebraic sets represented by triangular decomposition. In: ISSAC 2011, pp. 75–82. ACM (2011)

    Google Scholar 

  17. Cimatti, A., Griggio, A., Sebastiani, R.: A simple and flexible way of computing small unsatisfiable cores in SAT modulo theories. In: Marques-Silva, J., Sakallah, K.A. (eds.) SAT 2007. LNCS, vol. 4501, pp. 334–339. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72788-0_32

    Chapter  MATH  Google Scholar 

  18. Clark, R.L., Cameron, J.C., Root, T.W., Pfleger, B.F.: Insights into the industrial growth of cyanobacteria from a model of the carbon? Concentrating mechanism. AIChE J. 60(4), 1269–1277 (2014)

    Article  Google Scholar 

  19. Collins, G.E., Akritas, A.G.: Polynomial real root isolation using Descarte’s rule of signs. In: SYMSAC 1976, pp. 272–275. ACM (1976)

    Google Scholar 

  20. Dang, T., Dreossi, T., Piazza, C.: Parameter synthesis through temporal logic specifications. In: Bjørner, N., de Boer, F. (eds.) FM 2015. LNCS, vol. 9109, pp. 213–230. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19249-9_14

    Chapter  Google Scholar 

  21. Dang, T., Guernic, C.L., Maler, O.: Computing reachable states for nonlinear biological models. Theor. Comput. Sci. 412(21), 2095–2107 (2011)

    Article  MathSciNet  Google Scholar 

  22. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24

    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. Donzé, A., Maler, O., Bartocci, E., Nickovic, D., Grosu, R., Smolka, S.: On temporal logic and signal processing. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, pp. 92–106. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33386-6_9

    Chapter  MATH  Google Scholar 

  25. Gao, S., Kong, S., Clarke, E.M.: dReal: an SMT solver for nonlinear theories over the reals. In: Bonacina, M.P. (ed.) CADE 2013. LNCS (LNAI), vol. 7898, pp. 208–214. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-38574-2_14

    Chapter  Google Scholar 

  26. 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 

  27. Guthmann, O., Strichman, O., Trostanetski, A.: Minimal unsatisfiable core extraction for SMT. In: FMCAD 2016, pp. 57–64. IEEE (2016)

    Google Scholar 

  28. de Jong, H., Gouzé, J., Hernandez, C., Page, M., Sari, T., Geiselmann, J.: Qualitative simulations of genetic regulatory networks using piecewise linear models. Bull. Math. Biol. 66, 301–340 (2004)

    Article  MathSciNet  Google Scholar 

  29. Liffiton, M.H., Sakallah, K.A.: Algorithms for computing minimal unsatisfiable subsets of constraints. J. Autom. Reasoning 40(1), 1–33 (2008)

    Article  MathSciNet  Google Scholar 

  30. Madsen, C., Shmarov, F., Zuliani, P.: BioPSy: an SMT-based tool for guaranteed parameter set synthesis of biological models. In: Roux, O., Bourdon, J. (eds.) CMSB 2015. LNCS, vol. 9308, pp. 182–194. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23401-4_16

    Chapter  Google Scholar 

  31. Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12

    Chapter  MATH  Google Scholar 

  32. McCallum, S.: Solving polynomial strict inequalities using cylindrical algebraic decomposition. Comput. J. 36(5), 432–438 (1993). https://doi.org/10.1093/comjnl/36.5.432

    Article  MathSciNet  MATH  Google Scholar 

  33. Milias-Argeitis, A., Engblom, S., Bauer, P., Khammash, M.: Stochastic focusing coupled with negative feedback enables robust regulation in biochemical reaction networks. J. Roy. Soc. Interface 12(113) (2015)

    Article  Google Scholar 

  34. Poslavsky, S.: Rings: an efficient Java/Scala library for polynomial rings. Comput. Phys. Commun. 235, 400–413 (2019)

    Article  Google Scholar 

  35. Raman, V., Donzé, A., Sadigh, D., Murray, R.M., Seshia, S.A.: Reactive synthesis from signal temporal logic specifications. In: HSCC 2015, pp. 239–248. ACM (2015)

    Google Scholar 

  36. Rizk, A., Batt, G., Fages, F., Soliman, S.: A general computational method for robustness analysis with applications to synthetic gene networks. Bioinformatics 25(12) (2009)

    Article  Google Scholar 

  37. Strzeboński, A.: Solving systems of strict polynomial inequalities. J. Symbolic Comput. 29(3), 471–480 (2000)

    Article  MathSciNet  Google Scholar 

  38. Strzebonski, A.W.: An algorithm for systems of strong polynomial inequalities. Mathe. J. 4(4), 74–77 (1994)

    Google Scholar 

  39. Swat, M., Kel, A., Herzel, H.: Bifurcation analysis of the regulatory modules of the mammalian G1/S transition. Bioinformatics 20(10), 1506–1511 (2004)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

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

    Nikola Beneš, Luboš Brim, Martin Geletka, Samuel Pastva & David Šafránek

Authors
  1. Nikola Beneš
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luboš Brim
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Martin Geletka
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Samuel Pastva
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. David Šafránek
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Samuel Pastva .

Editor information

Editors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Wolfgang Ahrendt

  2. University of Oslo, Oslo, Norway

    Silvia Lizeth Tapia Tarifa

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Beneš, N., Brim, L., Geletka, M., Pastva, S., Šafránek, D. (2019). Accelerating Parameter Synthesis Using Semi-algebraic Constraints. In: Ahrendt, W., Tapia Tarifa, S. (eds) Integrated Formal Methods. IFM 2019. Lecture Notes in Computer Science(), vol 11918. Springer, Cham. https://doi.org/10.1007/978-3-030-34968-4_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-34968-4_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-34967-7

  • Online ISBN: 978-3-030-34968-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation