Recursive and Backward Reasoning in the Verification on Hybrid Systems

In this paper we introduce two improvements to the method of verification of hybrid systems by constraint propagation based abstraction refinement that we introduced earlier. The first improvement improves the recursive propagation of reachability information over the regions constituting the abstraction, and the second improvement reasons backward from the set of unsafe states, instead of reasoning forward from the set of initial states. Detailed computational experiments document the usefulness of these improvements.

[1]  Timothy J. Hickey,et al.  Metalevel Interval Arithmetic and Verifiable Constraint Solving , 2001, J. Funct. Log. Program..

[2]  Calin Belta,et al.  Reachability analysis of multi-affine systems , 2006, HSCC.

[3]  Nedialko S. Nedialkov,et al.  Validated solutions of initial value problems for ordinary differential equations , 1999, Appl. Math. Comput..

[4]  Stefan Ratschan,et al.  Continuous First-Order Constraint Satisfaction , 2002, AISC.

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

[6]  E. Walter,et al.  Applied Interval Analysis: With Examples in Parameter and State Estimation, Robust Control and Robotics , 2001 .

[7]  Olaf Stursberg,et al.  Reachability Analysis of a Class of Switched Continuous Systems by Integrating Rectangular Approximation and Rectangular Analysis , 1999, HSCC.

[8]  Mark R. Greenstreet,et al.  Hybrid Systems: Computation and Control , 2002, Lecture Notes in Computer Science.

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

[10]  Stefan Ratschan,et al.  Constraints for Continuous Reachability in the Verification of Hybrid Systems , 2006, AISC.

[11]  Stefan Ratschan,et al.  Safety verification of hybrid systems by constraint propagation-based abstraction refinement , 2007, TECS.

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

[13]  Pascal Van Hentenryck,et al.  CLP(Intervals) Revisited , 1994, ILPS.

[14]  Ernest Davis,et al.  Constraint Propagation with Interval Labels , 1987, Artif. Intell..

[15]  Dominique Schneider,et al.  Qualitative Analysis and Verification of Hybrid Models of Genetic Regulatory Networks: Nutritional Stress Response in , 2005, HSCC.

[16]  Frédéric Benhamou,et al.  Continuous and Interval Constraints , 2006, Handbook of Constraint Programming.

[17]  Goran Frehse,et al.  PHAVer: algorithmic verification of hybrid systems past HyTech , 2005, International Journal on Software Tools for Technology Transfer.

[18]  Arnaud Gotlieb,et al.  Dynamic Optimization of Interval Narrowing Algorithms , 1998, J. Log. Program..