Giuseppe Bombara
ABSTRACT
This paper introduces a framework for inference of timed temporal logic properties from data. The dataset is given as a finite set of pairs of finite-time system traces and labels, where the labels indicate whether the traces exhibit some desired behavior (e.g., a ship traveling along a safe route). We propose a decision-tree based approach for learning signal temporal logic classifiers. The method produces binary decision trees that represent the inferred formulae. Each node of the tree contains a test associated with the satisfaction of a simple formula, optimally tuned from a predefined finite set of primitives. Optimality is assessed using heuristic impurity measures, which capture how well the current primitive splits the data with respect to the traces' labels. We propose extensions of the usual impurity measures from machine learning literature to handle classification of system traces by leveraging upon the robustness degree concept. The proposed incremental construction procedure greatly improves the execution time and the accuracy compared to existing algorithms. We present two case studies that illustrate the usefulness and the computational advantages of the algorithms. The first is an anomaly detection problem in a maritime environment. The second is a fault detection problem in an automotive powertrain system.
- E. Asarin, A. Donzé, O. Maler, and D. Nickovic. Parametric identification of temporal properties. In Runtime Verification, pages 147--160. Springer, 2012. Google Scholar
Digital Library
- E. Bartocci, L. Bortolussi, L. Nenzi, and G. Sanguinetti. System design of stochastic models using robustness of temporal properties. Theoretical Computer Science, 587:3--25, July 2015. Google ScholarDigital Library
- E. Bartocci, L. Bortolussi, and G. Sanguinetti. Data-driven statistical learning of temporal logic properties. In Formal Modeling and Analysis of Timed Systems, pages 23--37. Springer, 2014.Google Scholar
- L. Breiman, J. Friedman, C. J. Stone, and R. A. Olshen. Classification and regression trees. CRC press, 1984.Google Scholar
- S. Bufo, E. Bartocci, G. Sanguinetti, M. Borelli, U. Lucangelo, and L. Bortolussi. 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, pages 391--403. Springer, Oct. 2014.Google Scholar
- V. Chandola, A. Banerjee, and V. Kumar. Anomaly Detection: A Survey. ACM Comput Surv, 41(3):15:1--15:58, July 2009. Google ScholarDigital Library
- T. H. Cormen. Introduction to Algorithms. MIT Press, third edition, July 2009. Google ScholarDigital Library
- A. Donzé, T. Ferrere, and O. Maler. Efficient robust monitoring for STL. In Computer Aided Verification, pages 264--279. Springer, 2013.Google ScholarCross Ref
- A. Donzé and O. Maler. Robust Satisfaction of Temporal Logic over Real-Valued Signals. In K. Chatterjee and T. A. Henzinger, editors, Formal Modeling and Analysis of Timed Systems, number 6246 in Lecture Notes in Computer Science, pages 92--106. Springer Berlin Heidelberg, 2010. Google ScholarDigital Library
- G. E. Fainekos and G. J. Pappas. Robustness of temporal logic specifications for continuous-time signals. Theor. Comput. Sci., 410(42):4262--4291, Sept. 2009. Google ScholarDigital Library
- E. A. Gol, E. Bartocci, and C. Belta. A formal methods approach to pattern synthesis in reaction diffusion systems. In Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, pages 108--113. IEEE, 2014.Google ScholarCross Ref
- R. Grosu, S. A. Smolka, F. Corradini, A. Wasilewska, E. Entcheva, and E. Bartocci. Learning and detecting emergent behavior in networks of cardiac myocytes. Commun. ACM, 52(3):97--105, 2009. Google ScholarDigital Library
- B. Hoxha, H. Abbas, and G. Fainekos. Benchmarks for temporal logic requirements for automotive systems. Proc Appl. Verification Contin. Hybrid Syst., 2014.Google Scholar
- L. Hyafil and R. L. Rivest. Constructing optimal binary decision trees is NP-complete. Information Processing Letters, 5(1):15--17, May 1976.Google ScholarCross Ref
- L. Ingber. Adaptive simulated annealing (ASA): Lessons learned. Control Cybern., 25:33--54, 1996.Google Scholar
- R. Isermann. Fault-diagnosis systems. Springer, 2006.Google Scholar
- X. Jin, A. Donzé, J. Deshmukh, and S. A. Seshia. Mining Requirements from Closed-Loop Control Models. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., PP(99):1--1, 2015.Google ScholarCross Ref
- A. Jones, Z. Kong, and C. Belta. Anomaly detection in cyber-physical systems: A formal methods approach. In Decision and Control (CDC), 2014 IEEE 53rd Annual Conference on, pages 848--853. IEEE, 2014.Google ScholarCross Ref
- Z. Kong, A. Jones, and C. Belta. Temporal Logics for Learning and Detection of Anomalous Behaviors. IEEE Trans. Autom. Control, 2016. inpress.Google Scholar
- Z. Kong, A. Jones, A. Medina Ayala, E. Aydin Gol, and C. Belta. Temporal Logic Inference for Classification and Prediction from Data. In Proceedings of the 17th International Conference on Hybrid Systems: Computation and Control, HSCC '14, pages 273--282, New York, NY, USA, 2014. ACM. Google ScholarDigital Library
- K. Kowalska and L. Peel. Maritime anomaly detection using Gaussian Process active learning. In 2012 15th International Conference on Information Fusion (FUSION), pages 1164--1171, July 2012.Google Scholar
- O. Maler and D. Nickovic. Monitoring Temporal Properties of Continuous Signals. In Y. Lakhnech and S. Yovine, editors, Formal Techniques, Modelling and Analysis of Timed and Fault-Tolerant Systems, number 3253 in Lecture Notes in Computer Science, pages 152--166. Springer Berlin Heidelberg, 2004.Google Scholar
- J. R. Quinlan. C4.5: Programs for Machine Learning. Elsevier, June 2014.Google ScholarDigital Library
- B. D. Ripley. Pattern recognition and neural networks. Cambridge university press, 1996. Google ScholarDigital Library
- R. Storn and K. Price. Differential Evolutiontextendash A Simple and Efficient Heuristic for global Optimization over Continuous Spaces. Journal of Global Optimization, 11(4):341--359, Dec. 1997. Google ScholarDigital Library
- H. Yang, B. Hoxha, and G. Fainekos. Querying Parametric Temporal Logic Properties on Embedded Systems. In Testing Software and Systems, number 7641 in Lecture Notes in Computer Science, pages 136--151. Springer, 2012.Google Scholar
- P. Zuliani, A. Platzer, and E. M. Clarke. Bayesian statistical model checking with application to Stateflow/Simulink verification. Form Methods Syst Des, 43(2):338--367, Aug. 2013. Google ScholarDigital Library
Index Terms
- A Decision Tree Approach to Data Classification using Signal Temporal Logic
Recommendations
Offline and Online Learning of Signal Temporal Logic Formulae Using Decision Trees
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 ...
Temporal logic inference for classification and prediction from data
HSCC '14: Proceedings of the 17th international conference on Hybrid systems: computation and controlThis paper presents an inference algorithm that can discover temporal logic properties of a system from data. Our algorithm operates on finite time system trajectories that are labeled according to whether or not they demonstrate some desirable system ...
Constructive linear-time temporal logic: Proof systems and Kripke semantics
In this paper we study a version of constructive linear-time temporal logic (LTL) with the ''next'' temporal operator. The logic is originally due to Davies, who has shown that the proof system of the logic corresponds to a type system for binding-time ...
Comments