English

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

R2 v1 2026-06-23T13:18:02.897Z