Technical Report: Property-Directed Verified Monitoring of Signal Temporal Logic

Signal Temporal Logic monitoring over numerical simulation traces has emerged as an effective approach to approximate verification of continuous and hybrid systems. In this report we explore an exact verification procedure for STL properties based on monitoring verified traces in the form of Taylor model flowpipes as produced by the Flow* verified integrator. We explore how tight integration with Flow*'s symbolic flowpipe representation can lead to more precise and more efficient monitoring. We then show how the performance of monitoring can be increased substantially by introducing masks, a property-directed refinement of our method which restricts flowpipe monitoring to the time regions relevant to the overall truth of a complex proposition. Finally, we apply our implementation of these methods to verifying properties of a challenging continuous system, evaluating the impact of each aspect of our procedure on monitoring performance.

[1]  George J. Pappas,et al.  Robust Sampling for MITL Specifications , 2007, FORMATS.

[2]  Martin Berz,et al.  Verified High-Order Inversion of Functional Depedencies and Interval Newton Methods , 2001, Reliab. Comput..

[3]  Daisuke Ishii,et al.  HySIA: Tool for Simulating and Monitoring Hybrid Automata Based on Interval Analysis , 2017, RV.

[4]  Jean-Baptiste Jeannin,et al.  dTL2: Differential Temporal Dynamic Logic with Nested Temporalities for Hybrid Systems , 2014, IJCAR.

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

[6]  Liang Zou,et al.  Abstraction of Elementary Hybrid Systems by Variable Transformation , 2014, FM.

[7]  Stefan Behnel,et al.  Cython: The Best of Both Worlds , 2011, Computing in Science & Engineering.

[8]  Daisuke Ishii,et al.  Monitoring Bounded LTL Properties Using Interval Analysis , 2015, Electron. Notes Theor. Comput. Sci..

[9]  Xin Chen,et al.  Decomposed Reachability Analysis for Nonlinear Systems , 2016, 2016 IEEE Real-Time Systems Symposium (RTSS).

[10]  Xin Chen,et al.  Reachability analysis of non-linear hybrid systems using Taylor Models , 2015 .

[11]  Martin Berz,et al.  Computation and Application of Taylor Polynomials with Interval Remainder Bounds , 1998, Reliab. Comput..

[12]  Garvit Juniwal,et al.  Robust online monitoring of signal temporal logic , 2015, Formal Methods in System Design.

[13]  Thomas A. Henzinger,et al.  Automatic Symbolic Verification of Embedded Systems , 1996, IEEE Trans. Software Eng..

[14]  Alberto Griggio,et al.  Verifying LTL Properties of Hybrid Systems with K-Liveness , 2014, CAV.

[15]  Xin Chen,et al.  Flow*: An Analyzer for Non-linear Hybrid Systems , 2013, CAV.

[16]  Davide Bresolin,et al.  HyLTL: a temporal logic for model checking hybrid systems , 2013, HAS.

[17]  Xin Chen,et al.  A Benchmark Suite for Hybrid Systems Reachability Analysis , 2015, NFM.

[18]  Dejan Nickovic,et al.  AMT: A Property-Based Monitoring Tool for Analog Systems , 2007, FORMATS.

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

[20]  Martin Berz,et al.  Verified Integration of ODEs and Flows Using Differential Algebraic Methods on High-Order Taylor Models , 1998, Reliab. Comput..

[21]  François Fages,et al.  On temporal logic constraint solving for analyzing numerical data time series , 2008, Theor. Comput. Sci..

[22]  Jane Hillston,et al.  Automatic verification of reliability requirements of spatio-temporal analysis using Three-Valued Spatio-Temporal Logic , 2017, VALUETOOLS.

[23]  Matthias Althoff,et al.  STL Model Checking of Continuous and Hybrid Systems , 2016, ATVA.

[24]  S. Leibler,et al.  Mechanisms of noise-resistance in genetic oscillators , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[25]  Wei Chen,et al.  dReach: δ-Reachability Analysis for Hybrid Systems , 2015, TACAS.

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

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

[28]  R. A. Silverman,et al.  Introductory Real Analysis , 1972 .

[29]  Dana Fisman,et al.  Temporal Reasoning on Incomplete Paths , 2018, ISoLA.

[30]  Daisuke Ishii,et al.  Monitoring Temporal Properties using Interval Analysis , 2016, IEICE Trans. Fundam. Electron. Commun. Comput. Sci..

[31]  J. M. Peña On the Multivariate Horner Scheme , 2000, SIAM J. Numer. Anal..

[32]  Edmund M. Clarke,et al.  dReal: An SMT Solver for Nonlinear Theories over the Reals , 2013, CADE.

[33]  Ian Stark,et al.  A More Sensitive Context , 2017, ArXiv.

[34]  Matthias Althoff,et al.  An Introduction to CORA 2015 , 2015, ARCH@CPSWeek.

[35]  Carla Piazza,et al.  Algorithmic Algebraic Model Checking I: Challenges from Systems Biology , 2005, CAV.

[36]  Nikolaj Bjørner,et al.  Z3: An Efficient SMT Solver , 2008, TACAS.

[37]  Patrice Godefroid,et al.  Model Checking Partial State Spaces with 3-Valued Temporal Logics , 1999, CAV.

[38]  Martin Berz,et al.  SUPPRESSION OF THE WRAPPING EFFECT BY TAYLOR MODEL- BASED VERIFIED INTEGRATORS: LONG-TERM STABILIZATION BY PRECONDITIONING , 2011 .

[39]  R. Baker Kearfott,et al.  Introduction to Interval Analysis , 2009 .

[40]  Martin Berz,et al.  Efficient Control of the Dependency Problem Based on Taylor Model Methods , 1999, Reliab. Comput..

[41]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

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

[43]  Kyungmin Bae,et al.  Bounded model checking of signal temporal logic properties using syntactic separation , 2019, Proc. ACM Program. Lang..