An improvement of the projection operator in cylindrical algebraic decomposition
ISSAC '90 Proceedings of the international symposium on Symbolic and algebraic computation
Symbolic Reachability Computation for Families of Linear Vector Fields
Journal of Symbolic Computation
Lateral Inhibition through Delta-Notch Signaling: A Piecewise Affine Hybrid Model
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Series of Abstractions for Hybrid Automata
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Reachability Analysis of Hybrid Systems via Predicate Abstraction
HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
Construction of Abstract State Graphs with PVS
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Experience with Predicate Abstraction
CAV '99 Proceedings of the 11th International Conference on Computer Aided Verification
ATVA'05 Proceedings of the Third international conference on Automated Technology for Verification and Analysis
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This paper examines the feasibility of predicate abstraction as a method for the reachability analysis of hybrid systems. A hybrid system can be abstracted into a purely discrete system by mapping the continuous state space into an equivalent finite discrete state space using a set of Boolean predicates and a decision procedure in the theory of real closed fields. It is then possible to find the feasible transitions between these states. In this paper, we propose new conditions for predicate abstraction which greatly reduce the number of transitions in the abstract discrete system. We also develop a computational technique for reachability analysis and apply it to a biological system of interest (the Delta-Notch lateral inhibition problem).