TeLEx: learning signal temporal logic from positive examples using tightness metric

We propose a novel passive learning approach, TeLex, to infer signal temporal logic (STL) formulas that characterize the behavior of a dynamical system using only observed signal traces of the system. First, we present a template-driven learning approach that requires two inputs: a set of observed traces and a template STL formula. The unknown parameters in the template can include time-bounds of the temporal operators, as well as the thresholds in the inequality predicates. TeLEx finds the value of the unknown parameters such that the synthesized STL property is satisfied by all the provided traces and it is tight. This requirement of tightness is essential to generating interesting properties when only positive examples are provided and there is no option to actively query the dynamical system to discover the boundaries of legal behavior. We propose a novel quantitative semantics for satisfaction of STL properties which enables TeLEx to learn tight STL properties without multidimensional optimization. The proposed new metric is also smooth. This is critical to enable the use of gradient-based numerical optimization engines and it produces a 30x to 100x speed-up with respect to the state-of-art gradient-free optimization. Second, we present a novel technique for automatically learning the structure of the STL formula by incrementally constructing more complex formula guided by the robustness metric of subformula. We demonstrate the effectiveness of the overall approach for learning STL formulas from only positive examples on a set of synthetic and real-world benchmarks.

[1]  Ashish Tiwari,et al.  TeLEx: Passive STL Learning Using Only Positive Examples , 2017, RV.

[2]  Sanjit A. Seshia,et al.  Mining Requirements From Closed-Loop Control Models , 2015, IEEE Trans. Comput. Aided Des. Integr. Circuits Syst..

[3]  Luc De Raedt,et al.  Inductive Logic Programming: Theory and Methods , 1994, J. Log. Program..

[4]  Georgios E. Fainekos,et al.  Mining parametric temporal logic properties in model-based design for cyber-physical systems , 2015, International Journal on Software Tools for Technology Transfer.

[5]  R. Storn,et al.  Differential Evolution: A Practical Approach to Global Optimization (Natural Computing Series) , 2005 .

[6]  Takumi Akazaki.  Falsification of Conditional Safety Properties for Cyber-Physical Systems with Gaussian Process Regression , 2016, RV.

[7]  Alberto L. Sangiovanni-Vincentelli,et al.  Model predictive control with signal temporal logic specifications , 2014, 53rd IEEE Conference on Decision and Control.

[8]  Ufuk Topcu,et al.  Synthesis of Joint Control and Active Sensing Strategies Under Temporal Logic Constraints , 2016, IEEE Transactions on Automatic Control.

[9]  Leslie G. Valiant,et al.  A theory of the learnable , 1984, CACM.

[10]  Susmit Jha,et al.  Automated Synthesis of Safe Autonomous Vehicle Control Under Perception Uncertainty , 2016, NFM.

[11]  Susmit Jha,et al.  On Optimal Control of Stochastic Linear Hybrid Systems , 2016, FORMATS.

[12]  Jorge Nocedal,et al.  Algorithm 778: L-BFGS-B: Fortran subroutines for large-scale bound-constrained optimization , 1997, TOMS.

[13]  Calin Belta,et al.  A Decision Tree Approach to Data Classification using Signal Temporal Logic , 2016, HSCC.

[14]  Houssam Abbas,et al.  Smooth operator: Control using the smooth robustness of temporal logic , 2017, 2017 IEEE Conference on Control Technology and Applications (CCTA).

[15]  Dejan Nickovic,et al.  Monitoring Temporal Properties of Continuous Signals , 2004, FORMATS/FTRTFT.

[16]  Rupak Majumdar,et al.  Quantifying Conformance Using the Skorokhod Metric , 2015, CAV.

[17]  George J. Pappas,et al.  Robustness of Temporal Logic Specifications , 2006, FATES/RV.

[18]  Alexandre Donzé,et al.  Breach, A Toolbox for Verification and Parameter Synthesis of Hybrid Systems , 2010, CAV.

[19]  Sanjit A. Seshia,et al.  A theory of formal synthesis via inductive learning , 2015, Acta Informatica.

[20]  Wanli Zuo,et al.  Learning from Positive and Unlabeled Examples: A Survey , 2008, 2008 International Symposiums on Information Processing.

[21]  Sophia Mã ¶ ller.  Formal Modeling and Analysis of Timed Systems , 2016, Lecture Notes in Computer Science.

[22]  Stephen Muggleton,et al.  Learning from Positive Data , 1996, Inductive Logic Programming Workshop.

[23]  Sriram Sankaranarayanan,et al.  S-TaLiRo: A Tool for Temporal Logic Falsification for Hybrid Systems , 2011, TACAS.

[24]  Calin Belta,et al.  Robust temporal logic model predictive control , 2015, 2015 53rd Annual Allerton Conference on Communication, Control, and Computing (Allerton).

[25]  Dejan Nickovic,et al.  Quantitative monitoring of STL with edit distance , 2016, Formal Methods in System Design.

[26]  Dimos V. Dimarogonas,et al.  Robust Control for Signal Temporal Logic Specifications using Average Space Robustness , 2016, ArXiv.

[27]  Francisco Facchinei,et al.  A Truncated Newton Algorithm for Large Scale Box Constrained Optimization , 2002, SIAM J. Optim..

[28]  Takeshi Koshiba,et al.  Learning Deterministic even Linear Languages From Positive Examples , 1997, Theor. Comput. Sci..

[29]  James Jay Horning,et al.  A study of grammatical inference , 1969 .

[30]  Ezio Bartocci,et al.  Data-Driven Statistical Learning of Temporal Logic Properties , 2014, FORMATS.

[31]  Ezio Bartocci,et al.  Temporal Logic Based Monitoring of Assisted Ventilation in Intensive Care Patients , 2014, ISoLA.

[32]  E. Mark Gold,et al.  Language Identification in the Limit , 1967, Inf. Control..

[33]  Alexandre Donzé,et al.  On Signal Temporal Logic , 2013, RV.

[34]  Calin Belta,et al.  Q-Learning for robust satisfaction of signal temporal logic specifications , 2016, 2016 IEEE 55th Conference on Decision and Control (CDC).

[35]  François Denis,et al.  Learning Regular Languages from Simple Positive Examples , 2001, Machine Learning.

[36]  Oded Maler,et al.  Robust Satisfaction of Temporal Logic over Real-Valued Signals , 2010, FORMATS.

[37]  Calin Belta,et al.  Temporal logic inference for classification and prediction from data , 2014, HSCC.

[38]  Houssam Abbas,et al.  Functional gradient descent method for Metric Temporal Logic specifications , 2014, 2014 American Control Conference.

[39]  Ezio Bartocci,et al.  A Robust Genetic Algorithm for Learning Temporal Specifications from Data , 2018, QEST.

[40]  Georgios E. Fainekos,et al.  Querying Parametric Temporal Logic Properties on Embedded Systems , 2012, ICTSS.

[41]  Houssam Abbas,et al.  Robustness-guided temporal logic testing and verification for Stochastic Cyber-Physical Systems , 2014, The 4th Annual IEEE International Conference on Cyber Technology in Automation, Control and Intelligent.

[42]  Dejan Nickovic,et al.  Checking Temporal Properties of Discrete, Timed and Continuous Behaviors , 2008, Pillars of Computer Science.