Polynomial-time algorithm for the orbit problem
Journal of the ACM (JACM)
Irreducibles and the composed product for polynomials over a finite field
Discrete Mathematics
Reachability analysis of dynamical systems having piecewise-constant derivatives
Theoretical Computer Science - Special issue on hybrid systems
Widening the Boundary between Decidable and Undecidable Hybrid Systems
CONCUR '02 Proceedings of the 13th International Conference on Concurrency Theory
On the Decidability of the Reachability Problem for Planar Differential Inclusions
HSCC '01 Proceedings of the 4th International Workshop on Hybrid Systems: Computation and Control
Robust simulations of turing machines with analytic maps and flows
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
Survey A survey of computational complexity results in systems and control
Automatica (Journal of IFAC)
The continuous Skolem-Pisot problem
Theoretical Computer Science
The orbit problem in higher dimensions
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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Dynamical systems allow to modelize various phenomena or processes by only describing their local behaviour. It is however useful to understand the behaviour in a more global way. Checking the reachability of a point for example is a fundamental problem. In this document we will show that this problem that is undecidable in the general case is in fact decidable for a natural class of continuous-time dynamical systems: linear systems. For this, we will use results from the algebraic numbers theory such as Gelfond-Schneider's theorem.