A Box-Based Distance between Regions for Guiding the Reachability Analysis of SpaceEx

A recent technique used in falsification methods for hybrid systems relies on distance-based heuristics for guiding the search towards a goal state. The question is whether the technique can be carried over to reachability analyses that use regions as their basic data structure. In this paper, we introduce a box-based distance measure between regions. We present an algorithm that, given two regions, efficiently computes the box-based distance between them. We have implemented the algorithm in SpaceEx and use it for guiding the region-based reachability analysis of SpaceEx. We illustrate the practical potential of our approach in a case study for the navigation benchmark.

[1]  S. Kupferschmid,et al.  Adapting an AI Planning Heuristic for Directed Model Checking , 2006, SPIN.

[2]  Albert Nymeyer,et al.  Guided Invariant Model Checking Based on Abstraction and Symbolic Pattern Databases , 2004, TACAS.

[3]  Rajeev Alur,et al.  A Temporal Logic of Nested Calls and Returns , 2004, TACAS.

[4]  Christos G. Cassandras,et al.  Verification-Integrated Falsification of Non-Deterministic Hybrid Systems , 2006 .

[5]  Lydia E. Kavraki,et al.  Hybrid Systems: From Verification to Falsification , 2007, CAV.

[6]  Oded Maler,et al.  Systematic Simulation Using Sensitivity Analysis , 2007, HSCC.

[7]  Malte Helmert,et al.  The Causal Graph Revisited for Directed Model Checking , 2009, SAS.

[8]  Ezio Bartocci,et al.  Learning and detecting emergent behavior in networks of cardiac myocytes , 2008, CACM.

[9]  Antoine Girard,et al.  Hybridization methods for the analysis of nonlinear systems , 2007, Acta Informatica.

[10]  Thomas A. Henzinger,et al.  Linear Phase-Portrait Approximations for Nonlinear Hybrid Systems , 1996, Hybrid Systems.

[11]  Michael S. Branicky,et al.  Nonlinear and Hybrid Control Via RRTs , 2002 .

[12]  Bernd Finkbeiner,et al.  Directed model checking with distance-preserving abstractions , 2006, International Journal on Software Tools for Technology Transfer.

[13]  Calin Belta,et al.  Hybrid Modeling and Simulation of Biomolecular Networks , 2001, HSCC.

[14]  Martin Wehrle,et al.  Abstractions and Pattern Databases: The Quest for Succinctness and Accuracy , 2011, TACAS.

[15]  C. Pinello,et al.  Automotive engine control and hybrid systems: challenges and opportunities , 2000, Proceedings of the IEEE.

[16]  Goran Frehse,et al.  Reachability Analysis of a Switched Buffer Network , 2007, HSCC.

[17]  C. Tomlin,et al.  Symbolic reachable set computation of piecewise affine hybrid automata and its application to biological modelling: Delta-Notch protein signalling. , 2004, Systems biology.

[18]  Bruce H. Krogh,et al.  Computational techniques for hybrid system verification , 2003, IEEE Trans. Autom. Control..

[19]  Goran Frehse.  PHAVer: Algorithmic Verification of Hybrid Systems Past HyTech , 2005, HSCC.

[20]  Antoine Girard,et al.  Verification Using Simulation , 2006, HSCC.

[21]  Ádám M. Halász,et al.  Understanding the Bacterial Stringent Response Using Reachability Analysis of Hybrid Systems , 2004, HSCC.

[22]  J. Hespanha,et al.  Models for Multi-Specie Chemical Reactions Using Polynomial Stochastic Hybrid Systems , 2005, Proceedings of the 44th IEEE Conference on Decision and Control.

[23]  Antoine Girard,et al.  SpaceEx: Scalable Verification of Hybrid Systems , 2011, CAV.

[24]  Bernhard Nebel,et al.  Faster Than Uppaal? , 2008, CAV.

[25]  Thomas A. Henzinger,et al.  Hybrid Systems: Computation and Control , 1998, Lecture Notes in Computer Science.

[26]  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).

[27]  Thomas A. Henzinger,et al.  Hybrid Systems III , 1995, Lecture Notes in Computer Science.

[28]  João Pedro Hespanha.  Polynomial Stochastic Hybrid Systems , 2005, HSCC.

[29]  Pravin Varaiya,et al.  What's decidable about hybrid automata? , 1995, STOC '95.

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

[31]  Ashish Tiwari,et al.  Symbolic Systems Biology: Hybrid Modeling and Analysis of Biological Networks , 2004, HSCC.

[32]  Andreas Podelski,et al.  ACSAR: Software Model Checking with Transfinite Refinement , 2007, SPIN.

[33]  Bernd Finkbeiner,et al.  Uppaal/DMC- Abstraction-Based Heuristics for Directed Model Checking , 2007, TACAS.

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

[35]  O. Maler,et al.  Hardware timing verification using KRONOS , 1996, Proceedings of the Seventh Israeli Conference on Computer Systems and Software Engineering.

[36]  Stefan Ratschan,et al.  Verification-Integrated Falsification of non-Deterministic Hybrid Systems , 2006, ADHS.

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

[38]  Stefan Edelkamp,et al.  Directed explicit-state model checking in the validation of communication protocols , 2004, International Journal on Software Tools for Technology Transfer.

[39]  P. Barbano,et al.  A coherent framework for multiresolution analysis of biological networks with "memory": Ras pathway, cell cycle, and immune system. , 2005, Proceedings of the National Academy of Sciences of the United States of America.

[40]  Calin Belta,et al.  Model Checking Genetic Regulatory Networks with Parameter Uncertainty , 2007, HSCC.

[41]  Ezio Bartocci,et al.  From Cardiac Cells to Genetic Regulatory Networks , 2011, CAV.

[42]  Emilio Frazzoli,et al.  Incremental Search Methods for Reachability Analysis of Continuous and Hybrid Systems , 2004, HSCC.