Abstract
We investigate online monitoring algorithms over dense-time and continuous-time signals for properties written in metric temporal logic (MTL). We consider an abstract algebraic semantics based on complete lattices. This semantics includes as particular cases the standard Boolean (qualitative) semantics and the widely used real-valued robustness (quantitative) semantics. Our semantics also extends to truth values that are partially ordered and allows the modeling of uncertainty in satisfaction. We propose a compositional approach for the construction of online monitors that transform exact representations of piecewise constant (dense-time and continuous-time) signals. These monitors are based on a class of infinite-state deterministic signal transducers that (1) are allowed to produce the output signal with some bounded delay relative to the input signal, and (2) do not introduce unbounded variability in the output signal. A key ingredient of our monitoring framework is an efficient algorithm for sliding-window aggregation over dense-time signals. We have implemented and experimentally evaluated our monitoring framework by comparing it to the recently proposed online monitoring tools Reelay and RTAMT.
Similar content being viewed by others
References
Abbas, H., Alur, R., Mamouras, K., et al.: Real-time decision policies with predictable performance. Proc. IEEE 106(9), 1593–1615 (2018). https://doi.org/10.1109/JPROC.2018.2853608
Abbas, H., Rodionova, A., Mamouras, K., et al.: Quantitative regular expressions for arrhythmia detection. IEEE/ACM Trans. Comput. Biol. Bioinform. 16(5), 1586–1597 (2019). https://doi.org/10.1109/TCBB.2018.2885274
Akazaki, T., Hasuo, I.: Time robustness in MTL and expressivity in hybrid system falsification. In: Kroening, D., Păsăreanu, C.S. (eds.) CAV 2015. LNCS, vol. 9207, pp. 356–374. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21668-3_21
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8
Alur, R., Mamouras, K.: An Introduction to the StreamQRE Language. Dependable Software Systems Engineering, vol. 50, pp. 1–24 (2017). https://doi.org/10.3233/978-1-61499-810-5-1
Alur, R., Feder, T., Henzinger, T.A.: The benefits of relaxing punctuality. J. ACM 43(1), 116–146 (1996). https://doi.org/10.1145/227595.227602
Alur, R., Mamouras, K., Stanford, C.: Automata-based stream processing. In: ICALP 2017. Leibniz International Proceedings in Informatics (LIPIcs), vol. 80, pp. 112:1–112:15. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhl (2017). https://doi.org/10.4230/LIPIcs.ICALP.2017.112
Alur, R., Mamouras, K., Ulus, D.: Derivatives of quantitative regular expressions. In: Aceto, L., Bacci, G., Bacci, G., et al. (eds.) Models, Algorithms, Logics and Tools: Essays Dedicated to Kim Guldstrand Larsen on the Occasion of His 60th Birthday. LNCS, vol. 10460, pp. 75–95. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63121-9_4
Alur, R., Mamouras, K., Stanford, C.: Modular quantitative monitoring. Proc. ACM Program. Lang. 3(POPL), 50:1–50:31 (2019). https://doi.org/10.1145/3290363
Alur, R., Fisman, D., Mamouras, K., et al.: Streamable regular transductions. Theor. Comput. Sci. 807, 15–41 (2020). https://doi.org/10.1016/j.tcs.2019.11.018
Bakhirkin, A., Ferrère, T., Maler, O.: Efficient parametric identification for STL. In: HSCC 2018, pp. 177–186. ACM, New York (2018). https://doi.org/10.1145/3178126.3178132
Bauer, A., Leucker, M., Schallhart, C.: Comparing LTL semantics for runtime verification. J. Log. Comput. 20(3), 651–674 (2010). https://doi.org/10.1093/logcom/exn075
Benveniste, A., Le Guernic, P., Jacquemot, C.: Synchronous programming with events and relations: the SIGNAL language and its semantics. Sci. Comput. Program. 16(2), 103–149 (1991). https://doi.org/10.1016/0167-6423(91)90001-E
Berry, G., Gonthier, G.: The esterel synchronous programming language: design, semantics, implementation. Sci. Comput. Program. 19(2), 87–152 (1992). https://doi.org/10.1016/0167-6423(92)90005-V
