skip to main content
research-article
Public Access

Offline and Online Learning of Signal Temporal Logic Formulae Using Decision Trees

Published: 26 March 2021 Publication History

Abstract

In this article, we focus on inferring high-level descriptions of a system from its execution traces. Specifically, we consider a classification problem where system behaviors are described using formulae of Signal Temporal Logic (STL). Given a finite set of pairs of system traces and labels, where each label indicates whether the corresponding trace exhibits some system property, we devised a decision-tree-based framework that outputs an STL formula that can distinguish the traces. We also extend this approach to the online learning scenario. In this setting, it is assumed that new signals may arrive over time and the previously inferred formula should be updated to accommodate the new data. The proposed approach presents some advantages over traditional machine learning classifiers. In particular, the produced formulae are interpretable and can be used in other phases of the system’s operation, such as monitoring and control. We present two case studies to illustrate the effectiveness of the proposed algorithms: (1) a fault detection problem in an automotive system and (2) an anomaly detection problem in a maritime environment.

References

[1]
Eugene Asarin, Alexandre Donzé, Oded Maler, and Dejan Nickovic. 2012. Parametric identification of temporal properties. In Proceedings of the Conference on Runtime Verification (RV’11) (Lecture Notes in Computer Science), Sarfraz Khurshid and Koushik Sen (Eds.), Vol. 7186. Springer, Berlin, 147--160.
[2]
Ezio Bartocci, Luca Bortolussi, Laura Nenzi, and Guido Sanguinetti. 2015. System design of stochastic models using robustness of temporal properties. Theor. Comput. Sci. 587 (July 2015), 3--25.
[3]
Ezio Bartocci, Luca Bortolussi, and Guido Sanguinetti. 2014. Data-driven statistical learning of temporal logic properties. In Formal Modeling and Analysis of Timed Systems. Springer, 23--37.
[4]
Giuseppe Bombara and Calin Belta. 2017. Signal clustering using temporal logics. In Runtime Verification (Lecture Notes in Computer Science). Springer, Cham, 121--137.
[5]
Giuseppe Bombara and Calin Belta. 2018. Online learning of temporal logic formulae for signal classification. In Proceedings of the European Control Conference.
[6]
Giuseppe Bombara, Cristian-Ioan Vasile, Francisco Penedo, Hirotoshi Yasuoka, and Calin Belta. 2016. A decision tree approach to data classification using signal temporal logic. In Proceedings of the 19th International Conference on Hybrid Systems: Computation and Control (HSCC’16). ACM, New York, NY, 1--10.
[7]
Leo Breiman, Jerome Friedman, Charles J. Stone, and Richard A. Olshen. 1984. Classification and Regression Trees. CRC Press.
[8]
Sara Bufo, Ezio Bartocci, Guido Sanguinetti, Massimo Borelli, Umberto Lucangelo, and Luca Bortolussi. 2014. Temporal logic based monitoring of assisted ventilation in intensive care patients. In Leveraging Applications of Formal Methods, Verification and Validation. Number 8803 in Lecture Notes in Computer Science. Springer, 391--403.
[9]
G. Chen, Z. Sabato, and Z. Kong. 2016. Active learning based requirement mining for cyber-physical systems. In Proceedings of the IEEE 55th Conference on Decision and Control (CDC’16). 4586--4593.
[10]
E. M. Clarke, Orna Grumberg, and Doron Peled. 1999. Model Checking. MIT Press.
[11]
Thomas H. Cormen. 2009. Introduction to Algorithms (3rd ed.). MIT Press.
[12]
Pedro Domingos and Geoff Hulten. 2000. Mining high-speed data streams. In Proceedings of the 6th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’00). ACM, New York, NY, 71--80.
[13]
Alexandre Donzé, Thomas Ferrere, and Oded Maler. 2013. Efficient robust monitoring for STL. In Computer Aided Verification. Springer, 264--279.
[14]
Alexandre Donzé and Oded Maler. 2010. Robust satisfaction of temporal logic over real-valued signals. In Formal Modeling and Analysis of Timed Systems, Krishnendu Chatterjee and Thomas A. Henzinger (Eds.). Number 6246 in Lecture Notes in Computer Science. Springer, Berlin, 92--106.
[15]
Georgios E. Fainekos and George J. Pappas. 2009. Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci. 410, 42 (Sept. 2009), 4262--4291.
[16]
Radu Grosu, Scott A. Smolka, Flavio Corradini, Anita Wasilewska, Emilia Entcheva, and Ezio Bartocci. 2009. Learning and detecting emergent behavior in networks of cardiac myocytes. Commun. ACM 52, 3 (2009), 97--105.
[17]
Trevor Hastie, Robert Tibshirani, and Jerome Friedman. 2016. The Elements of Statistical Learning: Data Mining, Inference, and Prediction (2nd ed.). Springer, New York, NY.
[18]
Bardh Hoxha, Houssam Abbas, and Georgios Fainekos. 2014. Benchmarks for temporal logic requirements for automotive systems. Proc. Appl. Verificat. Cont. Hybrid Syst. (2014).
