How Fast Can You Escape a Compact Polytope?
Dynamical Systems
2020-01-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.2001.08200,
title = {How Fast Can You Escape a Compact Polytope?},
author = {Julian D'Costa and Engel Lefaucheux and Joël Ouaknine and James Worrell},
journal= {arXiv preprint arXiv:2001.08200},
year = {2020}
}
Comments
Long version of a STACS 2020 paper