Analog computation via neural networks
Theoretical Computer Science
Computability with low-dimensional dynamical systems
Theoretical Computer Science
The algorithmic analysis of hybrid systems
Theoretical Computer Science - Special issue on hybrid systems
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
On the computational power of neural nets
Journal of Computer and System Sciences
Interconnected automata and linear systems: a theoretical framework in discrete-time
Proceedings of the DIMACS/SYCON workshop on Hybrid systems III : verification and control: verification and control
Complexity and real computation
Complexity and real computation
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
Mathematical control theory: deterministic finite dimensional systems (2nd ed.)
What's decidable about hybrid automata?
Journal of Computer and System Sciences
Deciding stability and mortality of piecewise affine dynamical systems
Theoretical Computer Science
The stability of saturated linear dynamical systems is undecidable
Journal of Computer and System Sciences
Introduction To Automata Theory, Languages, And Computation
Introduction To Automata Theory, Languages, And Computation
Complexity of stability and controllability of elementary hybrid systems
Automatica (Journal of IFAC)
On a Conjecture of Kurka. A Turing Machine with No Periodic Configurations
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
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We prove that several global properties (global convergence, global asymptotic stability, mortality, and nilpotence) of particular classes of discrete time dynamical systems are undecidable. Such results had been known only for point-to-point properties. We prove these properties undecidable for saturated linear dynamical systems, and for continuous piecewise affine dynamical systems in dimension three. We also describe some consequences of our results on the possible dynamics of such systems.