Verification of Real-Time Systems using Linear Relation Analysis
Formal Methods in System Design - Special issue on computer aided verification (CAV 93)
Newton—constraint programming over nonlinear constraints
Science of Computer Programming - Special issue on concurrent constraint programming
HYTECH: The Cornell HYbrid TECHnology Tool
Hybrid Systems II
The d/dt Tool for Verification of Hybrid Systems
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
Convex Optimization
Counterexample-guided predicate abstraction of hybrid systems
Theoretical Computer Science - Tools and algorithms for the construction and analysis of systems (TACAS 2003)
Approximate reachability for linear systems
HSCC'03 Proceedings of the 6th international conference on Hybrid systems: computation and control
Scalable analysis of linear systems using mathematical programming
VMCAI'05 Proceedings of the 6th international conference on Verification, Model Checking, and Abstract Interpretation
Algorithmic algebraic model checking i: challenges from systems biology
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
PHAVer: algorithmic verification of hybrid systems past hytech
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Reachability of uncertain linear systems using zonotopes
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Taylor approximation for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Safety verification of hybrid systems by constraint propagation based abstraction refinement
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
Generating polynomial invariants for hybrid systems
HSCC'05 Proceedings of the 8th international conference on Hybrid Systems: computation and control
A Policy Iteration Technique for Time Elapse over Template Polyhedra
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Symbolic analysis for improving simulation coverage of Simulink/Stateflow models
EMSOFT '08 Proceedings of the 8th ACM international conference on Embedded software
Image Computation for Polynomial Dynamical Systems Using the Bernstein Expansion
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Generating and Analyzing Symbolic Traces of Simulink/Stateflow Models
CAV '09 Proceedings of the 21st International Conference on Computer Aided Verification
Exact join detection for convex polyhedra and other numerical abstractions
Computational Geometry: Theory and Applications
Some Experience on the Software Engineering of Abstract Interpretation Tools
Electronic Notes in Theoretical Computer Science (ENTCS)
Generating invariants for non-linear hybrid systems by linear algebraic methods
SAS'10 Proceedings of the 17th international conference on Static analysis
Using redundant constraints for refinement
ATVA'10 Proceedings of the 8th international conference on Automated technology for verification and analysis
Automatic abstraction of non-linear systems using change of bases transformations
Proceedings of the 14th international conference on Hybrid systems: computation and control
Relational abstractions for continuous and hybrid systems
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Timed relational abstractions for sampled data control systems
CAV'12 Proceedings of the 24th international conference on Computer Aided Verification
Computation of polytopic invariants for polynomial dynamical systems using linear programming
Automatica (Journal of IFAC)
Reachability analysis of polynomial systems using linear programming relaxations
ATVA'12 Proceedings of the 10th international conference on Automated Technology for Verification and Analysis
Synthesizing switching controllers for hybrid systems by generating invariants
Theories of Programming and Formal Methods
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We propose techniques for the verification of hybrid systems using template polyhedra, i.e., polyhedra whose inequalities have fixed expressions but with varying constant terms. Given a hybrid system description and a set of template linear expressions as inputs, our technique constructs over-approximations of the reachable states using template polyhedra. Therefore, operations used in symbolic model checking such as intersection, union and post-condition across discrete transitions over template polyhedra can be computed efficiently using template polyhedra without requiring expensive vertex enumeration. Additionally, the verification of hybrid systems requires techniques to handle the continuous dynamics inside discrete modes. We propose a new flowpipe construction algorithm using template polyhedra. Our technique uses higher-order Taylor series expansion to approximate the time trajectories. The terms occurring in the Taylor series expansion are bounded using repeated optimization queries. The location invariant is used to enclose the remainder term of the Taylor series, and thus truncate the expansion. Finally, we have implemented our technique as a part of the tool TimePass for the analysis of affine hybrid automata.