The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function f : Rd → Rd and a convex polyhedron P in Rd, whether, for some initial point x0 in P, the trajectory of the unique solution to the differential equation x'(t) = f(x(t)), x(0) = x0, t ≥ 0, is entirely contained in P. We place this problem in ∃R, which lies between NP and PSPACE, by reducing it in polynomial time to the decision version of linear programming with real algebraic coefficients. Our algorithm makes use of spectral techniques and relies among others on tools from Diophantine approximation.
Submitted, 2016. 11 pages.
© 2016 Joao Sousa Pinto, Joel Ouaknine, and James Worrell.