Bonakdarpour, B., Fraigniaud, P., Rajsbaum, S., et al.: Decentralized asynchronous crash-resilient runtime verification. In: Desharnais, J., Jagadeesan, R. (eds.) CONCUR 2016. Leibniz International Proceedings in Informatics (LIPIcs), vol. 59, pp. 16:1–16:15. Schloss Dagstuhl–Leibniz-Zentrum für Informatik, Dagstuhly (2016). https://doi.org/10.4230/LIPIcs.CONCUR.2016.16
Caspi, P., Pilaud, D., Halbwachs, N., et al.: LUSTRE: a declarative language for real-time programming. In: POPL 1987, pp. 178–188. ACM, New York (1987). https://doi.org/10.1145/41625.41641
Chattopadhyay, A., Mamouras, K.: A verified online monitor for metric temporal logic with quantitative semantics. In: Deshmukh, J., Ničković, D. (eds.) RV 2020. LNCS, vol. 12399, pp. 383–403. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-60508-7_21
Cralley, J., Spantidi, O., Hoxha, B., et al.: TLTk: a toolbox for parallel robustness computation of temporal logic specifications. In: Deshmukh, J., Ničković, D. (eds.) RV 2020. LNCS, vol. 12399, pp. 404–416. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-60508-7_22
Deshmukh, J.V., Donzé, A., Ghosh, S., et al.: Robust online monitoring of signal temporal logic. Form. Methods Syst. Des. 51(1), 5–30 (2017). https://doi.org/10.1007/s10703-017-0286-7
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, Cham (2014). https://doi.org/10.1007/978-3-319-11164-3_19
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). https://doi.org/10.1007/978-3-642-15297-9_9
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)
Dreossi, T., Dang, T., Donzé, A., et al.: Efficient guiding strategies for testing of temporal properties of hybrid systems. In: Havelund, K., Holzmann, G., Joshi, R. (eds.) NFM 2015. LNCS, vol. 9058, pp. 127–142. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-17524-9_10
D’Souza, D., Tabareau, N.: On timed automata with input-determined guards. In: Lakhnech, Y., Yovine, S. (eds.) FTRTFT 2004, FORMATS 2004. LNCS, vol. 3253, pp. 68–83. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_7
Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410(42), 4262–4291 (2009). https://doi.org/10.1016/j.tcs.2009.06.021
Fainekos, G.E., Pappas, G.J.: Robustness of temporal logic specifications. In: Havelund, K., Núñez, M., Roşu, G., et al. (eds.) FATES 2006, RV 2006. LNCS, vol. 4262, pp. 178–192. Springer, Heidelberg (2006). https://doi.org/10.1007/11940197_12
Faulhaber, J.: Boost library documentation: interval container library. https://www.boost.org/doc/libs/1_76_0/libs/icl/doc/html/index.html (2021). Online; accessed August 20, 2021
Faymonville, P., Finkbeiner, B., Schwenger, M., et al.: Real-time stream-based monitoring (2017). CoRR. http://arxiv.org/abs/1711.03829. arXiv:1711.03829
Faymonville, P., Finkbeiner, B., Schledjewski, M., et al.: StreamLAB: stream-based monitoring of cyber-physical systems. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 421–431. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_24
Ferrère, T., Maler, O., Ničković, D., et al.: From real-time logic to timed automata. J. ACM 66(3), 19:1–19:31 (2019). https://doi.org/10.1145/3286976
Gorostiaga, F., Sánchez, C.: Striver: stream runtime verification for real-time event-streams. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 282–298. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03769-7_16
Hoxha, B., Abbas, H., Fainekos, G.E.: Benchmarks for temporal logic requirements for automotive systems. In: Frehse, G., Althoff, M. (eds.) ARCH@CPSWeek 2014. 2015 EPiC Series in Computing, vol. 34, pp. 25–30. EasyChair (2014). https://doi.org/10.29007/xwrs
Hoxha, B., Bach, H., Abbas, H., et al.: Towards formal specification visualization for testing and monitoring of cyber-physical systems. In: International Workshop on Design and Implementation of Formal Tools and Systems. DIFTS (2014)
Jakšić, S., Bartocci, E., Grosu, R., et al.: An algebraic framework for runtime verification. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 37(11), 2233–2243 (2018). https://doi.org/10.1109/TCAD.2018.2858460
Kahn, G.: The semantics of a simple language for parallel programming. In: Information Processing, vol. 74, pp. 471–475 (1974)
