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Data-Driven Statistical Learning of Temporal Logic Properties

  • Conference paper
Formal Modeling and Analysis of Timed Systems (FORMATS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8711))

Abstract

We present a novel approach to learn logical formulae characterising the emergent behaviour of a dynamical system from system observations. At a high level, the approach starts by devising a data-driven statistical abstraction of the system. We then propose general optimisation strategies for selecting formulae with high satisfaction probability, either within a discrete set of formulae of bounded complexity, or a parametric family of formulae. We illustrate and apply the methodology on two real world case studies: characterising the dynamics of a biological circadian oscillator, and discriminating different types of cardiac malfunction from electro-cardiogram data. Our results demonstrate that this approach provides a statistically principled and generally usable tool to logically characterise dynamical systems in terms of temporal logic formulae.

L.B. acknowledges partial support from the EU-FET project QUANTICOL (nr. 600708) and by FRA-UniTS. G.S. acknowledges support from the ERC under grant MLCS306999. E.B. acknowledges the support of the Austrian FFG project HARMONIA (nr. 845631).

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References

  1. Akaike, H.: A new look at the statistical model identification. IEEE Trans. Aut. Control 19(6), 716–723 (1974)

    Article  MATH  MathSciNet  Google Scholar 

  2. Allen, J.B.: Short term spectral analysis, synthesis, and modification by discrete fourier transform. IEEE Transactions on Acoustics, Speech, and Signal Processing 3, 235–238

    Google Scholar 

  3. Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  4. 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 

  5. Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: On the robustness of temporal properties for stochastic models. In: Proc. of HSB 2013, pp. 3–19 (2013)

    Google Scholar 

  6. Bartocci, E., Corradini, F., Di Berardini, M.R., Smolka, S.A., Grosu, R.: Modeling and simulation of cardiac tissue using hybrid I/O automata. Theor. Comput. Sci. 410(33-34), 3149–3165 (2009)

    Article  MATH  Google Scholar 

  7. Bartocci, E., Grosu, R., Karmarkar, A., Smolka, S.A., Stoller, S.D., Zadok, E., Seyster, J.: Adaptive runtime verification. In: Qadeer, S., Tasiran, S. (eds.) RV 2012. LNCS, vol. 7687, pp. 168–182. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  8. Bishop, C.M.: Pattern Recognition and Machine Learning. Springer (2006)

    Google Scholar 

  9. Bortolussi, L., Sanguinetti, G.: Learning and Designing Stochastic Processes from Logical Constraints. In: Joshi, K., Siegle, M., Stoelinga, M., D’Argenio, P.R. (eds.) QEST 2013. LNCS, vol. 8054, pp. 89–105. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  10. Calzone, L., Chabrier-Rivier, N., Fages, F., Soliman, S.: Machine learning biochemical networks from temporal logic properties. In: Priami, C., Plotkin, G. (eds.) Trans. on Comp. Sys. Bio. VI. LNCS (LNBI), vol. 4220, pp. 68–94. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  11. Chen, T., Diciolla, M., Kwiatkowska, M., Mereacre, A.: Time-bounded verification of CTMCs against real-time specifications. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 26–42. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  12. Donzé, A., Maler, O., Bartocci, E., Nickovic, D., Grosu, R., Smolka, S.A.: On temporal logic and signal processing. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 92–106. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  13. Georgoulas, A., Clark, A., Ocone, A., Gilmore, S., Sanguinetti, G.: A subsystems approach for parameter estimation of ode models of hybrid systems. In: Proc. of HSB 2012. EPTCS, vol. 92 (2012)

    Google Scholar 

  14. Grosu, R., Smolka, S.A., Corradini, F., Wasilewska, A., Entcheva, E., Bartocci, E.: Learning and detecting emergent behavior in networks of cardiac myocytes. Commun. ACM 52(3), 97–105 (2009)

