ABSTRACT
Signal Temporal Logic (STL) is a timed temporal logic formalism that has found widespread adoption for rigorous specification of properties in Cyber-Physical Systems. However, STL is unable to specify oscillatory properties commonly required in engineering design. This limitation can be overcome by the addition of additional operators, for example, signal-value freeze operators, or with first order quantification. Previous work on augmenting STL with such operators has resulted in intractable monitoring algorithms. We present the first efficient and scalable offline monitoring algorithms for STL augmented with independent freeze quantifiers. Our final optimized algorithm has a |ρ|log (|ρ|) dependence on the trace length |ρ| for most traces ρ arising in practice, and a |ρ|2 dependence in the worst case. We also provide experimental validation of our algorithms – we show the algorithms scale to traces having 100k time samples.
- R. Alur and D. L. Dill. 1994. A Theory of Timed Automata. Theor. Comput. Sci. 126, 2 (1994), 183–235.Google Scholar
Digital Library
- R. Alur and T. A. Henzinger. 1994. A Really Temporal Logic. J. ACM 41, 1 (1994), 181–204.Google ScholarDigital Library
- C. Baier and J. P. Katoen. 2008. Principles of model checking. MIT Press.Google ScholarDigital Library
- A. Bakhirkin and N. Basset. 2019. Specification and Efficient Monitoring Beyond STL(LNCS, Vol. 11428). Springer, 79–97.Google Scholar
- A. Bakhirkin, T. Ferrère, T. A. Henzinger, and D. Nickovic. 2018. The first-order logic of signals: keynote. In EMSOFT’18. IEEE, 1.Google Scholar
- E. Bartocci, J. V. Deshmukh, A. Donzé, G. Fainekos, O. Maler, D. Nickovic, and S. Sankaranarayanan. 2018. Specification-Based Monitoring of Cyber-Physical Systems: A Survey on Theory, Tools and Applications. In Lectures on Runtime Verification - Introductory and Advanced Topics. LNCS, Vol. 10457. Springer, 135–175.Google Scholar
- J. L. Bentley and A. C. Yao. 1976. An almost optimal algorithm for unbounded searching. Inform. Process. Lett. 5, 3 (1976), 82–87.Google ScholarCross Ref
- P. Bouyer, F. Chevalier, and N. Markey. 2010. On the expressiveness of TPTL and MTL. Inf. Comput. 208, 2 (2010), 97–116.Google ScholarCross Ref
- L. Brim, P. Dluhos, D. Safránek, and T. Vejpustek. 2014. STL*: Extending signal temporal logic with signal-value freezing operator. Inf. Comput. 236 (2014), 52–67.Google ScholarDigital Library
- J. V. Deshmukh, A. Donzé, S. Ghosh, X. Jin, G. Juniwal, and S. A. Seshia. 2017. Robust online monitoring of signal temporal logic. Formal Methods Syst. Des. 51, 1 (2017), 5–30.Google ScholarDigital Library
- A. Dokhanchi, B. Hoxha, C.E. Tuncali, and G. Fainekos. 2016. An efficient algorithm for monitoring practical TPTL specifications. In MEMOCODE’16. IEEE, 184–193.Google Scholar
- A. Donzé. 2010. Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems. In CAV’10(LNCS, Vol. 6174). Springer, 167–170.Google Scholar
- A. Donzé, T. Ferrère, and O. Maler. 2013. Efficient Robust Monitoring for STL. In CAV’13(LNCS 8044). Springer, 264–279.Google Scholar
- G. Ernst, S. Sedwards, Z. Zhang, and I. Hasuo. 2021. Falsification of Hybrid Systems Using Adaptive Probabilistic Search. ACM Trans. Model. Comput. Simul. 31, 3 (2021), 18:1–18:22.Google ScholarDigital Library
- G. Fainekos, B. Hoxha, and S. Sankaranarayanan. 2019. Robustness of Specifications and Its Applications to Falsification, Parameter Mining, and Runtime Monitoring with S-TaLiRo. In RV’19(LNCS, Vol. 11757). Springer, 27–47.Google Scholar