Kong, L., Mamouras, K.: StreamQL: a query language for processing streaming time series. Proc. ACM Program. Lang. 4(OOPSLA), 183:1–183:32 (2020). https://doi.org/10.1145/3428251
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2(4), 255–299 (1990). https://doi.org/10.1007/BF01995674
Lemire, D.: Streaming maximum-minimum filter using no more than three comparisons per element CoRR. (2006). arXiv:cs/0610046
Li, J., Maier, D., Tufte, K., et al.: No pane, no gain: efficient evaluation of sliding-window aggregates over data streams. SIGMOD Rec. 34(1), 39–44 (2005). https://doi.org/10.1145/1058150.1058158
Maler, O., Nickovic, D.: Monitoring temporal properties of continuous signals. In: Lakhnech, Y., Yovine, S. (eds.) FTRTFT 2004, FORMATS 2004. LNCS, vol. 3253, pp. 152–166. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30206-3_12
Maler, O., Nickovic, D., Pnueli, A.: Real time temporal logic: past, present, future. In: Pettersson, P., Yi, W. (eds.) FORMATS 2005. LNCS, vol. 3829, pp. 2–16. Springer, Heidelberg (2005). https://doi.org/10.1007/11603009_2
Maler, O., Nickovic, D., Pnueli, A.: From MITL to timed automata. In: Asarin, E., Bouyer, P. (eds.) FORMATS 2006. LNCS, vol. 4202, pp. 274–289. Springer, Heidelberg (2006). https://doi.org/10.1007/11867340_20
Maler, O., Ničković, D., Pnueli, A.: On synthesizing controllers from bounded-response properties. In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 95–107. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-73368-3_12
Mamouras, K., Wang, Z.: Online signal monitoring with bounded lag. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. (2020). https://doi.org/10.1109/TCAD.2020.3013053
Mamouras, K., Raghothaman, M., Alur, R., et al.: StreamQRE: modular specification and efficient evaluation of quantitative queries over streaming data. In: PLDI 2017, pp. 693–708. ACM, New York (2017). https://doi.org/10.1145/3062341.3062369
Mamouras, K., Chattopadhyay, A., Wang, Z.: Algebraic quantitative semantics for efficient online temporal monitoring. In: Groote, J.F., Larsen, K.G. (eds.) TACAS 2021. LNCS, vol. 12651, pp. 330–348. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-72016-2_18
Mamouras, K., Chattopadhyay, A., Wang, Z.: A compositional framework for quantitative online monitoring over continuous-time signals. In: Feng, L., Fisman, D. (eds.) RV 2021. LNCS, vol. 12974, pp. 142–163. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-60508-7_22
Ničković, D., Yamaguchi, T.: RTAMT: online robustness monitors from STL. In: Hung, D.V., Sokolsky, O. (eds.) ATVA 2020. LNCS, vol. 12302, pp. 564–571. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-59152-6_34
Pnueli, A., Zaks, A.: On the Merits of Temporal Testers. LNCS, vol. 5000, pp. 172–195. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-69850-0_11
Sánchez, C.: Online and offline stream runtime verification of synchronous systems. In: Colombo, C., Leucker, M. (eds.) RV 2018. LNCS, vol. 11237, pp. 138–163. Springer, Cham (2018). https://doi.org/10.1007/978-3-030-03769-7_9
The Valgrind Developers: Valgrind: an instrumentation framework for building dynamic analysis tools. https://valgrind.org/ (2021). Online; accessed August 20, 2021
Ulus, D.: the Reelay monitoring tool. https://doganulus.github.io/reelay/ (2020). Online; accessed August 20, 2020
Waga, M.: Online quantitative timed pattern matching with semiring-valued weighted automata. In: André, É., Stoelinga, M. (eds.) FORMATS 2019. LNCS, vol. 11750, pp. 3–22. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-29662-9_1
Funding
This research was supported in part by US National Science Foundation award 2008096.
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Competing Interests
The authors declare no competing interests.
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
About this article
Cite this article
Mamouras, K., Chattopadhyay, A. & Wang, Z. A compositional framework for algebraic quantitative online monitoring over continuous-time signals. Int J Softw Tools Technol Transfer 25, 557–573 (2023). https://doi.org/10.1007/s10009-023-00719-w
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10009-023-00719-w