The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
What's decidable about hybrid automata?
Journal of Computer and System Sciences
A Calculus of Communicating Systems
A Calculus of Communicating Systems
TACAS '95 Proceedings of the First International Workshop on Tools and Algorithms for Construction and Analysis of Systems
Approximate Reachability Analysis of Piecewise-Linear Dynamical Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Possibly Not Closed Convex Polyhedra and the Parma Polyhedra Library
SAS '02 Proceedings of the 9th International Symposium on Static Analysis
Counterexample-Guided Abstraction Refinement
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
Analysis of Hybrid Systems: An Ounce of Realism Can Save an Infinity of States
CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
LICS '96 Proceedings of the 11th Annual IEEE Symposium on Logic in Computer Science
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 Nonlinear Systems Using a Nonlinear Hybridization
HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
Theoretical Computer Science
Language-based abstraction refinement for hybrid system verification
VMCAI'07 Proceedings of the 8th international conference on Verification, model checking, and abstract interpretation
Reachability problems for hybrid automata
RP'11 Proceedings of the 5th international conference on Reachability problems
Efficient bounded reachability computation for rectangular automata
RP'11 Proceedings of the 5th international conference on Reachability problems
On timed simulation relations for hybrid systems and compositionality
FORMATS'06 Proceedings of the 4th international conference on Formal Modeling and Analysis of Timed Systems
Reachability analysis of non-linear planar autonomous systems
FSEN'11 Proceedings of the 4th IPM international conference on Fundamentals of Software Engineering
On approximative reachability analysis of biochemical dynamical systems
Transactions on Computational Systems Biology XIV
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We show how to automatically construct and refine rectangular abstractions of systems of linear differential equations. From a hybrid automaton whose dynamics are given by a system of linear differential equations, our method computes automatically a sequence of rectangular hybrid automata that are increasingly precise overapproximations of the original hybrid automaton. We prove an optimality criterion for successive refinements. We also show that this method can take into account a safety property to be verified, refining only relevant parts of the state space. The practicability of the method is illustrated on a benchmark case study.