PHAVer: algorithmic verification of hybrid systems past HyTech

In 1995, HyTech broke new ground as a potentially powerful tool for verifying hybrid systems. But due to practical and systematic limitations it is only applicable to relatively simple systems. We address the main problems of HyTech with PHAVer, a new tool for the exact verification of safety properties of hybrid systems with piecewise constant bounds on the derivatives, so-called linear hybrid automata. Affine dynamics are handled by on-the-fly overapproximation and partitioning of the state space based on user-provided constraints and the dynamics of the system. PHAVer features exact arithmetic in a robust implementation that, based on the Parma Polyhedra Library, supports arbitrarily large numbers. To force termination and manage the complexity of the polyhedral computations, we propose methods to conservatively limit the number of bits and constraints of polyhedra. Experimental results for a navigation benchmark and a tunnel diode circuit demonstrate the effectiveness of the approach.

[1]  Thomas A. Henzinger,et al.  The Algorithmic Analysis of Hybrid Systems , 1995, Theor. Comput. Sci..

[2]  Lars Hedrich,et al.  On Discrete Modeling and Model Checking for Nonlinear Analog Systems , 2002, CAV.

[3]  Thomas A. Henzinger,et al.  Using HyTech to Synthesize Control Parameters for a Steam Boiler , 1995, Formal Methods for Industrial Applications.

[4]  Thomas A. Henzinger,et al.  HYTECH: a model checker for hybrid systems , 1997, International Journal on Software Tools for Technology Transfer.

[5]  Roberto Bagnara,et al.  Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library , 2002, SAS.

[6]  Ansgar Fehnker,et al.  Benchmarks for Hybrid Systems Verification , 2004, HSCC.

[7]  Thomas A. Henzinger,et al.  Hybrid Automata: An Algorithmic Approach to the Specification and Verification of Hybrid Systems , 1992, Hybrid Systems.

[8]  Thomas A. Henzinger,et al.  Automatic Rectangular Refinement of Affine Hybrid Systems , 2005, FORMATS.

[9]  Ka Lok Man,et al.  Formal verification of Chi models using PHAVer (extended version) , 2006 .

[10]  Goran Frehse,et al.  Compositional verification of hybrid systems using simulation relations , 2005 .

[11]  Nancy A. Lynch,et al.  Hybrid I/O automata , 1995, Inf. Comput..

[12]  Goran Frehse,et al.  On Timed Simulation Relations for Hybrid Systems and Compositionality , 2006, FORMATS.

[13]  H. Wong-Toi,et al.  Some lessons from the HYTECH experience , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[14]  Stefan Ratschan,et al.  Safety Verification of Hybrid Systems by Constraint Propagation Based Abstraction Refinement , 2005, HSCC.

[15]  Gerardo Lafferriere,et al.  Symbolic Reachability Computation for Families of Linear Vector Fields , 2001, J. Symb. Comput..

[16]  Thomas A. Henzinger,et al.  HYTECH: the next generation , 1995, Proceedings 16th IEEE Real-Time Systems Symposium.

[17]  Thomas A. Henzinger,et al.  Beyond HYTECH: Hybrid Systems Analysis Using Interval Numerical Methods , 2000, HSCC.

[18]  Robert P. Goldman,et al.  Applications of model checking at Honeywell Laboratories , 2001, SPIN '01.

[19]  Olaf Stursberg,et al.  Efficient Representation and Computation of Reachable Sets for Hybrid Systems , 2003, HSCC.

[20]  O. Stursberg,et al.  Approximating switched continuous systems by rectangular automata , 1999, 1999 European Control Conference (ECC).

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

[22]  Stefan Kowalewski,et al.  An Evaluation of two Recent Reachability Analysis Tools for Hybrid Systems , 2006, ADHS.

[23]  Thomas A. Henzinger,et al.  The theory of hybrid automata , 1996, Proceedings 11th Annual IEEE Symposium on Logic in Computer Science.

[24]  Thomas Stauner,et al.  Modelling and Verification using Linear Hybrid Automata -- a Case Study , 2000 .

[25]  Rajeev Alur,et al.  Modeling and analysis of hybrid systems , 2003 .

[26]  HalbwachsNicolas,et al.  Verification of Real-Time Systems using Linear Relation Analysis , 1997 .

[27]  Howard Wong-Toi,et al.  Automated Analysis of an Audio Control Protocol , 1995, CAV.

[28]  Egon Börger,et al.  Formal methods for industrial applications : specifying and programming the steam boiler control , 1996 .

[29]  Pei-Hsin Ho,et al.  Automatic Analysis of Hybrid Systems , 1996 .

[30]  Alberto Bemporad,et al.  Verification of Hybrid Systems via Mathematical Programming , 1999, HSCC.

[31]  Howard Wong-Toi,et al.  Symbolic approximations for verifying real-time systems , 1995 .

[32]  Nicolas Halbwachs,et al.  Verification of Real-Time Systems using Linear Relation Analysis , 1997, Formal Methods Syst. Des..

[33]  B. Krogh,et al.  Towards formal verification of analog designs , 2004, ICCAD 2004.

[34]  Jörg Preußig,et al.  Formale Überprüfung der Korrektheit von Steuerungen mittels rektangulärer Automaten , 2000 .

[35]  Olaf Stursberg,et al.  A Case Study in Tool-Aided Analysis of Discretely Controlled Continuous Systems: The Two Tanks Problem , 1997, Hybrid Systems.

[36]  Andreas Podelski,et al.  Model Checking of Hybrid Systems: From Reachability Towards Stability , 2006, HSCC.

[37]  Olaf Stursberg,et al.  An assessment of the current status of algorithmic approaches to the verification of hybrid systems , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[38]  Rob A. Rutenbar,et al.  Time Domain Verification of Oscillator Circuit Properties , 2006, Electron. Notes Theor. Comput. Sci..

[39]  Thomas A. Henzinger,et al.  An Algorithm for the Approximative Analysis of Rectangular Automata , 1998, FTRTFT.

[40]  Thomas A. Henzinger,et al.  Automatic symbolic verification of embedded systems , 1993, 1993 Proceedings Real-Time Systems Symposium.

[41]  Rob A. Rutenbar,et al.  Verifying analog oscillator circuits using forward/backward abstraction refinement , 2006, Proceedings of the Design Automation & Test in Europe Conference.

[42]  T. Henzinger,et al.  Algorithmic Analysis of Nonlinear Hybrid Systems , 1998, CAV.

[43]  G. Frehse,et al.  Assume-guarantee reasoning for hybrid I/O-automata by over-approximation of continuous interaction , 2004, 2004 43rd IEEE Conference on Decision and Control (CDC) (IEEE Cat. No.04CH37601).

[44]  RatschanStefan,et al.  Safety verification of hybrid systems by constraint propagation-based abstraction refinement , 2007 .