- G. E. Fainekos and G. J. Pappas. 2009. Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410, 42 (2009), 4262–4291.Google ScholarDigital Library
- G. E. Fainekos, S. Sankaranarayanan, K. Ueda, and H. Yazarel. 2012. Verification of automotive control applications using S-TaLiRo. In ACC’12. IEEE, 3567–3572.Google Scholar
- B. Ghorbel and V. S. Prabhu. 2022. Linear Time Monitoring for One Variable TPTL. In HSCC ’22. ACM, 5:1–5:11.Google Scholar
- B. Ghorbel and V. S. Prabhu. 2023. Quantitative Robustness for Signal Temporal Logic with Time-Freeze Quantifiers. IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems 42, 12 (2023), 4436–4449.Google ScholarDigital Library
- A. Grez, F. Mazowiecki, M. Pilipczuk, G. Puppis, and C. Riveros. 2021. Dynamic Data Structures for Timed Automata Acceptance. In IPEC’ 21(LIPIcs, Vol. 214). Schloss Dagstuhl - Leibniz-Zentrum für Informatik, 20:1–20:18.Google Scholar
- J. Kapinski, X. Jin, J. Deshmukh, A. Donzé, T. Yamaguchi, H. Ito, T. Kaga, S. Kobuna, and S. Seshia. 2016. ST-Lib: A Library for Specifying and Classifying Model Behaviors. SAE Technical Paper Series.Google Scholar
- Z. Kong, A. Jones, and C. Belta. 2017. Temporal Logics for Learning and Detection of Anomalous Behavior. IEEE Trans. Autom. Control. 62, 3 (2017), 1210–1222.Google ScholarCross Ref
- W. Liu, N. Mehdipour, and C. Belta. 2022. Recurrent Neural Network Controllers for Signal Temporal Logic Specifications Subject to Safety Constraints. IEEE Control. Syst. Lett. 6 (2022), 91–96.Google ScholarCross Ref
- O. Maler and D. Nickovic. 2004. Monitoring Temporal Properties of Continuous Signals. In FORMATS/FTRTFT. Springer, 152–166.Google Scholar
- O. Maler and D. Nickovic. 2013. Monitoring properties of analog and mixed-signal circuits. STTT 15, 3 (2013), 247–268.Google ScholarDigital Library
- N. Markey and J-F. Raskin. 2006. Model checking restricted sets of timed paths. Theor. Comput. Sci. 358, 2-3 (2006), 273–292.Google ScholarDigital Library
- V. S. Prabhu and M. Savaliya. 2022. Towards Efficient Input Space Exploration for Falsification of Input Signal Class Augmented STL. In MEMOCODE’ 22. IEEE, 1–11.Google Scholar
- V. Raman, A. Donzé, M. Maasoumy, R.M. Murray, A.L. Sangiovanni-Vincentelli, and S.A. Seshia. 2017. Model Predictive Control for Signal Temporal Logic Specification. CoRR abs/1703.09563 (2017). arXiv:1703.09563Google Scholar
- V. Raman, A. Donzé, D. Sadigh, R. M. Murray, and S. A. Seshia. 2015. Reactive synthesis from signal temporal logic specifications. In HSCC’15. ACM, 239–248.Google Scholar
- G. Rosu and K. Havelund. 2001. Synthesizing Dynamic Programming Algorithms From Linear Temporal Logic Formulae. Technical Report.Google Scholar
- S. Sankaranarayanan, S. A. Kumar, F. Cameron, B. W. Bequette, G. Fainekos, and D.M. Maahs. 2017. Model-based falsification of an artificial pancreas control system. SIGBED Rev. 14, 2 (2017), 24–33.Google ScholarDigital Library
- M. Waga and I. Hasuo. 2018. Moore-Machine Filtering for Timed and Untimed Pattern Matching. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 37, 11 (2018), 2649–2660.Google ScholarCross Ref
- M. Waga, I. Hasuo, and K. Suenaga. 2017. Efficient Online Timed Pattern Matching by Automata-Based Skipping. In FORMATS’ 17, Proceedings(LNCS 10419). Springer, 224–243.Google Scholar
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