    Article  Google Scholar 

  15. Jha, S.K., Clarke, E.M., Langmead, C.J., Legay, A., Platzer, A., Zuliani, P.: A Bayesian approach to model checking biological systems. In: Degano, P., Gorrieri, R. (eds.) CMSB 2009. LNCS, vol. 5688, pp. 218–234. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  16. Kalajdzic, K., Bartocci, E., Smolka, S.A., Stoller, S.D., Grosu, R.: Runtime Verification with Particle Filtering. In: Legay, A., Bensalem, S. (eds.) RV 2013. LNCS, vol. 8174, pp. 149–166. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  17. Kong, Z., Jones, A., Ayala, A.M., Gol, E.A., Belta, C.: Temporal Logic Inference for Classification and Prediction from Data. In: Proc. of HSCC 2014, pp. 273–282. ACM (2014)

    Google Scholar 

  18. Lee, C., Chen, F., Roşu, G.: Mining parametric specifications. In: Proc. of ICSE 2011, pp. 591–600. ACM (2011)

    Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. Moody, G.B., Mark, R.G.: The impact of the MIT-BIH arrhythmia database. IEEE Eng. Med. Biol. Mag. 20(3), 45–50 (2001)

    Article  Google Scholar 

  21. Ocone, A., Millar, A.J., Sanguinetti, G.: Hybrid regulatory models: a statistically tractable approach to model regulatory network dynamics. Bioinformatics 29(7), 910–916 (2013)

    Article  Google Scholar 

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

    Google Scholar 

  23. Rabiner, L.R.: A tutorial on hidden Markov models and selected applications in speech recognition. Proceedings of the IEEE 77(2), 257–286 (1989)

    Article  Google Scholar 

  24. Rasmussen, C.E., Williams, C.K.I.: Gaussian Processes for Machine Learning. MIT Press (2006)

    Google Scholar 

  25. Srinivas, N., Krause, A., Kakade, S.M., Seeger, M.W.: Information-theoretic regret bounds for gaussian process optimization in the bandit setting. IEEE Transactions on Information Theory 58(5), 3250–3265 (2012)

    Article  MathSciNet  Google Scholar 

  26. Stoller, S.D., Bartocci, E., Seyster, J., Grosu, R., Havelund, K., Smolka, S.A., Zadok, E.: Runtime Verification with State Estimation. In: Khurshid, S., Sen, K. (eds.) RV 2011. LNCS, vol. 7186, pp. 193–207. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  27. Xiaoqing, J., Donzé, A., Deshmukh, J.V., Seshia, S.A.: Mining Requirements from Closed-loop Control Models. In: Proc. of HSCC 2013, pp. 43–52. ACM (2013)

    Google Scholar 

  28. Yang, H., Hoxha, B., Fainekos, G.: Querying Parametric Temporal Logic Properties on Embedded Systems. In: Nielsen, B., Weise, C. (eds.) ICTSS 2012. LNCS, vol. 7641, pp. 136–151. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

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Author information

Authors and Affiliations

  1. Faculty of Informatics, Vienna University of Technology, Austria

    Ezio Bartocci

  2. DMG, University of Trieste, Italy

    Luca Bortolussi

  3. CNR/ISTI, Pisa, Italy

    Luca Bortolussi

  4. School of Informatics, University of Edinburgh, UK

    Guido Sanguinetti

  5. SynthSys, Centre for Synthetic and Systems Biology, University of Edinburgh, UK

    Guido Sanguinetti

Authors
  1. Ezio Bartocci
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  2. Luca Bortolussi
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  3. Guido Sanguinetti
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Editor information

Editors and Affiliations

  1. Bâtiment C, Inria, Campus Universitaire de Beaulieu, 35042, Rennes Cedex, France

    Axel Legay

  2. Distributed and Complex Systems Group, Centre Equation, VERIMAG, 2 Avenue de Vignate, 38610, Gieres, France

    Marius Bozga

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© 2014 Springer International Publishing Switzerland

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Bartocci, E., Bortolussi, L., Sanguinetti, G. (2014). Data-Driven Statistical Learning of Temporal Logic Properties. In: Legay, A., Bozga, M. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2014. Lecture Notes in Computer Science, vol 8711. Springer, Cham. https://doi.org/10.1007/978-3-319-10512-3_3

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  • DOI: https://doi.org/10.1007/978-3-319-10512-3_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10511-6

  • Online ISBN: 978-3-319-10512-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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