Level Set Methods for Computation in Hybrid Systems
HSCC '00 Proceedings of the Third International Workshop on Hybrid Systems: Computation and Control
Using Abstractions for the Verification of Linear Hybrid Systems
CAV '94 Proceedings of the 6th International Conference on Computer Aided Verification
Safety verification of hybrid systems by constraint propagation-based abstraction refinement
ACM Transactions on Embedded Computing Systems (TECS)
Abstractions for hybrid systems
Formal Methods in System Design
The temporal logic of programs
SFCS '77 Proceedings of the 18th Annual Symposium on Foundations of Computer Science
Approximating Continuous Systems by Timed Automata
FMSB '08 Proceedings of the 1st international workshop on Formal Methods in Systems Biology
Model checking liveness properties of genetic regulatory networks
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Verification of continuous dynamical systems by timed automata
Formal Methods in System Design
Lyapunov abstractions for inevitability of hybrid systems
Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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We look at the problem of proving inevitability of continuous dynamical systems. An inevitability property says that a region of the state space will eventually be reached: this is a type of liveness property from the computer science viewpoint, and is related to attractivity of sets in dynamical systems. We consider a method of Maler and Batt to make an abstraction of a continuous dynamical system to a timed automaton, and show that a potentially infinite number of splits will be made if the splitting of the state space is made arbitrarily. To solve this problem, we define a method which creates a finite-sized timed automaton abstraction for a class of linear dynamical systems, and show that this timed abstraction proves inevitability.