## How fast can you escape a compact polytope?

*Julian D'Costa*, *Engel Lefaucheux*,
*Joël
Ouaknine*,
and *James Worrell*
The Continuous Polytope Escape Problem (CPEP) asks whether every
trajectory of a linear differential equation initialised within a
convex polytope eventually escapes the polytope. We provide a
polynomial-time algorithm to decide CPEP for compact polytopes. We
also establish a quantitative uniform upper bound on the time required
for every trajectory to escape the given polytope. In addition, we
establish iteration bounds for termination of discrete linear loops
via reduction to the continuous case.

*Proceedings of STACS 20*, LIPIcs 154, 2020. 20 pages.

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© 2020 Julian D'Costa, Engel Lefaucheux, Joël
Ouaknine, and James Worrell.

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