XX : 2 On the Polyhedral Escape Problem for Linear Dynamical Systems

The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function f : R → R and a convex polyhedron P ⊂ R with rational descriptions, whether there exists an initial point x0 in P such that the trajectory of the unique solution to the differential equation { ẋ(t) = f(x(t)) x(0) = x0 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. 1998 ACM Subject Classification F.2.m (Analysis of Algorithms and Problem Complexity)