{"paper":{"title":"On the Polytope Escape Problem for Continuous Linear Dynamical Systems","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"cs.CC","authors_text":"James Worrell, Jo\\~ao Sousa-Pinto, Jo\\\"el Ouaknine","submitted_at":"2015-07-11T22:56:01Z","abstract_excerpt":"The Polyhedral Escape Problem for continuous linear dynamical systems consists of deciding, given an affine function $f: \\mathbb{R}^{d} \\rightarrow \\mathbb{R}^{d}$ and a convex polyhedron $\\mathcal{P} \\subseteq \\mathbb{R}^{d}$, whether, for some initial point $\\boldsymbol{x}_{0}$ in $\\mathcal{P}$, the trajectory of the unique solution to the differential equation $\\dot{\\boldsymbol{x}}(t)=f(\\boldsymbol{x}(t))$, $\\boldsymbol{x}(0)=\\boldsymbol{x}_{0}$, is entirely contained in $\\mathcal{P}$. We show that this problem is decidable, by reducing it in polynomial time to the decision version of linea"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.03166","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}