[19]
Bardh Hoxha, Adel Dokhanchi, and Georgios Fainekos. 2018. Mining parametric temporal logic properties in model-based design for cyber-physical systems. Int. J. Softw. Tools Technol. Transfer 20, 1 (Feb. 2018), 79--93.
[20]
Laurent Hyafil and Ronald L. Rivest. 1976. Constructing optimal binary decision trees is NP-complete. Inform. Process. Lett. 5, 1 (May 1976), 15--17.
[21]
Lester Ingber. 1996. Adaptive simulated annealing (ASA): Lessons learned. Control Cybernet. 25 (1996), 33--54.
[22]
Rolf Isermann. 2006. Fault-Diagnosis Systems. Springer.
[23]
Hassan Ismail Fawaz, Germain Forestier, Jonathan Weber, Lhassane Idoumghar, and Pierre-Alain Muller. 2019. Deep learning for time series classification: A review. Data Min. Knowl. Discov. 33, 4 (July 2019), 917--963.
[24]
Susmit Jha, Ashish Tiwari, Sanjit A. Seshia, Tuhin Sahai, and Natarajan Shankar. 2017. TeLEx: Passive STL learning using only positive examples. In Runtime Verification (Lecture Notes in Computer Science). Springer, Cham, 208--224.
[25]
Ruoming Jin and Gagan Agrawal. 2003. Efficient decision tree construction on streaming data. In Proceedings of the 9th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining (KDD’03). ACM, New York, NY, 571--576.
[26]
Xiaoqing Jin, Alexandre Donzé, Jyotirmoy Deshmukh, and Sanjit A. Seshia. 2015. Mining requirements from closed-loop control models. IEEE Trans. Comput.-Aided Design Integr. Circ. Syst. 99, 34 (2015), 1--1.
[27]
Michael J. Kearns and Umesh Virkumar Vazirani. 1994. An Introduction to Computational Learning Theory. MIT Press, Cambridge, MA.
[28]
Z. Kong, A. Jones, and C. Belta. 2017. Temporal logics for learning and detection of anomalous behavior. IEEE Trans. Automat. Control 62, 3 (Mar. 2017), 1210--1222.
[29]
K. Kowalska and L. Peel. 2012. Maritime anomaly detection using Gaussian process active learning. In Proceedings of the 15th International Conference on Information Fusion (FUSION’12). 1164--1171.
[30]
Changliu Liu, Tomer Arnon, Christopher Lazarus, Clark Barrett, and Mykel J. Kochenderfer. 2019. Algorithms for verifying deep neural networks. Retrieved from https://arXiv:1903.06758
[31]
Oded Maler and Dejan Nickovic. 2004. Monitoring temporal properties of continuous signals. In Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems, Yassine Lakhnech and Sergio Yovine (Eds.). Number 3253 in Lecture Notes in Computer Science. Springer Berlin Heidelberg, 152--166.
[32]
Apurva Narayan, Greta Cutulenco, Yogi Joshi, and Sebastian Fischmeister. 2018. Mining timed regular specifications from system traces. ACM Trans. Embed. Comput. Syst. 17, 2 (Jan. 2018), 46:1–46:21.
[33]
Daniel Neider and Ivan Gavran. 2018. Learning linear temporal properties. In Proceedings of the Formal Methods in Computer Aided Design (FMCAD’18). 1--10.
[34]
Laura Nenzi, Simone Silvetti, Ezio Bartocci, and Luca Bortolussi. 2018. A robust genetic algorithm for learning temporal specifications from data. In Quantitative Evaluation of Systems (Lecture Notes in Computer Science), Annabelle McIver and Andras Horvath (Eds.). Springer International Publishing, 323--338.
[35]
J. Ross Quinlan. 2014. C4.5: Programs for Machine Learning. Elsevier.
[36]
Brian D. Ripley. 1996. Pattern Recognition and Neural Networks. Cambridge University Press.
[37]
L. Rutkowski, M. Jaworski, L. Pietruczuk, and P. Duda. 2015. A new method for data stream mining based on the misclassification error. IEEE Trans. Neural Netw. Learn. Syst. 26, 5 (May 2015), 1048--1059.
[38]
Y. Shi and R. Eberhart. 1998. A modified particle swarm optimizer. In Proceedings of the IEEE International Conference on Evolutionary Computation Proceedings. 69--73.
[39]
Rainer Storn and Kenneth Price. 1997. Differential evolution—A simple and efficient heuristic for global optimization over continuous spaces. J. Global Optimiz. 11, 4 (Dec. 1997), 341--359.
[40]
Paul E. Utgoff, Neil C. Berkman, and Jeffery A. Clouse. 1997. Decision tree induction based on efficient tree restructuring. Mach. Learn. 29, 1 (Oct. 1997), 5--44.
[41]
P. Vaidyanathan, R. Ivison, G. Bombara, N. A. DeLateur, R. Weiss, D. Densmore, and C. Belta. 2017. Grid-based temporal logic inference. In Proceedings of the IEEE 56th Annual Conference on Decision and Control (CDC’17). 5354--5359.
[42]
Marcell Vazquez-Chanlatte, Jyotirmoy V. Deshmukh, Xiaoqing Jin, and Sanjit A. Seshia. 2017. Logical clustering and learning for time-series data. In Computer Aided Verification (Lecture Notes in Computer Science). Springer, Cham, 305--325.
[43]
Paolo Zuliani, André Platzer, and Edmund M. Clarke. 2013. Bayesian statistical model checking with application to Stateflow/Simulink verification. Formal Methods Syst. Design 43, 2 (Aug. 2013), 338--367.

