Abstract
We introduce a new logic called Signal Convolution Logic (\(\text {SCL}\)) that combines temporal logic with convolutional filters from digital signal processing. \(\text {SCL}\) enables to reason about the percentage of time a formula is satisfied in a bounded interval. We demonstrate that this new logic is a suitable formalism to effectively express non-functional requirements in Cyber-Physical Systems displaying noisy and irregular behaviours. We define both a qualitative and quantitative semantics for it, providing an efficient monitoring procedure. Finally, we prove \(\text {SCL}\) at work to monitor the artificial pancreas controllers that are employed to automate the delivery of insulin for patients with type-1 diabetes.
E.B. and L.N. acknowledge the partial support of the Austrian National Research Network S 11405-N23 (RiSE/SHiNE) of the Austrian Science Fund (FWF). E.B., L.N. and S.S. acknowledge the partial support of the ICT COST Action IC1402 (ARVI).
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Notes
- 1.
This operation is in fact a cross-correlation, but here we use the same convention of the deep learning community and call it convolution.
- 2.
\(\mathcal {N}(\mu ,\sigma ^2)\) is the Gaussian distribution with mean \(\mu \) and variance \(\sigma ^2\).
References
Akazaki, Takumi, Hasuo, Ichiro: Time robustness in MTL and expressivity in hybrid system falsification. In: Kroening, Daniel, Păsăreanu, Corina S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 356–374. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21668-3_21
Bartocci, E., Bortolussi, L., Nenzi, L.: A temporal logic approach to modular design of synthetic biological circuits. In: Proceedings of CMSB, pp. 164–177. Springer, Berlin (2013)
Bartocci, E., Bortolussi, L., Nenzi, L., Sanguinetti, G.: System design of stochastic models using robustness of temporal properties. Theor. Comput. Sci. 587, 3–25 (2015)
Bartocci, Ezio, Deshmukh, Jyotirmoy, Donzé, Alexandre, Fainekos, Georgios, Maler, Oded, Ničković, Dejan, Sankaranarayanan, Sriram: Specification-based monitoring of cyber-physical systems: a survey on theory, tools and applications. In: Bartocci, Ezio, Falcone, Yliès (eds.) Lectures on Runtime Verification. LNCS, vol. 10457, pp. 135–175. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-75632-5_5
Cameron, Fraser, Fainekos, Georgios, Maahs, David M., Sankaranarayanan, Sriram: Towards a verified artificial pancreas: challenges and solutions for runtime verification. In: Bartocci, Ezio, Majumdar, Rupak (eds.) RV 2015. LNCS, vol. 9333, pp. 3–17. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-23820-3_1
Donzé, Alexandre: Breach, a toolbox for verification and parameter synthesis of hybrid systems. In: Touili, Tayssir, Cook, Byron, Jackson, Paul (eds.) CAV 2010. LNCS, vol. 6174, pp. 167–170. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-14295-6_17
Donzé, Alexandre, Maler, Oded: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, Krishnendu, Henzinger, Thomas A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-15297-9_9
Fainekos, G.E., Sankaranarayanan, S., Ueda, K., Yazarel, H.: Verification of automotive control applications using S-TaLiRo. In: Proceedings of ACC. IEEE (2012)
Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)
Hovorka, R., Canonico, V., Chassin, L.J., Haueter, U., Massi-Benedetti, M., Federici, M.O., Pieber, T.R., Schaller, H.C., Schaupp, L., Vering, T.: Nonlinear model predictive control of glucose concentration in subjects with type 1 diabetes. Physiol. Meas. 25(4), 905 (2004)
Jha, S., Raman, V., Sadigh, D., Seshia, S.A.: Safe autonomy under perception uncertainty using chance-constrained temporal logic. J. Autom. Reason. 60(1), 43–62 (2018)
Li, J., Nuzzo, P., Sangiovanni-Vincentelli, A., Xi, Y., Li, D.: Stochastic contracts for cyber-physical system design under probabilistic requirements. In: Proceedings of MEMOCODE, pp. 5–14. ACM (2017)
Maler, Oded, Nickovic, Dejan: Monitoring temporal properties of continuous signals. In: Lakhnech, Yassine, Yovine, Sergio (eds.) FORMATS/FTRTFT -2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12
Rodionova, A., Bartocci, E., Ničković, D., Grosu, R.: Temporal logic as filtering. In: Proceedings of HSCC 2016, pp. 11–20. ACM (2016)
Sadigh, D., Kapoor, A.: Safe control under uncertainty with probabilistic signal temporal logic. In: Robotics: Science and Systems XII, University of Michigan, Ann Arbor, Michigan, USA, June 18 - June 22, 2016 (2016)
Sankaranarayanan, S., Fainekos, G.: Falsification of temporal properties of hybrid systems using the cross-entropy method. In: Proc. of HSCC. pp. 125–134 (2012)
Sankaranarayanan, S., Kumar, S.A., Cameron, F., Bequette, B.W., Fainekos, G., Maahs, D.M.: Model-based falsification of an artificial pancreas control system. SIGBED Rev. 14(2), 24–33 (2017). Mar
Shmarov, F., Paoletti, N., Bartocci, E., Lin, S., Smolka, S.A., Zuliani, P.: SMT-based synthesis of safe and robust PID controllers for stochastic hybrid systems. In: Proceedings of HVC, pp. 131–146 (2017)
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Silvetti, S., Nenzi, L., Bartocci, E., Bortolussi, L. (2018). Signal Convolution Logic. In: Lahiri, S., Wang, C. (eds) Automated Technology for Verification and Analysis. ATVA 2018. Lecture Notes in Computer Science(), vol 11138. Springer, Cham. https://doi.org/10.1007/978-3-030-01090-4_16
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