2026-07-22T21:28:30Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:11910 2024-03-06T10:48:59Z ddc:004 open_access

How Fast Can You Escape a Compact Polytope? D'Costa, Julian Lefaucheux, Engel Ouaknine, Joël Worrell, James Continuous linear dynamical systems termination 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Julian D'Costa and Engel Lefaucheux and Joël Ouaknine and James Worrell 2020 Is Part Of LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.STACS.2020.49 urn:nbn:de:0030-drops-119105 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.49 eng https://creativecommons.org/licenses/by/3.0/legalcode