Cited By

View all
  • (2024)Concurrent Learning of Control Policy and Unknown Safety Specifications in Reinforcement LearningIEEE Open Journal of Control Systems10.1109/OJCSYS.2024.34183063(266-281)Online publication date: 2024
  • (2024)Hand It to Me Formally! Data-Driven Control for Human-Robot Handovers With Signal Temporal LogicIEEE Robotics and Automation Letters10.1109/LRA.2024.34474769:10(9039-9046)Online publication date: Oct-2024
  • (2024)On Generating Explanations for Reinforcement Learning Policies: An Empirical StudyIEEE Control Systems Letters10.1109/LCSYS.2024.35193018(3027-3032)Online publication date: 2024
  • Show More Cited By

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM Transactions on Cyber-Physical Systems
ACM Transactions on Cyber-Physical Systems  Volume 5, Issue 3
July 2021
296 pages
ISSN:2378-962X
EISSN:2378-9638
DOI:10.1145/3458848
  • Editor:
  • Chenyang Lu
Issue’s Table of Contents
Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

Publisher

Association for Computing Machinery

New York, NY, United States

Journal Family

Publication History

Published: 26 March 2021
Accepted: 01 November 2020
Revised: 01 October 2020
Received: 01 May 2020
Published in TCPS Volume 5, Issue 3

Permissions

Request permissions for this article.

Check for updates

Author Tags

  1. Signal temporal logic
  2. anomaly detection
  3. classification
  4. decision trees
  5. formal methods
  6. impurity measure
  7. logic inference
  8. online learning
  9. specification mining
  10. supervised learning

Qualifiers

  • Research-article
  • Research
  • Refereed

Funding Sources

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)354
  • Downloads (Last 6 weeks)43
Reflects downloads up to 14 Feb 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Concurrent Learning of Control Policy and Unknown Safety Specifications in Reinforcement LearningIEEE Open Journal of Control Systems10.1109/OJCSYS.2024.34183063(266-281)Online publication date: 2024
  • (2024)Hand It to Me Formally! Data-Driven Control for Human-Robot Handovers With Signal Temporal LogicIEEE Robotics and Automation Letters10.1109/LRA.2024.34474769:10(9039-9046)Online publication date: Oct-2024
  • (2024)On Generating Explanations for Reinforcement Learning Policies: An Empirical StudyIEEE Control Systems Letters10.1109/LCSYS.2024.35193018(3027-3032)Online publication date: 2024
  • (2024)Online legal driving behavior monitoring for self-driving vehiclesNature Communications10.1038/s41467-024-44694-515:1Online publication date: 9-Jan-2024
  • (2024)Cooperative control of heterogeneous multi-agent systems under spatiotemporal constraintsAnnual Reviews in Control10.1016/j.arcontrol.2024.10094657(100946)Online publication date: 2024
  • (2024)Learning Temporal Task Specifications From DemonstrationsExplainable and Transparent AI and Multi-Agent Systems10.1007/978-3-031-70074-3_5(81-98)Online publication date: 6-May-2024
  • (2024)Adaptable Configuration of Decentralized MonitorsFormal Techniques for Distributed Objects, Components, and Systems10.1007/978-3-031-62645-6_11(197-217)Online publication date: 13-Jun-2024
  • (2024)Synthesizing Efficiently Monitorable Formulas in Metric Temporal LogicVerification, Model Checking, and Abstract Interpretation10.1007/978-3-031-50521-8_13(264-288)Online publication date: 15-Jan-2024
  • (2023)Learning Linear Temporal Properties for Autonomous Robotic SystemsIEEE Robotics and Automation Letters10.1109/LRA.2023.32633688:5(2930-2937)Online publication date: May-2023
  • (2023)STL: Surprisingly Tricky Logic (for System Validation)2023 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)10.1109/IROS55552.2023.10342290(8613-8620)Online publication date: 1-Oct-2023
  • Show More Cited By

View Options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

HTML Format

View this article in HTML Format.

HTML Format

Login options

Full Access

Figures

Tables

Media

Share

Share

Share this Publication link

Share on social media