Abstract
Requirements of cyberphysical systems (CPS) can be rigorously specified using Signal Temporal Logic (STL). STL comes equipped with semantics that are able to quantify how robustly a given signal satisfies an STL property. In a setting where signal values over the entire time horizon of interest are available, efficient algorithms for offline computation of the robust satisfaction value have been proposed. Only a few methods exist for the online setting, i.e., where only a partial signal trace is available and rest of the signal becomes available in increments (such as in a real system or during numerical simulations). In this paper, we formalize the semantics for robust online monitoring of partial signals using the notion of robust satisfaction intervals (\(\mathtt {RoSI}\)s). We propose an efficient algorithm to compute the \(\mathtt {RoSI}\) and demonstrate its usage on two real-world case studies from the automotive domain and massively-online CPS education. As online algorithms permit early termination when the satisfaction or violation of a property is found, we show that savings in computationally expensive simulations far outweigh any overheads incurred by the online approach.
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Notes
- 1.
We omit the case of \(\mathbf {U}_I\) here for lack of space, although the rewriting approach of [7] can be adapted here and is implemented in our tool.
- 2.
We remark that \(\varphi \) is equivalent to \(\Box _{[0,a]} \left( (y > 0) \implies \Diamond _{[b,c]}(x>0)\right) \), which is a common formula used to express a timed causal relation between two signals.
References
Annpureddy, Y., Liu, C., Fainekos, G., Sankaranarayanan, S.: S-TaLiRo: a tool for temporal logic falsification for hybrid systems. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 254–257. Springer, Heidelberg (2011)
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, E., Bortolussi, L., Sanguinetti, G.: Data-driven statistical learning of temporal logic properties. In: Legay, A., Bozga, M. (eds.) FORMATS 2014. LNCS, vol. 8711, pp. 23–37. Springer, Heidelberg (2014)
Deshmukh, J.V., Donzé, A., Ghosh, S., Jin, X., Juniwal, G., Seshia, S.A.: Robust Online Monitoring of Signal Temporal Logic (2015). arXiv pre-print
Dokhanchi, A., Hoxha, B., Fainekos, G.: On-line monitoring for temporal logic robustness. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 231–246. Springer, Heidelberg (2014)
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)
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)
Donzé, A., Juniwal, G., Jensen, J.C., Seshia, S.A.: CPSGrader website. http://www.cpsgrader.org
Donzé, A., Maler, O.: Robust satisfaction of temporal logic over real-valued signals. In: Chatterjee, K., Henzinger, T.A. (eds.) FORMATS 2010. LNCS, vol. 6246, pp. 92–106. Springer, Heidelberg (2010)
Eisner, C., Fisman, D., Havlicek, J., Lustig, Y., McIsaac, A., Van Campenhout, D.: Reasoning with temporal logic on truncated paths. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 27–39. Springer, Heidelberg (2003)
Fainekos, G., Sankaranarayanan, S., Ueda, K., Yazarel, H.: Verification of automotive control applications using S-TaLiRo. In: Proceedings of the American Control Conference (2012)
Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009)
Ho, H.-M., Ouaknine, J., Worrell, J.: Online monitoring of metric temporal logic. In: Bonakdarpour, B., Smolka, S.A. (eds.) RV 2014. LNCS, vol. 8734, pp. 178–192. Springer, Heidelberg (2014)
Hoxha, B., Abbas, H., Fainekos, G.: Benchmarks for temporal logic requirements for automotive systems. In: Proceedings of Applied Verification for Continuous and Hybrid Systems (2014)
Jin, X., Donzé, A., Deshmukh, J.V., Seshia, S.A.: Mining requirements from closed-loop control models. In: Proceedings of Hybrid Systems: Computation and Control, pp. 43–52 (2013)
Jones, A., Kong, Z., Belta, C.: Anomaly detection in cyber-physical systems: a formal methods approach. In: Proceedings of IEEE Conference on Decision and Control, pp. 848–853 (2014)
Juniwal, G., Donzé, A., Jensen, J.C., Seshia, S.A.: CPSGrader: synthesizing temporal logic testers for auto-grading an embedded systems laboratory. In: Proceedings of Conference on Embedded Software, October 2014
Kong, Z., Jones, A., Medina Ayala, A., Aydin Gol, E., Belta, C.: Temporal logic inference for classification and prediction from data. In: Proceedings of Hybrid Systems: Computation and Control, pp. 273–282 (2014)
Lemire, D.: Streaming Maximum-Minimum Filter Using no More Than Three Comparisons per Element (2006). arXiv preprint cs/0610046
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)
Nickovic, D., Maler, O.: AMT: a property-based monitoring tool for analog systems. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 304–319. Springer, Heidelberg (2007)
Acknowledgments
This work was supported in part by TerraSwarm, one of six centers of STARnet, a Semiconductor Research Corporation program sponsored by MARCO and DARPA, by NSF Expeditions grant CCF-1139138, and by Toyota under the CHESS center at UC Berkeley.
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Deshmukh, J.V., Donzé, A., Ghosh, S., Jin, X., Juniwal, G., Seshia, S.A. (2015). Robust Online Monitoring of Signal Temporal Logic. In: Bartocci, E., Majumdar, R. (eds) Runtime Verification. Lecture Notes in Computer Science(), vol 9333. Springer, Cham. https://doi.org/10.1007/978-3-319-23820-3_4
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